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As a metaheuristic method for the continuous optimization problem, the grey wolf optimizer (GWO) has attracted much attention from researchers because the method is reported to be superior to other methods. However, some works show that the GWO is too specialized only to problems having the zero-optimal solution, which can lead to a significant deterioration of the efficiency for other problems. In this paper, we, first, theoretically prove the shift-dependence of the GWO, which is the underlying cause of the over-specialization of the GWO, and we experimentally analyze the property by using a larger number of problems. Secondly, we propose am shift-invariant GWO, GWO-SR, and, modify the GWO-SR by adding two methods: an adjustment technique the size of the search area and a mutation process to enhance the diversity of the search (GWO-AS) Finally, we show advantages of two proposed GWOs by comparing them with other metaheuristic methods.

Convolutional neural networks (CNNs) offer unrivaled performance in profiling side-channel analysis. This claim is corroborated by numerous results where CNNs break targets protected with masking and hiding countermeasures. One hiding countermeasure commonly investigated in related works is desynchronization (misalignment). The conclusions usually state that CNNs can break desynchronization as they are shift-invariant. This paper investigates that claim in more detail and reveals that the situation is more complex. While CNNs have certain shift-invariance, it is insufficient for commonly encountered scenarios in deep learning-based side-channel analysis. We investigate data augmentation to improve the shift-invariance and, in a more powerful version, ensembles of data augmentation. Our results show that the proposed techniques work very well and improve the attack significantly, even for an order of magnitude. [ABSTRACT FROM AUTHOR]

Deep Learning (DL) based Side-Channel Analysis (SCA) has been extremely popular recently. DL-based SCA can easily break implementations protected by masking countermeasures. DL-based SCA has also been highly successful against implementations protected by various trace desynchronization-based countermeasures like random delay, clock jitter and shuffling. Over the years, many DL models have been explored to perform SCA. Recently, Transformer Network (TN) based model has also been introduced for SCA. Though the previously introduced TN-based model is successful against implementations jointly protected by masking and random delay countermeasures, it is not scalable to long traces (having a length greater than a few thousand) due to its quadratic time and memory complexity. This work proposes a novel shift-invariant TN-based model with linear time and memory complexity. he contributions of the work are two-fold. First, we introduce a novel TN-based model called EstraNet for SCA. EstraNet has linear time and memory complexity in trace length, significantly improving over the previously proposed TN-based model’s quadratic time and memory cost. EstraNet is also shift-invariant, making it highly effective against countermeasures like random delay and clock jitter. Secondly, we evaluated EstraNet on three SCA datasets of masked implementations with random delay and clock jitter effect. Our experimental results show that EstraNet significantly outperforms several benchmark models, demonstrating up to an order of magnitude reduction in the number of attack traces required to reach guessing entropy 1.

Complex-valued shift-invariant canonical polyadic decomposition (CPD) under a spatial phase sparsity constraint (pcsCPD) shows excellent separation performance when applied to band-pass filtered complex-valued multi-subject fMRI data. However, some useful information may also be eliminated when using a band-pass filter to suppress unwanted noise. As such, we propose an alternating rank- ${R}$ and rank-1 least squares optimization to relax the CPD model. Based upon this optimization method, we present a novel constrained CPD algorithm with temporal shift-invariance and spatial sparsity and orthonormality constraints. More specifically, four steps are conducted until convergence for each iteration of the proposed algorithm: 1) use rank- ${R}$ least-squares fit under spatial phase sparsity constraint to update shared spatial maps after phase de-ambiguity; 2) use orthonormality constraint to minimize the cross-talk between shared spatial maps; 3) update the aggregating mixing matrix using rank- ${R}$ least-squares fit; 4) utilize shift-invariant rank-1 least-squares on a series of rank-1 matrices reconstructed by each column of the aggregating mixing matrix to update shared time courses, and subject-specific time delays and intensities. The experimental results of simulated and actual complex-valued fMRI data show that the proposed algorithm improves the estimates for task-related sensorimotor and auditory networks, compared to pcsCPD and tensorial spatial ICA. The proposed alternating rank- ${R}$ and rank-1 least squares optimization is also flexible to improve CPD-related algorithm using alternating least squares.

Digital signal processing relies on the Nyquist-Shannon sampling theorem that applies to and requires a continuous signal with limited bandwidth. However, many systems or networks of signal processing involve nonlinear functions, which could generate new frequency components beyond the original bandwidth and lead to aliasing. Indeed, aliasing-induced shift variance has long been a nuisance and unsolved problem in convolutional neural networks and has recently been found to severely impair the performance of machine learning applications. The same problem exists in other fields such as computational lithography. In this paper, a new method and algorithms are introduced to solve the problem of aliasing induced by nonlinear functions involving operations other than linear convolutions and pointwise multiplications. Said new method and algorithms employ implicitly defined functions that are implemented via iterations of polynomial operations so that aliasing is completely avoided by upsampling signals before polynomial operations and limiting signal spectra before downsampling. Theoretical analyses and exemplary algorithms are presented to implement nonlinear functions commonly used in signal processing networks. In particular, exemplary embodiments and numerical experiments are reported to illustrate and verify aliasing-free operations of Wiener-Padé approximants, which are already universal in their ability to approximate any continuous activation functions to the desired accuracy.

We present a novel and computationally simple solution to the problem of determining the number of exponentials in a given time-series, which is applicable to both white and colored noise. The solution is based on a novel and non-asymptotic goodness-of-fit metric, referred to as invariant-signal-subspace matching (ISSM). This metric is aimed at matching pairs of signal-subspaces, created by exploiting the shift-invariance property of the Hankel data-matrix. A pair of such subspaces, together with their corresponding projection matrices, is created for every hypothesized number of exponentials, and the number of exponentials is then determined as that for which the distance between the pair of projection matrices is minimized. We prove the consistency of this criterion for the high signal-to-noise-ratio limit and also prove it for the large-sample limit, conditioned on the noise being white. We also extend this criterion to include multiple pairs of invariant subspace, readily created from the Hankel data-matrix, thus enabling to improve its performance at a slight increase in its computational load. Simulation results, demonstrating the superior performance of the solution over the existing solutions, for both colored and white noise, are included. [ABSTRACT FROM AUTHOR]

Complex-valued shift-invariant canonical polyadic decomposition (CPD) under a spatial phase sparsity constraint (pcsCPD) shows excellent separation performance when applied to band-pass filtered complex-valued multi-subject fMRI data. However, some useful information may also be eliminated when using a band-pass filter to suppress unwanted noise. As such, we propose an alternating rank- ${R}$ and rank-1 least squares optimization to relax the CPD model. Based upon this optimization method, we present a novel constrained CPD algorithm with temporal shift-invariance and spatial sparsity and orthonormality constraints. More specifically, four steps are conducted until convergence for each iteration of the proposed algorithm: 1) use rank- ${R}$ least-squares fit under spatial phase sparsity constraint to update shared spatial maps after phase de-ambiguity; 2) use orthonormality constraint to minimize the cross-talk between shared spatial maps; 3) update the aggregating mixing matrix using rank- ${R}$ least-squares fit; 4) utilize shift-invariant rank-1 least-squares on a series of rank-1 matrices reconstructed by each column of the aggregating mixing matrix to update shared time courses, and subject-specific time delays and intensities. The experimental results of simulated and actual complex-valued fMRI data show that the proposed algorithm improves the estimates for task-related sensorimotor and auditory networks, compared to pcsCPD and tensorial spatial ICA. The proposed alternating rank- ${R}$ and rank-1 least squares optimization is also flexible to improve CPD-related algorithm using alternating least squares. [ABSTRACT FROM AUTHOR]

We address the problem of tensor decomposition in application to direction-of-arrival (DOA) estimation for two-dimensional transmit beamspace (TB) multiple-input multiple-output (MIMO) radar. A general higher-order tensor model that enables computationally efficient DOA estimation is designed. Whereas other tensor decomposition-based methods treat all factor matrices as arbitrary, the essence of the proposed DOA estimation method is to fully exploit the Vandermonde structure of the factor matrices to take advantage of the shift-invariance between and within different transmit subarrays. Specifically, the received signal of TB MIMO radar is expressed as a higher-order tensor. A computationally efficient tensor decomposition method is proposed to decompose the Vandermonde factor matrices. The generators of the Vandermonde factor matrices are computed to estimate the phase rotations between subarrays, which can be utilized as a look-up table for finding target DOAs. The proposed tensor model and the DOA estimation algorithm are also straightforwardly applicable for the one-dimensional TB MIMO radar case. It is further shown that our proposed approach can be used in a more general scenario where the transmit subarrays with arbitrary but identical configuration can be non-uniformly displaced. We also show that both the tensor rank of the signal tensor and the matrix rank of a particular matrix derived from the signal tensor are identical to the number of targets. Thus, the number of targets can be estimated via matrix rank determination. Simulation results illustrate the performance improvement of the proposed DOA estimation method as compared to other tensor decomposition-based techniques for TB MIMO radar. [ABSTRACT FROM AUTHOR]

The goal of multi object tracking is to find location of the target objects in number of consecutive frames of a video. Tracking of multiple human objects in a scene is one of the challenging problems in computer vision applications due to illumination variation, object occlusion, abrupt motion etc. This paper introduces a new method for multiple human object tracking by exploiting the properties of Daubechies complex wavelet transform and Zernike moment. The proposed method uses combination of Daubechies complex wavelet transform and Zernike moment as a feature of objects. The motivation behind using combination of these two as a feature of object, because shift invariance and better edge representation properties make Daubechies complex wavelet transform suitable for locating object in consecutive frames whereas translation invariant property of Zernike moment is also helpful for correct object identification in consecutive frames. The proposed method is capable to handle full occlusion, partial occlusion, split and object re-enter problems. The experimental results validate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

• A novel shift-invariant rank-(L , L , 1, 1) BTD with 3D spatial pooling and orthonormalization for multi-subject fMRI data separation. • Two loading matrices of shared SMs, shared TCs, subject-specific time delays and strengths can be decomposed by the proposed method. • The proposed 3D weighted spatial pooling preprocessing compresses and smooths multi-subject fMRI data, and assigns a higher weight to in-brain voxels but a lower weight to out-brain voxels, which reduces the size and improves robustness to noise. • To deal with the high spatiotemporal variability, the proposed methods relaxes the rank-(L , L , 1, 1) BTD model of the reduced fMRI data by incorporating temporal shift-invariance and spatial orthonormality constraints. The rank-(L , L , 1, 1) block term decomposition (BTD) model shows better separation performance for multi-subject fMRI data by preserving the high-way structure of fMRI data than canonical polyadic decomposition (CPD). However, multi-subject fMRI data are noisy and have high spatiotemporal variability. To address these limitations, this paper proposes a novel 3D weighted spatial pooling preprocessing that compresses and smooths multi-subject fMRI data and assigns a higher weight to in-brain voxels but a lower weight to out-brain voxels. This strategy not only largely reduces the size of spatial images but also improves the robustness to noise. Furthermore, to address the high spatiotemporal variability, the rank-(L , L , 1, 1) BTD model of the reduced fMRI data is relaxed by incorporating temporal shift-invariance and spatial orthonormality constraints to extract pooled multi-subject shared spatial maps, shared time courses, subject-specific time delays and intensities. Finally, multi-subject intact shared spatial maps are obtained based on shift-invariant rank-(L , L , 1, 1) BTD of intact fMRI data. The simulated and experimental fMRI data experiments both verify that the proposed method achieves better separation performance and stronger robustness to noise than rank-(L , L , 1, 1) BTD with a spatial orthonormality constraint and a method combining independent component analysis and shift-invariant CPD. Moreover, the proposed method with 3D spatial pooling yields better separation performance than that with 2D spatial pooling, because 3D spatial pooling preserves refined voxels, thereby retaining more information of adjacent slices. [ABSTRACT FROM AUTHOR]

Signal processing via subspace-based methods require subspace estimates taken from either the eigenvectors of the sample covariance matrix or the principal singular vectors of the received data matrix. The subspaces spanned by the singular vectors or eigenvectors are perturbed away from ground truth due to the additive noise in the received data. The perturbation reduces the accuracy of algorithms that make use of these estimates. A statistically optimal estimate of the unperturbed subspace in terms of the perturbed signal and orthogonal subspaces has been derived and is accurate up to the first-order terms in the additive noise matrix (Vaccaro, 2019). Here, the second-order optimal approximation for the unperturbed subspace is derived and applied to a uniform linear array (ULA) processing model for both full and sparse geometries. The approximation provides little improvement for a full ULA highlighting the importance of first-order terms for a fully sampled geometry. However, for a sparse array, the source estimation performance is much more clearly improved for a low signal-to-noise ratio (SNR) environment with few temporal samples. • Decomposition of received array data matrix provides zeroth-order perturbed subspace basis. • Second-order perturbation analysis increases optimality of noise-free subspace estimation. • Second-order subspace optimality depends on performance of numerical method used. • Estimation error halved employing second-order over first-order statistics for some shift-invariant arrays. [ABSTRACT FROM AUTHOR]

In this paper, a low-redundant cosine-modulated nonuniform filter bank (LR-CMNFB) and its design method are proposed. The proposed LR-CMNFB consists of two parallel subsystems which have the same frequency division scheme. The nonuniform analysis and synthesis filters of the first subsystem are formed by directly merging the consecutive cosine-modulated versions of a lowpass prototype filter, and the filters of the second subsystem are derived to meet the aliasing cancelation condition. Since the aliasing of the two subsystems is structurally canceled without guardband constraint on the filter location, the shift-invariance and flexible nonuniform frequency division, two important properties in many signal and image processing applications, can be achieved simultaneously at the cost of low redundancy (that is less than 2). From a particular analysis on the filter characteristic and the reconstruction error of the whole system, it is found that the good characteristics of filters and the good reconstruction performance of LR-CMNFB can be jointly obtained by constraining the prototype filter to be the linear-phase spectral factor of a 2 Mth band filter. Several design examples are given to illustrate the performance of the proposed LR-CMNFB and its potential in practical applications. [ABSTRACT FROM AUTHOR]

Coherent lower previsions generalize the expected values and they are defined on the class of all real random variables on a finite non-empty set. Well known construction of coherent lower previsions by means of lower probabilities, or by means of super-modular capacities-based Choquet integrals, do not cover this important class of functionals on real random variables. In this paper, a new approach to the construction of coherent lower previsions acting on a finite space is proposed, exemplified and studied. It is based on special decomposition integrals recently introduced by Even and Lehrer, in our case the considered decomposition systems being single collections and thus called collection integrals. In special case when these integrals, defined for non-negative random variables only, are shift-invariant, we extend them to the class of all real random variables, thus obtaining so called super-additive integrals. Our proposed construction can be seen then as a normalized super-additive integral. We discuss and exemplify several particular cases, for example, when collections determine a coherent lower prevision for any monotone set function. For some particular collections, only particular set functions can be considered for our construction. Conjugated coherent upper previsions are also considered.

In the catenary status detection system based on the image processing, quality of the captured catenary image is critical. In order to obtain a high quality image for further analysis, this paper proposes a new catenary image denoising method based on lifting wavelet-based contourlet transform with cycle shift-invariance (LWBCTCS). In this method, the lifting wavelet is first constructed based on wavelet transform (WT). Then, to decrease the redundancy of contourlet transform (CT), the lifting wavelet-based contourlet transform (LWBCT) is built by using the lifting wavelet to replace the Laplacian pyramid (LP) transform of CT. Finally, the LWBCT with the cycle shift-invariance (LWBCTCS) algorithm is combined to reduce the pseudo-Gibbs phenomena of LWBCT. The proposed method not only has the virtues of multi-scale and multi-direction, but also reduces the visual artifacts in the denoised image. The results of comparative experiments with captured catenary image show that the proposed method can achieve satisfactory denoising performance, in particular, for catenary image with abundant texture and detail outline information. It not only eliminates noise but also preserves the textures and details simultaneously. Besides, comprehensive consideration of the denoising performance shows that the proposed algorithm in terms of the signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR) and mean squared error (MSE) is stable than those conventional denoising algorithms, including WT, CT, curvelet transform (CV) and BLS-GSM methods. The visual quality as well as quantitative metrics is superior than those conventional denoising methods. [ABSTRACT FROM AUTHOR]

We explore the nature of the solution space for the Golomb nested recursion . On this solution space, we define a natural equivalence relation and restrict our attention to non-equivalent solutions. We describe and prove an algorithm that determines whether a given set of initial conditions generates a solution. Up to equivalence, there is a unique solution whose forward differences are eventually either 0 or 1, namely, the Golomb sequence , generated by the initial condition . This sequence is asymptotic to ; we conjecture that this is true of every solution. We further conjecture that each solution has what we call a generational structure that abstracts combinatorial properties of . It appears that for any given solution, its generations are composed of only a finite number of building blocks. [ABSTRACT FROM AUTHOR]

We propose a novel feature extraction approach for 3D facial expression recognition by incorporating non-rigid registration in face-model-free analysis, which in turn makes feasible data-driven, i.e., feature-model-free recognition of expressions. The resulting simplicity of feature representation is due to the fact that facial information is adapted to the input faces via shape model-free dense registration, and this provides a dynamic feature extraction mechanism. This approach eliminates the necessity of complex feature representations as required in the case of static feature extraction methods, where the complexity arises from the necessity to model the local context; higher degree of complexity persists in deep feature hierarchies enabled by end-to-end learning on large-scale datasets. Face-model-free recognition implies independence from limitations and biases due to committed face models, bypassing complications of model fitting, and avoiding the burden of manual model construction. We show via information gain maps that non-rigid registration enables extraction of highly informative features, as it provides invariance to local-shifts due to physiognomy (subject invariance) and residual pose misalignments; in addition, it allows estimation of local correspondences of expressions. To maximize the recognition rate, we use the strategy of employing a rich but computationally manageable set of local correspondence structures, and to this effect we propose a framework to optimally select multiple registration references. Our features are re-sampled surface curvature values at individual coordinates which are chosen per expression-class and per reference pair. We show the superior performance of our novel dynamic feature extraction approach on three distinct recognition problems, namely, action unit detection, basic expression recognition, and emotion dimension recognition. [ABSTRACT FROM AUTHOR]

The space of one-sided infinite words plays a crucial rôle in several parts of Theoretical Computer Science. Usually, it is convenient to regard this space as a metric space, the Cantor space. It turned out that for several purposes topologies other than the one of the Cantor space are useful, e.g. for studying fragments of first-order logic over infinite words or for a topological characterisation of random infinite words. It is shown that these topologies refine the topology of the Cantor space. Moreover, from common features of these topologies we extract properties which characterise a large class of topologies. It turns out that, for this general class of topologies, the corresponding closure and interior operators respect the shift operations and also, to some extent, the definability of sets of infinite words by finite automata. [ABSTRACT FROM AUTHOR]

Moving object tracking is one of the challenging problems in computer vision and it has numerous applications in surveillance system, traffic monitoring etc. The goal of object tracking algorithm is to locate a moving object in consecutive video frames. Tracking of moving object in a video becomes difficult due to random motion of objects. This paper introduces a new algorithm for moving object tracking by exploiting the properties of Daubechies complex wavelet transform and Zernike moment. The proposed method uses combination of Daubechies complex wavelet transform and Zernike moment as a feature of object. The motivation behind using combination of these two as a feature of object, because shift invariance and better edge representation property make Daubechies complex wavelet transform suitable for locating object in consecutive frames whereas rotation invariance properties of Zernike moment is also helpful for correct object identification in consecutive frames. Therefore combination of these two as feature of object gives better results. The proposed method matches Zernike moments of Daubechies complex wavelet coefficients of object in the first frame to next consecutive frames. The experimental results and performance evaluation parameters validate that the proposed method gives better performance against other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

We prove a new shift-invariance property of the colored TASEP. From the shift-invariance of the colored stochastic six-vertex model (proved in Borodin-Gorin-Wheeler or Galashin), one can get a shift-invariance property of the colored TASEP at one time, and our result generalizes this to multiple times. Our proof takes the single-time shift-invariance as an input, and uses analyticity of the probability functions and induction arguments. We apply our shift-invariance to prove a distributional identity between the finishing times of the oriented swap process and the point-to-line passage times in exponential last-passage percolation, which is conjectured by Bisi-Cunden-Gibbons-Romik and Bufetov-Gorin-Romik, and is also equivalent to a purely combinatorial identity related to the Edelman-Greene correspondence. With known results from last-passage percolation, we also get new asymptotic results on the colored TASEP and the finishing times of the oriented swap process. [ABSTRACT FROM AUTHOR]

Cardiac Phase-resolved Blood-Oxygen-Level Dependent (CP-BOLD) MRI provides a unique opportunity to image an ongoing ischemia at rest. However, it requires post-processing to evaluate the extent of ischemia. To address this, here we propose an unsupervised ischemia detection (UID) method which relies on the inherent spatio-temporal correlation between oxygenation and wall motion to formalize a joint learning and detection problem based on dictionary decomposition. Considering input data of a single subject, it treats ischemia as an anomaly and iteratively learns dictionaries to represent only normal observations (corresponding to myocardial territories remote to ischemia). Anomaly detection is based on a modified version of One-class Support Vector Machines (OCSVM) to regulate directly the margins by incorporating the dictionary-based representation errors. A measure of ischemic extent (IE) is estimated, reflecting the relative portion of the myocardium affected by ischemia. For visualization purposes an ischemia likelihood map is created by estimating posterior probabilities from the OCSVM outputs, thus obtaining how likely the classification is correct. UID is evaluated on synthetic data and in a 2D CP-BOLD data set from a canine experimental model emulating acute coronary syndromes. Comparing early ischemic territories identified with UID against infarct territories (after several hours of ischemia), we find that IE, as measured by UID, is highly correlated (Pearson’s r=0.84) with respect to infarct size. When advances in automated registration and segmentation of CP-BOLD images and full coverage 3D acquisitions become available, we hope that this method can enable pixel-level assessment of ischemia with this truly non-invasive imaging technique. [ABSTRACT FROM AUTHOR]

Image denoising is a basic procedure of image processing, and the purpose of image denoising is to remove noises entirely and well preserve image boundaries and texture information simultaneously. However, conventional filtering methods easily lead to the loss of texture and details information. This paper proposes a new image denoising method to improve this problem, first proposing a new structure called dual contourlet transform (DCT) which is improved from contourlet transform and dual tree complex wavelet transform (DTCWT). The DCT employs a dual tree Laplacian Pyramid (LP) transform to improve the shift invariance and adopts directional filter banks (DFB) to achieve higher directional selectivity. Compared to other existing structures of multiresolution analysis, the main advantage of the DCT is that it not only possesses the advantages of other structures, but also it has simple structure and easy to implement. The most noteworthy is the redundancy of DCT is 8/3 at most; it is the envy of other existing structures. Second, after studying the distribution of DCT coefficients and the correlation between the interscale and intrascale dependencies, we take this account into denoising and use bivariate threshold function on DCT coefficients. Simulation experiments show that the proposed method achieves better performance than those outstanding denoising algorithms in terms of peak signal-to-noise ratio (PSNR), as well as visual quality. In addition, to verify the validity of our method, we give the difference between the original image and the denoised image that rarely used in other denoising literatures. [ABSTRACT FROM AUTHOR]

Abstract: For the quality of the fused outcome is determined by the amount of the information captured from the source images, thus, a multi-modal medical image fusion method is developed in the shift-invariant shearlet transform (SIST) domain. The two-state Hidden Markov Tree (HMT) model is extended into the SIST domain to describe the dependent relationships of the SIST coefficients of the cross-scale and inter-subbands. Base on the model, we explain why the conventional Average–Maximum fusion scheme is not the best rule for medical image fusion, and therefore a new scheme is developed, where the probability density function and standard deviation of the SIST coefficients are employed to calculate the fused coefficients. Finally, the fused image is obtained by directly applying the inverse SIST. Integrating the SIST and the HMT model, more spatial feature information of the singularities and more functional information contents can be preserved and transferred into the fused results. Visual and statistical analyses demonstrate that the fusion quality can be significantly improved over that of five typical methods in terms of entropy and mutual information, edgeinformation, standarddeviation, peak signal to noise and structural similarity. Besides, color distortion can be suppressed to a great extent, providing a better visual sense. [Copyright &y& Elsevier]

This paper aims to identify approaches that generate appropriate synthetic data (computer generated) for cardiac phase-resolved blood–oxygen-level-dependent (CP-BOLD) MRI. CP-BOLD MRI is a new contrast agent- and stress-free approach for examining changes in myocardial oxygenation in response to coronary artery disease. However, since signal intensity changes are subtle, rapid visualization is not possible with the naked eye. Quantifying and visualizing the extent of disease relies on myocardial segmentation and registration to isolate the myocardium and establish temporal correspondences and ischemia detection algorithms to identify temporal differences in BOLD signal intensity patterns. If transmurality of the defect is of interest pixel-level analysis is necessary and thus a higher precision in registration is required. Such precision is currently not available affecting the design and performance of the ischemia detection algorithms. In this work, to enable algorithmic developments of ischemia detection irrespective to registration accuracy, we propose an approach that generates synthetic pixel-level myocardial time series. We do this by 1) modeling the temporal changes in BOLD signal intensity based on sparse multi-component dictionary learning, whereby segmentally derived myocardial time series are extracted from canine experimental data to learn the model; and 2) demonstrating the resemblance between real and synthetic time series for validation purposes. We envision that the proposed approach has the capacity to accelerate development of tools for ischemia detection while markedly reducing experimental costs so that cardiac BOLD MRI can be rapidly translated into the clinical arena for the noninvasive assessment of ischemic heart disease. [ABSTRACT FROM AUTHOR]

Many signal processing algorithms utilize singular vectors of the data received by a sensor array or eigenvectors of the sample covariance matrix. The performance of such subspace-based algorithms can be substantially improved by using the optimal signal or noise subspace estimate instead of using the subspaces spanned by the eigenvectors or the singular vectors. The optimal signal and noise subspaces are estimated by exploiting the shift-invariant structure of the sensor array. We develop a methodology to find the optimal subspaces in sparse arrays that possess shift-invariant structure and interpolate the optimal subspaces to match the subspaces of the fully populated arrays with an equal aperture. These shift-invariant sparse arrays' direction of arrival estimation performance is superior compared to the methods that use eigenvectors or singular vectors directly. Our method also encompasses any symmetric array that is not shift-invariant, thus broadening the class of sparse arrays where our method can be applied. [ABSTRACT FROM AUTHOR]

Abstract: We positively resolve Problem 8.2 stated in [A. Pietsch, Traces on operator ideals and related linear forms on sequence ideals (Part I), Indag. Math. (N.S.) (2013) http://dx.doi.org/10.1016/j.indag.2012.08.008]. The question was whether, in the Hilbert space setting, completeness carries over from quasi-normed shift-monotone sequence ideals to the associated quasi-normed operator ideals. In fact, our technique provides even a solution of Problem 14.1.7 in Pietsch’s book “Operator Ideals” (1978). It turns out that all quasi-normed operator ideals over Banach spaces generated by complete quasi-normed symmetric sequence ideals via arbitrary additive -numbers are complete. So the completeness problem is solved completely. [Copyright &y& Elsevier]

Dual-tree transforms have recently received much attention for the properties of shift-invariance and directional-selectivity. However, their designs generally encounter fractional-delay constraints, and become more complicated for providing linear-phase (LP) individual filters and flexible directional-selectivity, two important properties in image processing. In this paper, we propose an alternative shift-invariant and directional-selective transform-the dual-tree cosine-modulated filter bank (DTCMFB). In the proposed DTCMFB, its primal and dual filter banks are derived by cosine-modulating one LP prototype filter, and thus its design involves no fractional-delay constraints. Meanwhile, the derived modulation technique guarantees each individual filter to be LP and the LP condition is satisfied without any constraint on the prototype filter. By separable operations, the DTCMFB is extended to two-dimensions. The resulting 2D DTCMFB can provide much more flexible directional-selectivity. Finally, several simulations are given to verify the proposed DTCMFB, and the experiments on nonlinear approximation and image denoising are presented to demonstrate its potential in image processing. [ABSTRACT FROM AUTHOR]

Abstract: Wavelet analysis has been widely applied to mechanical fault diagnosis. Aiming at the problems of current wavelet basis, such as low time–frequency sampling, asymmetry and poor shift-invariance, this paper develops a new family of dense framelets with two generators and some desirable properties. To perform the corresponding framelet transform, three-channel iterated filterbank should be used, where the first and the third channel is decimated while the second channel is undecimated. This arrangement is very helpful for extracting the fault feature of the mid and low frequency band signal components and obtaining some symmetric framelets. To obtain framelets with high symmetry and a specified number of vanishing moments, B-spline and maximally flat linear FIR filter are, respectively, used to design filterbank. Three symmetric framelets and one framelets with symmetric low-pass filter and high-pass filter are constructed. Compared with the higher density framelets and orthonormal wavelets, the proposed framelets have better shift-invariance and denoising performance. Finally, the proposed framelets are applied to fault diagnosis of two gearboxes. The results show that the proposed framelets can be effectively applied to mechanical fault diagnosis and is superior to other commonly-used framelets/wavelets. [Copyright &y& Elsevier]

Medical image fusion plays an important role in clinical applications, such as image-guided surgery, image-guided radiotherapy, non-invasive diagnosis and treatment planning. Shearlet is a novel multi-scale geometric analysis (MGA) tool proposed recently. In order to overcome the drawback of the shearlet-based fusion methods that the pseudo-Gibbs phenomenon is easily caused around the singularities of the fused image, a new multi-modal medical image fusion method is proposed in shift-invariant shearlet transform domain. First, the original images are decomposed into lowpass sub-bands and highpass sub-bands; then, the lowpass sub-bands and high sub-bands are combined according to the fusion rules, respectively. All the operations are performed in shift-invariant shearlet domain. The final fused image is obtained by directly applying inverse shift-invariant shearlet transform to the fused lowpass sub-bands and highpass sub-bands. Experimental results demonstrate that the proposed method can not only suppress the pseudo-Gibbs phenomenon efficiently, but perform better than the popular wavelet transform-based method, contourlet transform-based method and non-subsampled contourlet transform-based method. [ABSTRACT FROM AUTHOR]

Abstract: This article addresses the issue of representing electroencephalographic (EEG) signals in an efficient way. While classical approaches use a fixed Gabor dictionary to analyze EEG signals, this article proposes a data-driven method to obtain an adapted dictionary. To reach an efficient dictionary learning, appropriate spatial and temporal modeling is required. Inter-channels links are taken into account in the spatial multivariate model, and shift-invariance is used for the temporal model. Multivariate learned kernels are informative (a few atoms code plentiful energy) and interpretable (the atoms can have a physiological meaning). Using real EEG data, the proposed method is shown to outperform the classical multichannel matching pursuit used with a Gabor dictionary, as measured by the representative power of the learned dictionary and its spatial flexibility. Moreover, dictionary learning can capture interpretable patterns: this ability is illustrated on real data, learning a P300 evoked potential. [Copyright &y& Elsevier]

Abstract: Purpose: To investigate dose deformation-invariance in adaptive prostate radiation treatment. Methods: A 19 patient prostate cancer-cohort with 8–13 CTs/patient is used. The 79.2Gy plans are developed on the reference image using seven 6 and 18MV intensity-modulated beams with identical RTOG 0126 objectives. Dose on the subsequent images is evaluated in two ways: (A1) Dose is recalculated on each image. (A2) The initially planned dose distribution is copied to each image. A2 assumes dose-invariance in the accelerator-coordinate-system. Effects of patient miss-alignment are simulated by 27 per-patient image shifts; 0 and ±10mm in left–right, anterior–posterior and superior–inferior directions. The per-voxel dose differences for each patient image, total accumulated patient dose, and dose–volume metrics (CTV-D98 and -D90, bladder- and rectum-D50, -D35, -D25 and -D15) are used to compare A1 and A2. Results: The per-voxel mean percent difference in A1 and A2 dose over all patient images at 6MV is (0.01±1.56)% and at 18MV is (0.00±0.96)%. For 6MV and 18MV plans, the root-mean-square-percentage-error (RMSPE) in A2 over all patient image shifts are CTV-D98=0.94 and 0.55, CTV-D90=0.92 and 0.55, rectum-D50, -D35, -D25 and -D15=1.00, 0.96, 0.86, 0.80 and 0.84, 0.96, 0.92, 1.05; and bladder-D50, -D35, -D25, -D15=1.07, 0.88, 0.78, 0.72 and 1.61, 0.93, 0.67, 0.51. The dose differences are not correlated to the dice-similarity coefficients; with respective correlation-coefficients for CTV, rectum and bladder being −0.17, −0.17 and 0.081. Conclusions: Assumption of shift- and deformation-invariant dose distributions on an average introduces <2% error in evaluated dose–volume metrics for 6 and 18MV IMRT prostate plans. Use of invariant dose distributions has a potential to reduce online re-planning time and permit pre-planning based on tissue deformation models. [Copyright &y& Elsevier]

Abstract: An novel edge detection approach is proposed. Firstly, the nonsubsampled contourlet transform is used to decompose the original image into low frequency approximation image and the high frequency subbands. Then, because of nonsubsampled contourlet transform shift-invariance, the original image corresponding gradient magnitude is redefined in every scale. Finally, different scales gradient is synthesized into the image dege. The experimental results of edge detection for several test images are provided to demonstrate the approach. [Copyright &y& Elsevier]