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The authors used resting-state fMRI in a prospective study to compare whole-brain functional connectivity between patients with good and poor outcomes, implementing support vector machine learning. They automatically predicted coma outcome using resting-state fMRI and also compared the prediction based on resting-state fMRI with the outcome prediction based on DWI. Of 17 eligible patients who completed the study procedure (among 351 patients screened), 9 regained consciousness and 8 remained comatose. They found higher functional connectivity in patients recovering consciousness, with greater changes occurring within and between the occipitoparietal and temporofrontal regions. Coma outcome prognostication based on resting-state fMRI machine learning was very accurate, notably for identifying patients with good outcome. They conclude that resting-state fMRI might bridge the gap left in early prognostication of postanoxic patients in a coma by identifying those with both good and poor outcomes., BACKGROUND AND PURPOSE: Early outcome prediction of postanoxic patients in a coma after cardiac arrest proves challenging. Current prognostication relies on multimodal testing, using clinical examination, electrophysiologic testing, biomarkers, and structural MR imaging. While this multimodal prognostication is accurate for predicting poor outcome (ie, death), it is not sensitive enough to identify good outcome (ie, consciousness recovery), thus leaving many patients with indeterminate prognosis. We specifically assessed whether resting-state fMRI provides prognostic information, notably in postanoxic patients in a coma with indeterminate prognosis early after cardiac arrest, specifically for good outcome., MATERIALS AND METHODS: We used resting-state fMRI in a prospective study to compare whole-brain functional connectivity between patients with good and poor outcomes, implementing support vector machine learning. Then, we automatically predicted coma outcome using resting-state fMRI and also compared the prediction based on resting-state fMRI with the outcome prediction based on DWI., RESULTS: Of 17 eligible patients who completed the study procedure (among 351 patients screened), 9 regained consciousness and 8 remained comatose. We found higher functional connectivity in patients recovering consciousness, with greater changes occurring within and between the occipitoparietal and temporofrontal regions. Coma outcome prognostication based on resting-state fMRI machine learning was very accurate, notably for identifying patients with good outcome (accuracy, 94.4%; area under the receiver operating curve, 0.94). Outcome predictors using resting-state fMRI performed significantly better (P < .05) than DWI (accuracy, 60.0%; area under the receiver operating curve, 0.63)., CONCLUSIONS: Indeterminate prognosis might lead to major clinical uncertainty and significant variations in life-sustaining treatments. Resting-state fMRI might bridge the gap left in early prognostication of postanoxic patients in a coma by identifying those with both good and poor outcomes.

Background Effects of beta-amyloid accumulation on neuronal function precede the clinical manifestation of Alzheimer's disease (AD) by years and affect distinct cognitive brain networks. As previous studies suggest a link between beta-amyloid and dysregulation of excitatory and inhibitory neurotransmitters, we aimed to investigate the impact of GABA and glutamate on beta-amyloid related functional connectivity. Methods 29 cognitively unimpaired old-aged adults (age = 70.03 ± 5.77 years) were administered 11C-Pittsburgh Compound B (PiB) positron-emission tomography (PET), and MRI at 7 Tesla (7T) including blood oxygen level dependent (BOLD) functional MRI (fMRI) at rest for measuring static and dynamic functional connectivity. An advanced 7T MR spectroscopic imaging (MRSI) sequence based on the free induction decay acquisition localized by outer volume suppression’ (FIDLOVS) technology was used for gray matter specific measures of GABA and glutamate in the posterior cingulate and precuneus (PCP) region. Results GABA and glutamate MR-spectra indicated significantly higher levels in gray matter than in white matter. A global effect of beta-amyloid on functional connectivity in the frontal, occipital and inferior temporal lobes was observable. Interactive effects of beta-amyloid with gray matter GABA displayed positive PCP connectivity to the frontomedial regions, and the interaction of beta-amyloid with gray matter glutamate indicated positive PCP connectivity to frontal and cerebellar regions. Furthermore, decreased whole-brain but increased fronto-occipital and temporo-parietal dynamic connectivity was found, when GABA interacted with regional beta-amyloid deposits in the amygdala, frontal lobe, hippocampus, insula and striatum. Conclusions GABA, and less so glutamate, may moderate beta-amyloid related functional connectivity. Additional research is needed to better characterize their interaction and potential impact on AD., NeuroImage: Clinical, 22, ISSN:2213-1582

Background Prodromal positive psychotic symptoms and anxiety are two strong risk factors for schizophrenia in 22q11.2 deletion syndrome (22q11DS). The analysis of large-scale brain network dynamics during rest is promising to investigate aberrant brain function and identify potentially more reliable biomarkers. Methods We retrieved and examined dynamic properties of large-scale functional brain networks using innovation-driven coactivation patterns. The study included resting-state functional magnetic resonance scans from 78 patients with 22q11DS and 85 healthy control subjects. After group comparison of temporal brain network activation properties, functional signatures of prodromal psychotic symptoms and anxiety were extracted using multivariate partial least squares correlation. Results Patients with 22q11DS had shorter activation in cognitive brain networks, longer activation in emotion processing networks, and generally increased segregation between brain networks. The functional signature of prodromal psychotic symptoms confirmed an implication of cingulo-prefrontal salience network activation duration and coupling. Further, the functional signature of anxiety uncovered an implication of amygdala activation and coupling, indicating differential roles of dorsal and ventral subdivisions of the anterior cingulate and medial prefrontal cortices. Coupling of amygdala with the dorsal anterior cingulate and medial prefrontal cortices was promoting anxiety, whereas coupling with the ventral anterior cingulate and medial prefrontal cortices had a protective function. Conclusions Using innovation-driven coactivation patterns for dynamic large-scale brain network analysis, we uncovered patterns of brain network activation duration and coupling that are relevant in clinical risk factors for psychosis in 22q11DS. Our results confirm that the dynamic nature of brain network activation contains essential function to develop clinically relevant imaging markers of psychosis vulnerability.

The increasing availability of network data is leading to a growing interest in processing of signals on graphs. One notable tool for extending conventional signal-processing operations to networks is the graph Fourier transform that can be obtained as the eigendecomposition of the graph Laplacian. In this letter, we used the graph Fourier transform to define a new method for generating surrogate graph signals. The approach is based on sign-randomization of the graph Fourier coefficients and, therefore, the correlation structure of the surrogate graph signals (i.e., smoothness on the graph topology) is imposed by the measured data. The proposed method of surrogate data generation can be widely applied for nonparametric statistical hypothesis testing. Here, we showed a proof-of-concept with a high-density electroencephalography dataset.

Motor deficit is a prominent feature among stroke survivors. Robot-assisted therapies have been proposed as a strategy to boost rehabilitation, by allowing therapy to be provided in a more reproducible and intense manner, while quantitatively monitoring patient’s improvement. However, those approaches have so far not shown superiority over conventional treatments. One potential solution to reach better outcomes would be to personalize the treatment. In this regard, a better understanding of the mechanisms underlying motor recovery is pivotal to tailor therapy to each patient. Here, we explored the cortical changes occurring during robotic training. We recorded resting-state fMRI before and after the treatment in three sub-acute post-stroke survivors, and we investigated the functional connectivity between motor regions. We observed a cortical reorganization following training, consistent with motor improvements.

Stroke is a devastating neurological condition, often causing severe functional and cognitive deficits, sharply diminishing the patient’s quality of life. Among others, robot-assisted rehabilitation has been widely proposed to enhance the rehabilitation outcome. However, clinical scores and robotic parameters often used to inform rehabilitative-decision process are unfit to fully describe the neural reorganization that occur after a brain insult. The lack of reliable, simple, and sensitive neural biomarkers has potentially limited the clinical translation of these advanced rehabilitative technologies. Here, we show that EEG-topographic measures can be extracted as robust and sensitive biomarkers of stroke recovery to inform robotic therapies.

BACKGROUND AND PURPOSE:Multidelay arterial spin-labeling is a promising emerging method in clinical practice. The effect of imaging parameters in multidelay arterial spin-labeling on estimated cerebral blood flow measurements remains unknown. We directly compared 3-delay versus 7-delay sequences, assessing the difference in the estimated transit time and blood flow. MATERIALS AND METHODS:This study included 87 cognitively healthy controls (78.7 3.8 years of age; 49 women). We assessed delay and transit time-uncorrected and transit time-corrected CBF maps. Data analysis included voxelwise permutation-based between-sequence comparisons of 3-delay versus 7-delay, within-sequence comparison of transit time-uncorrected versus transit time-corrected maps, and average CBF calculations in regions that have been shown to differ. RESULTS:The 7-delay sequence estimated a higher CBF value than the 3-delay for the transit time-uncorrected and transit time-corrected maps in regions corresponding to the watershed areas (transit time-uncorrected = 27.62 +/- 12.23 versus 24.58 +/- 11.70 mL/min/100 g, Cohen's d = 0.25; transit time-corrected = 33.48 +/- 14.92 versus 30.16 +/- 14.32 mL/min/100 g, Cohen's d = 0.23). In the peripheral regions of the brain, the estimated delay was found to be longer for the 3-delay sequence (1.52408 +/- 0.25236 seconds versus 1.47755 +/- 0.24242 seconds, Cohen's d = 0.19), while the inverse was found in the center of the brain (1.39388 +/- 0.22056 seconds versus 1.42565 +/- 0.21872 seconds, Cohen's d = 0.14). Moreover, 7-delay had lower hemispheric asymmetry. CONCLUSIONS:The results of this study support the necessity of standardizing acquisition parameters in multidelay arterial spin-labeling and identifying basic parameters as a confounding factor in CBF quantification studies. Our findings conclude that multidelay arterial spin-labeling sequences with a high number of delays estimate higher CBF values than those with a lower number of delays.

Objective Essential tremor (ET) represents the most common movement disorder. Drug-resistant ET can benefit from standard stereotactic procedures (deep brain stimulation or radiofrequency thalamotomy) or alternatively minimally invasive high-focused ultrasound or radiosurgery. All aim at same target, thalamic ventro-intermediate nucleus (Vim). Methods The study included a cohort of 17 consecutive patients, with ET, treated only with left unilateral stereotactic radiosurgical thalamotomy (SRS-T) between September 2014 and August 2015. The mean time to tremor improvement was 3.32 months (SD 2.7, 0.5-10). Neuroimaging data were collected at baseline (n = 17). Standard tremor scores, including activities of daily living (ADL) and tremor score on treated hand (TSTH), were completed pretherapeutically and 1 year later. We further correlate these scores with baseline inter-connectivity in twenty major large-scale brain networks. Results We report as predictive three networks, with the interconnected statistically significant clusters: primary motor cortex interconnected with inferior olivary nucleus, bilateral thalamus interconnected with motor cerebellum lobule V2 (ADL), and anterior default-mode network interconnected with Brodmann area 103 (TSTH). For all, more positive pretherapeutic interconnectivity correlated with higher drop in points on the respective scores. Age, disease duration, or time-to-response after SRS-T were not statistically correlated with pretherapeutic brain connectivity measures (P > .05). The same applied to pretherapeutic tremor scores, after using the same methodology described above. Conclusions Our findings have clinical implications for predicting clinical response after SRS-T. Here, using pretherapeutic magnetic resonance imaging and data processing without prior hypothesis, we show that pretherapeutic network(s) interconnectivity strength predicts tremor arrest in drug-na\"ive ET, following stereotactic radiosurgical thalamotomy.

Recent advances in neurofeedback based on real-time functional magnetic resonance imaging (fMRI) allow for learning to control spatially localized brain activity in the range of millimeters across the entire brain. Realtime fMRI neurofeedback studies have demonstrated the feasibility of self-regulating activation in specific areas that are involved in a variety of functions, such as perception, motor control, language, and emotional processing. In most of these previous studies, participants trained to control activity within one region of interest (ROI). In the present study, we extended the neurofeedback approach by now training healthy participants to control the interhemispheric balance between their left and right visual cortices. This was accomplished by providing feedback based on the difference in activity between a target visual ROI and the corresponding homologue region in the opposite hemisphere. Eight out of 14 participants learned to control the differential feedback signal over the course of 3 neurofeedback training sessions spread over 3 days, i.e., they produced consistent increases in the visual target ROI relative to the opposite visual cortex. Those who learned to control the differential feedback signal were subsequently also able to exert that control in the absence of neurofeedback. Such learning to voluntarily control the balance between cortical areas of the two hemispheres might offer promising rehabilitation approaches for neurological or psychiatric conditions associated with pathological asymmetries in brain activity patterns, such as hemispatial neglect, dyslexia, or mood disorders. (C) 2014 Elsevier Inc. All rights reserved.

We present a framework for the design of wavelet transforms tailored to data defined on multislice graphs (i.e., multiplex or dynamic graphs). Graphs with multiple types of interactions are ubiquitous in real life, motivating the extension of wavelets to these complex domains. Our framework generalizes the recently proposed spectral graph wavelet transform (SGWT) [D. Hammond, P. Vandergheynst, and R. Gribonval, “Wavelets on Graphs via Spectral Graph Theory,” Appl. Comput. Harmon. Anal., vol. 30, pp. 129-150, Mar. 2011], which is designed in the spectral (frequency) domain of an arbitrary finite weighted graph. We extend the SGWT to form a tight frame, which conserves energy in the wavelet domain, and define the relationship between conventional and spectral graph wavelets. We then propose a design for multislice graphs that is based on the higher-order singular value decomposition (HOSVD), a powerful tool from multilinear algebra. In particular, the multiple adjacency matrices are stacked to form a tensor and the HOSVD decomposition provides information about its third-order structure, analogous to that provided by matrix factorizations. We obtain a set of “eigennetworks” and from these graph wavelets, which exploit the variability across the graphs. We demonstrate the feasibility of our method 1) by capturing different orientations of a gray-scale image and 2) by decomposing brain signals from functional magnetic resonance imaging. We show its effectiveness to identify variability across graph edges and provide meaningful decompositions.

Attention deficit hyperactivity disorder (ADHD) is accompanied by resting-state alterations, including abnormal activity, connectivity and asymmetry of the default-mode network (DMN). Concurrently, recent studies suggested a link between ADHD and the presence of polymorphisms within the gene BAIAP2 (i.e., brain-specific angiogenesis inhibitor 1-associated protein 2), known to be differentially expressed in brain hemispheres. The clinical and neuroimaging correlates of this polymorphism are still unknown. We investigated the association between BAIAP2 polymorphisms and DMN functional connectivity (FC) asymmetry as well as behavioral measures in ADHD adults. Resting-state fMRI was acquired from 30 ADHD and 15 healthy adults. For each subject, rs7210438 and rs8079626 within the gene BAIAP2 were genotyped. ADHD severity, impulsiveness and anger were assessed for the ADHD group. Using multivariate analysis of variance, we found that genetic features do have an impact on DMN FC asymmetry. In particular, polymorphism rs8079626 affects medial frontal gyrus and inferior parietal lobule connectivity asymmetry, lower for AA than AG/GG carriers. Further, when combining FC asymmetry and the presence of the rs8079626 variant, we successfully predicted increased externalization of anger in ADHD. In conclusion, a complex interplay between genetic vulnerability and inter-hemispherical DMN FC asymmetry plays a role in emotion regulation in adult ADHD.

Background Patients who experience severe brain injuries are at risk of secondary brain damage, because of delayed vasospasm and edema. Traditionally, many of these patients are kept on prolonged bed rest in order to maintain adequate cerebral blood flow, especially in the case of subarachnoid hemorrhage. On the other hand, prolonged bed rest carries important morbidity. There may be a clinical benefit in early mobilization and our hypothesis is that early gradual mobilization is safe in these patients. The aim of this study was to observe and quantify the changes in sympathetic activity, mainly related to stress, and blood pressure in gradual postural changes by the verticalization robot (Erigo®) and after training by a lower body ergometer (MOTOmed-letto®), after prolonged bed rest of minimum 7 days. Methods Thirty patients with severe neurological injuries were randomized into 3 groups with different protocols of mobilization: Standard, MOTOmed-letto® or Erigo® protocol. We measured plasma catecholamines, metanephrines and blood pressure before, during and after mobilization. Results Blood pressure does not show any significant difference between the 3 groups. The analysis of the catecholamines suggests a significant increase in catecholamine production during Standard mobilization with physiotherapists and with MOTOmed-letto® and no changes with Erigo®. Conclusions This preliminary prospective randomized study shows that the mobilization of patients with severe brain injuries by means of Erigo® does not increase the production of catecholamines. It means that Erigo® is a well-tolerated method of mobilization and can be considered a safe system of early mobilization of these patients. Further studies are required to validate our conclusions. Trial registration The study was registered in the ISRCTN registry with the trial registration number ISRCTN56402432 . Date of registration: 08.03.2016. Retrospectively registered.

The 16 papers in this special section focused on advanced signal processing techniques for brain networks. Network models of the brain have become an important tool of modern neurosciences to study fundamental organizational principles of brain structure & function. Their connectivity is captured by the so-called connectome, the complete set of structural and functional links of the network. Advancing current methodology remains an important need in the field; e.g., increasing large-scale models; incorporating multimodal information in multiplex graph models; dealing with dynamical aspects of network models; and matching data-driven and theoretical models. These challenges form multiple opportunities to develop and adapt emerging signal processing theories and methods at the interface of graph theory, machine learning, applied statistics, simulation, and so on, to play a key role in analysis and modeling and to bring our understanding of brain networks to the next level for key applications in cognitive and clinical neurosciences, including brain-computer interfaces.

We propose near-affine-invariant texture descriptors derived from isotropic wavelet frames for the characterization of lung tissue patterns in high-resolution computed tomography (HRCT) imaging. Affine invariance is desirable to enable learning of nondeterministic textures without a priori localizations, orientations, or sizes. When combined with complementary gray-level histograms, the proposed method allows a global classification accuracy of 76.9% with balanced precision among five classes of lung tissue using a leave-one-patient-out cross validation, in accordance with clinical practice.

We present a functional framework for the design of tight steerable wavelet frames in any number of dimensions. The 2-D version of the method can be viewed as a generalization of Simoncelli's steerable pyramid that gives access to a larger palette of steerable wavelets via a suitable parametrization. The backbone of our construction is a primal isotropic wavelet frame that provides the multiresolution decomposition of the signal. The steerable wavelets are obtained by applying a one-to-many mapping (N th-order generalized Riesz transform) to the primal ones. The shaping of the steerable wavelets is controlled by an M x M unitary matrix (where M is the number of wavelet channels) that can be selected arbitrarily; this allows for a much wider range of solutions than the traditional equiangular configuration (steerable pyramid). We give a complete functional description of these generalized wavelet transforms and derive their steering equations. We describe some concrete examples of transforms, including some built around a Mallat-type multiresolution analysis of L-2(R-d), and provide a fast Fourier transform-based decomposition algorithm. We also propose a principal-component-based method for signal-adapted wavelet design. Finally, we present some illustrative examples together with a comparison of the denoising performance of various brands of steerable transforms. The results are in favor of an optimized wavelet design (equalized principal component analysis), which consistently performs best.

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions ( dor= 2). To that end, we introduce a self-reversible, Nth-order extension of the Riesz transform. We prove that this generalized transform has the following remarkable properties: shift-invariance, scale-invariance, inner-product preservation, and steerability. The pleasing consequence is that the transform maps any primary wavelet frame (or basis) of [Formula: see text] into another "steerable" wavelet frame, while preserving the frame bounds. The concept provides a functional counterpart to Simoncelli's steerable pyramid whose construction was primarily based on filterbank design. The proposed mechanism allows for the specification of wavelets with any order of steerability in any number of dimensions; it also yields a perfect reconstruction filterbank algorithm. We illustrate the method with the design of a novel family of multidimensional Riesz-Laplace wavelets that essentially behave like the N th-order partial derivatives of an isotropic Gaussian kernel.

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-valued (primary) wavelet basis of L(2) (R(2)) into a complex one. The Riesz operator is also steerable in the sense that it give access to the Hilbert transform of the signal along any orientation. Having set those foundations, we specify a primary polyharmonic spline wavelet basis of L(2) (R(2)) that involves a single Mexican-hat-like mother wavelet (Laplacian of a B-spline). The important point is that our primary wavelets are quasi-isotropic: they behave like multiscale versions of the fractional Laplace operator from which they are derived, which ensures steerability. We propose to pair these real-valued basis functions with their complex Riesz counterparts to specify a multiresolution monogenic signal analysis. This yields a representation where each wavelet index is associated with a local orientation, an amplitude and a phase. We give a corresponding wavelet-domain method for estimating the underlying instantaneous frequency. We also provide a mechanism for improving the shift and rotation-invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect-reconstruction filterbanks. We illustrate the specific feature-extraction capabilities of the representation and present novel examples of wavelet-domain processing; in particular, a robust, tensor-based analysis of directional image patterns, the demodulation of interferograms, and the reconstruction of digital holograms.

In this contribution, we study the notion of affine invariance (specifically, invariance to the shifting, scaling, and rotation of the coordinate system) as a starting point for the development of mathematical tools and approaches useful in the characterization and analysis of multivariate fractional Brownian motion (fBm) fields. In particular, using a rigorous and powerful distribution theoretic formulation, we extend previous results of Blu and Unser (2006) to the multivariate case, showing that polyharmonic splines and fBm processes can be seen as the (deterministic vs stochastic) solutions to an identical fractional partial differential equation that involves a fractional Laplacian operator. We then show that wavelets derived from polyharmonic splines have a behavior similar to the fractional Laplacian, which also turns out to be the whitening operator for fBm fields. This fact allows us to study the probabilistic properties of the wavelet transform coefficients of fBm-like processes, leading for instance to ways of estimating the Hurst exponent of a multiparameter process from its wavelet transform coefficients. We provide theoretical and experimental verification of these results. To complement the toolbox available for multiresolution processing of stochastic fractals, we also introduce an extended family of multidimensional multiresolution spaces for a large class of (separable and nonseparable) lattices of arbitrary dimensionality.

Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an $ \ell_{ 1 } $ -regularization constraint, which favors sparse solutions in the wavelet domain. This can be achieved quite efficiently thanks to the iterative algorithm developed by Daubechies et al., 2004. In this paper, we apply this technique and extend it for the reconstruction of dynamic (spatio-temporal) PET data. Moreover, instead of using classical wavelets in the temporal dimension, we introduce exponential-spline wavelets (E-spline wavelets) that are specially tailored to model time activity curves (TACs) in PET. We show that the exponential-spline wavelets naturally arise from the compartmental description of the dynamics of the tracer distribution. We address the issue of the selection of the “optimal” E-spline parameters (poles and zeros) and we investigate their effect on reconstruction quality. We demonstrate the usefulness of spatio-temporal regularization and the superior performance of E-spline wavelets over conventional Battle-Lemarié wavelets in a series of experiments: the 1-D fitting of TACs, and the tomographic reconstruction of both simulated and clinical data. We find that the E-spline wavelets outperform the conventional wavelets in terms of the reconstructed signal-to-noise ratio (SNR) and the sparsity of the wavelet coefficients. Based on our simulations, we conclude that replacing the conventional wavelets with E-spline wavelets leads to equal reconstruction quality for a 40% reduction of detected coincidences, meaning an improved image quality for the same number of counts or equivalently a reduced exposure to the patient for the same image quality.

Model-based statistical analysis of functional magnetic resonance imaging (fMRI) data relies on the general linear model and statistical hypothesis testing. Due to the large number of intracranial voxels, it is important to deal with the multiple comparisons problem. Many fMRI analysis tools utilize Gaussian random field theory to obtain a more sensitive thresholding; this typically involves Gaussian smoothing as a preprocessing step. Wavelet-based statistical parametric mapping (WSPM) is an alternative method to obtain parametric maps from non-smoothed data. It relies on adaptive thresholding of the parametric maps in the wavelet domain, followed by voxel-wise statistical testing. The procedure is conservative; it uses Bonferroni correction for strong type I error control. Yet, its sensitivity is close to SPM's due to the excellent denoising properties of the wavelet transform. Here, we adapt the false discovery rate (FDR) principle to the WSPM framework. Although explicit p-values cannot be obtained, we show that it is possible to retrieve the FDR threshold by a simple iterative scheme. We then validate the approach with an event-related visual stimulation task. Our results show better sensitivity with preservation of spatial resolution; i.e., activation clusters align well with the gray matter structures in the visual cortex. The spatial resolution of the activation maps is even high enough to easily identify a voxel that is very likely to be caused by the draining-vein effect.

Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gradient-Laplace operator. Starting from first principles, we show that a single-generator wavelet can be defined analytically and that it yields a semi-orthogonal complex basis of L-2 (R-2), irrespective of the dilation matrix used. We also provide an efficient FFT-based filterbank implementation. We then propose a slightly redundant version of the transform that is nearly translation -invariant and that is optimized for better steerability (Gaussian-like smoothing kernel). We call it the Marr-like wavelet pyramid because it essentially replicates the processing steps in Marr's theory of early vision. We use it to derive a primal wavelet sketch which is a compact description of the image by a multiscale, subsampled edge map. Finally, we provide an efficient iterative algorithm for the reconstruction of an image from its primal wavelet sketch.

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer advantages in terms of flexibility (shape of the basis functions) and shift-invariance. In this paper, we propose a framework for improved wavelet analysis based on an appropriate pairing of a wavelet basis with a mildly redundant version of itself (frame). The processing is accomplished in four steps: 1) redundant wavelet analysis, 2) wavelet-domain processing, 3) projection of the results onto the wavelet basis, and 4) reconstruction of the signal from its nonredundant wavelet expansion. The wavelet analysis is pyramid-like and is obtained by simple modification of Mallat's filterbank algorithm (e.g., suppression of the down-sampling in the wavelet channels only). The key component of the method is the subband regression filter (Step 3) which computes a wavelet expansion that is maximally consistent in the least squares sense with the redundant wavelet analysis. We demonstrate that this approach significantly improves the performance of soft-threshold wavelet denoising with a moderate increase in computational cost. We also show that the analysis filters in the proposed framework can be adjusted for improved feature detection; in particular, a new quincunx Mexican-hat-like wavelet transform that is fully reversible and essentially behaves the (gamma/2)th Laplacian of a Gaussian.

Predicting the conversion of amnestic mild cognitive impairment (aMCI) to Alzheimer's disease (AD) is a challenging problem for which machine learning could be of great use. In this work, we aim at assessing the independent and joint value of imaging (structural MRI, resting-state functional MRI (rsfMRI)) and clinical data in classifying stable versus progressive aMCI. Surprisingly, we found no previous studies using rsfMRI to predict conversion of MCI to AD. We use singular value decomposition as a feature extractor before combining modalities. We reach accuracies of up to 82% using rsfMRI, 86% using sMRI and rsfMRI combined, and 77% using a combination of all modalities.

In this paper, an overview with unification of techniques that deploy the wavelet transform in the spatial domain for the analysis of functional magnetic resonance imaging (fMRI) is presented.

We present a new family of two-dimensional and three-dimensional orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order /spl lambda/, which may be noninteger. We can also prove that they yield wavelet bases of L/sub 2/(R/sup 2/) for any /spl lambda/>0. The wavelets are fractional in the sense that the approximation error at a given scale a decays like O(a/sup /spl lambda//); they also essentially behave like fractional derivative operators. To make our construction practical, we propose a fast Fourier transform-based implementation that turns out to be surprisingly fast. In fact, our method is almost as efficient as the standard Mallat algorithm for separable wavelets.

The dilation matrix associated with the three-dimensional (3-D) face-centered cubic (FCC) sublattice is often considered to be the natural 3-D extension of the two-dimensional (2-D) quincunx dilation matrix. However, we demonstrate that both dilation matrices are of different nature: while the 2-D quincunx matrix is a similarity transform, the 3-D FCC matrix is not. More generally, we show that is impossible to obtain a dilation matrix that is a similarity transform and performs downsampling of the Cartesian lattice by a factor of two in more than two dimensions. Furthermore, we observe that the popular 3-D FCC subsampling scheme alternates between three different lattices: Cartesian, FCC, and quincunx. The latter one provides a less isotropic sampling density, a property that should be taken into account to properly orient 3-D data before processing using such a subsampling matrix.

This paper proposes a new family of bivariate, non-separable splines, called hex-splines, especially designed for hexagonal lattices. The starting point of the construction is the indicator function of the Voronoi cell, which is used to define in a natural way the first-order hex-spline. Higher order hex-splines are obtained by successive convolutions. A mathematical analysis of this new bivariate spline family is presented. In particular, we derive a closed form for a hex-spline of arbitrary order. We also discuss important properties, such as their Fourier transform and the fact they form a Riesz basis. We also highlight the approximation order. For conventional rectangular lattices, hex-splines revert to classical separable tensor-product B-splines. Finally, some prototypical applications and experimental results demonstrate the usefulness of hex-splines for handling hexagonally sampled data.

A new fuzzy filter is presented for the noise reduction of images corrupted with additive noise. The filter consists of two stages. The first stage computes a fuzzy derivative for eight different directions. The second stage uses these fuzzy derivatives to perform fuzzy smoothing by weighting the contributions of neighboring pixel values. Both stages are based on fuzzy rules which make use of membership functions. The filter can be applied iteratively to effectively reduce heavy noise. In particular, the shape of the membership functions is adapted according to the remaining noise level after each iteration, making use of the distribution of the homogeneity in the image. A statistical model for the noise distribution can be incorporated to relate the homogeneity to the adaptation scheme of the membership functions. Experimental results are obtained to show the feasibility of the proposed approach. These results are also compared to other filters by numerical measures and visual inspection.

BACKROUND AND PURPOSE: Shoulder apprehension is defined as anxiety and resistance in patients with a history of anterior glenohumeral instability. It remains unclear whether shoulder apprehension is the result of true recurrent instability or a memorized subjective sensation. We tested whether visual presentation of apprehension videos modifies functional brain networks associated with motor resistance and anxiety. MATERIALS AND METHODS: This prospective study includes 15 consecutive right-handed male patients with shoulder apprehension (9 with right shoulder apprehension, 6 with left shoulder apprehension; 27.5 +/- 6.4 years) and 10 healthy male right-handed age-matched control participants (29.0 +/- 4.7 years). Multimodal MR imaging included 1) functional connectivity tensorial independent component analysis, 2) task-related general linear model analysis during visual stimulation of movies showing typical apprehension movements vs control videos, 3) voxel-based morphometry analysis of GM, and 4) tract-based spatial statistics analysis of WM. RESULTS: Patients with shoulder apprehension had significant (P < .05 corrected) increase in task-correlated functional connectivity, notably in the bilateral primary sensory-motor area and dorsolateral prefrontal cortex and, to a lesser degree, the bilateral dorsomedial prefrontal cortex, anterior insula, and dorsal anterior cingulate cortex (+148% right, +144% left). Anticorrelated functional connectivity decreased in the higher-level visual and parietal areas (-185%). There were no potentially confounding structural changes in GM or WM. CONCLUSIONS: Shoulder apprehension induces specific reorganization in apprehension-related functional connectivity of the primary sensory-motor areas (motor resistance), dorsolateral prefrontal cortex (cognitive control of motor behavior), and the dorsal anterior cingulate cortex/dorsomedial prefrontal cortex and anterior insula (anxiety and emotional regulation).

The observation and description of the living brain has attracted a lot of research over the past centuries. Many noninvasive imaging modalities have been developed, such as topographical techniques based on the electromagnetic field potential [i.e., electroencephalography (EEG) and magnetoencephalography (MEG)], and tomography approaches including positron emission tomography and magnetic resonance imaging (MRI). Here we will focus on functional MRI (fMRI) since it is widely deployed for clinical and cognitive neurosciences today, and it can reveal brain function due to neurovascular coupling (see ?From Brain Images to fMRI Time Series?). It has led to a much better understanding of brain function, including the description of brain areas with very specialized functions such as face recognition. These neuroscientific insights have been made possible by important methodological advances in MR physics, signal processing, and mathematical modeling.

Objective Topographical EEG analysis gives access to the coherent activation within global functional networks in resting-state. For these so-called microstates a temporal organization according to fractal structure has been demonstrated in healthy participants. Here we tested whether these fractal properties would be affected in multiple sclerosis (MS) patients. Methods We acquired 256-channel EEG in 53 minimally-disable relapsing-remitting MS patients (mean age 37.6 y, EDSS ⩽ 4 , mean disease duration 9.9 y, 45 females), and 49 healthy controls (mean age 36.4 y, 33 females). We analyzed 5 min of wakefulness at rest, and isolated the 4 predominant topographies, well known from literature. Using a wavelet framework and detrended fluctuation analysis we estimated temporal fractality and long-range dependency. Results We found significant differences between MS patients and controls in terms of a decreased Hurst exponent ( p = 0.01), and an increased entropy ( p = 0.01) in patients, indicating disturbed fractal order. Moreover, a high Hurst exponent strongly predicted a high depression score in patients ( p R 2 = 0.245), but not in controls. Conclusions In MS patients, higher order temporal complexity of topographical EEG fluctuations is disturbed, predicting patient’s depression score. Key message Features of temporal complexity in topographical EEG fluctuations could serve as a potential marker of brain state in relapsing-remitting MS.

Analytic sensing is a new mathematical framework to estimate the parameters of a multi-dipole source model from boundary measurements. The method deploys two working principles. First, the sensing principle relates the boundary measurements to the volumetric interactions of the sources with the so-called "analytic sensor," a test function that is concentrated around a singular point outside the domain of interest. Second, the annihilation principle allows retrieving the projection of the dipoles' positions in a single shot by polynomial root finding. Here, we propose to apply analytic sensing in a local way; i.e., the poles are not surrounding the complete domain. By combining two local projections of the (nearby) dipolar sources, we are able to reconstruct the full 3-D information. We demonstrate the feasibility of the proposed approach for both synthetic and experimental data, together with the theoretical lower bounds of the localization error.

Total variation (TV) is a powerful method that brings great benefit for edge-preserving regularization. Despite being widely employed in image processing, it has restricted applicability for 1-D signal processing since piecewise-constant signals form a rather limited model for many applications. Here we generalize conventional TV in 1-D by extending the derivative operator, which is within the regularization term, to any linear differential operator. This provides flexibility for tailoring the approach to the presence of nontrivial linear systems and for different types of driving signals such as spike-like, piecewise-constant, and so on. Conventional TV remains a special case of this general framework. We illustrate the feasibility of the method by considering a nontrivial linear system and different types of driving signals.

We present an analytical form of ground-truth k-space data for the 2-D Shepp-Logan brain phantom in the presence of multiple and non-homogeneous receiving coils. The analytical form allows us to conduct realistic simulations and validations of reconstruction algorithms for parallel MRI. The key contribution of our work is to use a polynomial representation of the coil's sensitivity. We show that this method is particularly accurate and fast with respect to the conventional methods. The implementation is made available to the community.

We consider images probed through incomplete and noisy Fourier coverages, both in the context of radio interferometry (RI) and of magnetic resonance imaging (MRI). We show that the quality of signal reconstruction can be significantly enhanced by the introduction of a linear chirp modulation, which induces a spread spectrum phenomenon.

During open brain surgery we acquire perfusion images non-invasively using laser Doppler imaging. The regions of brain activity show a distinct signal in response to stimulation providing intraoperative functional brain maps of remarkably strong contrast.

Using Monte Carlo simulations for a semi-infinite medium representing a skeletal muscle tissue, it is demonstrated that the zero- and first-order moments of the power spectrum for a representative pixel of a full-field laser-Doppler imager behave differently from classical laser-Doppler flowmetry. In particular, the zero-order moment has a very low sensitivity to tissue blood volume changes, and it becomes completely insensitive if the probability for a photon to interact with a moving red blood cell is above 0.05. It is shown that the loss in sensitivity is due to the strong forward scatter of the propagating photons in biological tissues (i.e., anisotropy factor g = 0.9). The first-order moment is linearly related to the root mean square of the red blood cell velocity (the Brownian component), and there is also a positive relationship with tissue blood volume. The most common physiological interpretation of the first-order moment is as tissue blood volume times expectation of the blood velocity (in probabilistic terms). In this sense, the use of the first-order moment appears to be a reasonable approach for qualitative real-time blood flow monitoring, but it does not allow us to obtain information on blood velocity or volume independently. Finally, it is shown that the spatial and temporal resolution trade-off imposed by the CMOS detectors, used in full-field laser-Doppler hardware, may lead to measurements that vary oppositely with the underlying physiological quantities. Further improvements on detectors' sampling rate will overcome this limitation.

The identification and accurate location of centers of brain activity are vital both in neuro-surgery and brain research. This study aimed to provide a non-invasive, non-contact, accurate, rapid and user-friendly means of producing functional images intraoperatively. To this end a full field Laser Doppler imager was developed and integrated within the surgical microscope and perfusion images of the cortical surface were acquired during awake surgery whilst the patient performed a predetermined task. The regions of brain activity showed a clear signal (10–20% with respect to the baseline) related to the stimulation protocol which lead to intraoperative functional brain maps of strong statistical significance and which correlate well with the preoperative fMRI and intraoperative cortical electro-stimulation. These initial results achieved with a prototype device and wavelet based regressor analysis (the hemodynamic response function being derived from MRI applications) demonstrate the feasibility of LDI as an appropriate technique for intraoperative functional brain imaging.

Accurate knowledge of an imaging system's point spread function (PSF) is crucial for successful deconvolution. For fluorescence microscopy, PSF estimations based on either theoretical models or experimental measurements are available. However, due to the axially shift-variant nature of the PSF, neither method guarantees an estimate that is valid for the entire object space. In this work, we present a reduced- parameter version of a state-of-the-art theoretical model. We give a maximum-likelihood based algorithm for the estimation of its parameters, and we show how a fit of our model to two axially isolated point source measurements in an experimental setup can be used to accurately reproduce measured PSFs within the entire specimen.

Growth and form in biology are often associated with some level of fractality. Fractal characteristics have also been noted in a number of imaging modalities. These observations make fractal modelling relevant in the context of bio-imaging. In this paper, we introduce a simple and yet rigorous innovation model for multi-dimensional fractional Brownian motion (fBm) and provide the computational tools for the analysis of such processes in a multi-resolution framework. The key point is that these processes can be whitened by application of the appropriate fractional Lapla-cian operator which has a corresponding polyharmonic wavelet. We examine the case of MRI and mammography images through comparison with theoretical results, which underline the suitability of fractal models in the study of bio-textures.

Source localization from EEG surface measurements is an important problem in neuro-imaging. We propose a new mathematical framework to estimate the parameters of a multi- dipole source model. To that aim, we perform 2-D analytic sensing in multiple planes. The estimation of the projection on each plane of the dipoles' positions, which is a non-linear problem, is reduced to polynomial root finding. The 3-D information is then recovered as a special case of tomographic reconstruction. The feasibility of the proposed approach is shown for both synthetic and experimental data.

International audience; A new grid conversion method is proposed to re-sample between two 2-D periodic lattices with the same sampling density. The main feature of our approach is the symmetric reversibility, which means that when using the same algorithm for the converse operation, then the initial data is recovered exactly. To that purpose, we decompose the lattice conversion process into (at most) three successive shear operations. The translations along the shear directions are implemented by 1-D fractional delay operators, which revert to simple 1-D convolutions, with appropriate filters that yield the property of symmetric reversibility. We show that the method is fast and provides high-quality resampled images. Applications of our approach can be found in various settings, such as grid conversion between the hexagonal and the Cartesian lattice, or fast implementation of affine transformations such as rotations.

We introduce a new semi-orthogonal complex wavelet basis of L2(R2). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single-generator wavelet that is shifted on the coset positions of the subsampling matrix. Next, we propose the "wavelet Marr pyramid" for an extension of the new basis that achieves near shift-invariance and steerability (using a Gaussian-like smoothing kernel), for a mild redundancy factor only. This new wavelet pyramid decomposition closely mimicks the basic operations of Marx's framework for early vision. The pyramid is implemented by a fast filterbank algorithm using the FFT.