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Coded aperture is a promising approach for capturing the 4-D light field (LF), in which the 4-D data are compressively modulated into 2-D coded measurements that are further decoded by reconstruction algorithms. The bottleneck lies in the reconstruction algorithms, resulting in rather limited reconstruction quality. To tackle this challenge, we propose a novel learning-based framework for the reconstruction of high-quality LFs from acquisitions via learned coded apertures. The proposed method incorporates the measurement observation into the deep learning framework elegantly to avoid relying entirely on data-driven priors for LF reconstruction. Specifically, we first formulate the compressive LF reconstruction as an inverse problem with an implicit regularization term. Then, we construct the regularization term with a deep efficient spatial-angular separable convolutional sub-network in the form of local and global residual learning to comprehensively explore the signal distribution free from the limited representation ability and inefficiency of deterministic mathematical modeling. Furthermore, we extend this pipeline to LF denoising and spatial super-resolution, which could be considered as variants of coded aperture imaging equipped with different degradation matrices. Extensive experimental results demonstrate that the proposed methods outperform state-of-the-art approaches to a significant extent both quantitatively and qualitatively, i.e., the reconstructed LFs not only achieve much higher PSNR/SSIM but also preserve the LF parallax structure better on both real and synthetic LF benchmarks. The code will be publicly available at https://github.com/MantangGuo/DRLF. [ABSTRACT FROM AUTHOR]

The inverse scattering problem related to the localization of metal bars embedded within a finite-dimensional dielectric was studied in two-dimensional geometry. The dielectric was placed in air and illuminated from the outside using a linear microwave source and a multi-monostatic configuration. The discontinuity at the interface between the air and the dielectric causes reflections that are neglected if a simple linear Born approximation of scattering is assumed. Herein, a new formulation was proposed based on a quadratic approximation of the scattering equation. The formulation maintained the interaction between the metal bars and the dielectric edge, whereas the mutual coupling between the bars was neglected. By exploiting the knowledge of the permittivity of the dielectric and the shape of its section, a relatively simple approximate expression for the scattered field was derived, which allowed for formulation of an inverse linear problem. Numerical examples demonstrated the feasibility of this approach. [ABSTRACT FROM AUTHOR]

We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high‐intensity ultrasound propagation as widely used in medical imaging and therapy. The usual nonlinear term in the standard model using the Westervelt equation in pressure formulation is of the form ppt. However, this should be considered as a low‐order approximation to a more complex physical model where higher order terms will be required. Here we assume a more general case where the form taken is f(p) pt and f is unknown and must be recovered from data measurements. Corresponding to the typical measurement setup, the overposed data consist of time trace observations of the acoustic pressure at a single point or on a one‐dimensional set Σ representing the receiving transducer array at a fixed time. Additionally to an analysis of well‐posedness of the resulting pde, we show injectivity of the linearized forward map from f to the overposed data and use this as motivation for several iterative schemes to recover f. Numerical simulations will also be shown to illustrate the efficiency of the methods. [ABSTRACT FROM AUTHOR]

The formulation and implementation of the Love’s condition constraint for the source reconstruction method (SRM) in near-field antenna measurements are analyzed in the context of inverse problems. To this end, the SRM is first analyzed to identify the nonunique or nonradiating (NR) current sources which may be present. Next, the advantages and disadvantages of general regularization techniques, which may address the NR currents, are presented which serve to motivate the use of the Love’s condition constraint. The main methods of formulating the constraint are then presented, one of which is a novel technique developed for this article. Following this, the formulation methods are analyzed in order to predict the similarities and differences of the methods in the context of addressing the NR currents of the SRM. This analysis is reinforced by simulated antenna measurements. In particular, the novel formulation method is demonstrated to provide a greater regularizing effect (in the examples considered), at the cost of computational complexity. [ABSTRACT FROM AUTHOR]

In this paper, two classical inverse spectral problems are investigated, namely, the inverse second-order Sturm-Liouville problem and the inverse fourth-order Sturm-Liouville problem. Based on Lidskii's theorem, we derive trace formulas showing relations between the unknown coefficients and eigenvalues explicitly for both problems. According to those trace formulas, two efficient algorithms are proposed to recover the symmetric potential from one spectrum for second-order Sturm-Liouville problem and two coefficients simultaneously from three spectra for fourth-order Sturm-Liouville problem, respectively. Numerical results are presented to illustrate the effectiveness of the proposed reconstruction algorithms. [ABSTRACT FROM AUTHOR]

This paper examines a combined supervised-unsupervised framework involving dictionary-based blind learning and deep supervised learning for MR image reconstruction from under-sampled k-space data. A major focus of the work is to investigate the possible synergy of learned features in traditional shallow reconstruction using adaptive sparsity-based priors and deep prior-based reconstruction. Specifically, we propose a framework that uses an unrolled network to refine a blind dictionary learning-based reconstruction. We compare the proposed method with strictly supervised deep learning-based reconstruction approaches on several datasets of varying sizes and anatomies. We also compare the proposed method to alternative approaches for combining dictionary-based methods with supervised learning in MR image reconstruction. The improvements yielded by the proposed framework suggest that the blind dictionary-based approach preserves fine image details that the supervised approach can iteratively refine, suggesting that the features learned using the two methods are complementary. [ABSTRACT FROM AUTHOR]

Tomographic image reconstruction is generally an ill-posed linear inverse problem. Such ill-posed inverse problems are typically regularized using prior knowledge of the sought-after object property. Recently, deep neural networks have been actively investigated for regularizing image reconstruction problems by learning a prior for the object properties from training images. However, an analysis of the prior information learned by these deep networks and their ability to generalize to data that may lie outside the training distribution is still being explored. An inaccurate prior might lead to false structures being hallucinated in the reconstructed image and that is a cause for serious concern in medical imaging. In this work, we propose to illustrate the effect of the prior imposed by a reconstruction method by decomposing the image estimate into generalized measurement and null components. The concept of a hallucination map is introduced for the general purpose of understanding the effect of the prior in regularized reconstruction methods. Numerical studies are conducted corresponding to a stylized tomographic imaging modality. The behavior of different reconstruction methods under the proposed formalism is discussed with the help of the numerical studies. [ABSTRACT FROM AUTHOR]

This article presents a supershape augmented shape reconstruction algorithm for electrical impedance tomography, aiming at high-quality reconstructions with respect to multiphase conductivity distributions. Within the proposed algorithm, the reconstructed inclusions are composed of basic shape primitives expressed through a supershape formula. To allow automatic topological evolution, multiple Boolean operations, including three basic Boolean operations and compound Boolean operations, are employed so that the candidate shape primitives can be intersected, subtracted, and merged to form different shapes. The proposed algorithm is tested using simulations and water tank experimental data. Moreover, robustness studies considering varying initial guesses and differing signal-to-noise ratios are performed. It is demonstrated that the proposed algorithm is able to preserve detailed features of inclusions under detection and provide reliable estimates of unknown conductivity values and the interface properties. [ABSTRACT FROM AUTHOR]

The idea of accounting for a priori shape information is gaining increasing levels of interest and traction in the electrical impedance tomography (EIT) reconstruction. A supershape-based reconstruction approach is proposed for EIT. We begin by assuming that the conductivity profile to be reconstructed in the measured domain is piecewise constant distributed. Using this formulation, the image reconstruction problem is transformed into a shape reconstruction problem. The inclusion boundary (e.g., interface between the inclusion and the background) to be estimated is treated as a supershape and expressed through a single equation—the so-called super formula. We illustrate the performance of the proposed approach using synthetic and experimental water tank data. In addition, robustness studies considering different regularization types ($L_{1}$ and $L_{2}$ norms), varying noise levels and different initial settings are tested of the proposed approach. Four evaluation matrices relative size coverage ratio (RCR), structural similarity index (SSIM), relative contrast (RCo), and correlation coefficient (CC) are used to quantitatively evaluate the performance of the proposed method. Both the simulation and experimental results show that the supershape-based method leads to reliable and robust reconstructions and improves the ability to simultaneously reconstruct objects with smooth boundaries and/or sharp features. The proposed approach provides an excellent opportunity for the shape reconstruction framework to express a wide variety of shapes, including geometric primitives. Supershapes can simply represent regular polygons and natural shapes with various symmetries while maintaining a parametric representation. [ABSTRACT FROM AUTHOR]

X-ray inspection systems are critical in medical, non-destructive testing, and security applications, with systems typically measuring attenuation along straight-line paths connecting sources and detectors. Computed tomography (CT) systems can provide higher-quality images than single- or dual-view systems, but the need to measure many projections leads to greater system cost and complexity. Typically, off-angle Compton scattered photons are treated as noise during tomographic inversion. We seek to maximize the image quality of limited-view systems by combining attenuation data with measurements of Compton-scattered photons, exploiting the fact that the broken-ray paths followed by scattered photons provide additional geometric sampling of the scene. We describe a single-scatter forward model for Compton-scatter data measured with energy-resolving detectors, and demonstrate a reconstruction algorithm for density that combines both attenuation and scatter measurements. The experimental results suggest that including Compton-scattered data in the reconstruction process can improve image quality for density reconstruction using limited-view systems.

Electrical impedance tomography (EIT) is a noninvasive technique estimating the conductivity inside an observation domain from its peripheral measurements and owns many industrial and biomedical applications. Inclusion reconstruction is one of the key problems in EIT. However, the high-resolution inclusion reconstruction is challenging due to the ill-posedness and nonlinearity of EIT. The shape reconstruction methods focusing on recovering the shape of the inclusion is one kind of advanced methods to enhance the EIT resolution. To achieve high-performance shape reconstruction, a parametric geometric constraint boundary reconstruction (PGCBR) framework is proposed. The shape reconstruction is implemented by minimizing the energy function of the inclusion boundary represented by the parametric snake model. To accelerate the convergence, the Newton method is adopted to solve the energy minimization problem. The first- and second-order partial derivatives of the energy terms are calculated with the EIT shape sensitivity formula. A series of numerical tests evaluated the influences of the key factors, e.g., the basis function and the number of the knot and interpolating points, of PGCBR on its reconstruction performance and proved its robustness against the measurement noise. The following experimental tests, including both single- and multiphase conductivity cases, further proved the advantages of PGCBR over the nonparametric method. [ABSTRACT FROM AUTHOR]

For full-waveform inversion (FWI), building the salt structure velocity model is a challenging problem. In the absence of a high-fidelity initial model, low-frequency seismic data are indispensable for accurate reconstruction of the long-wavelength components of salt domes, which are often missing in field data. The envelope isolates the amplitude information from the seismic data and has a stronger linear relationship with the velocity than the seismic data. It is used to enhance the convexity of the objective function in an envelope inversion (EI). However, the properties of the envelope are not effectively utilized in EI due to the lack of their proper understanding. In order to solve the problems that EI has in building the salt structure velocity, such as the cycle-skipping problem, the gradient calculation problem caused by the waveform Fréchet derivative, and the multisolution problem caused by the missing polarity information of the envelope, we propose a multiscale direct signed EI (MSDSEI) based on the direct envelope Fréchet derivative and multiscale signed envelope. The development process from EI to MSDSEI also inspired us to understand the physical mechanism involved in the low-frequency components of the envelope: the signed envelope can be regarded as a low-pass filter of the reflection sequences in the subsurface. Thus, we use the smoothness and phase-independent properties of the envelope to propose an envelope-based full-band seismic data reconstruction method for multiscale FWI. Finally, the performance of various EI methods is verified on the Sigsbee2A model. [ABSTRACT FROM AUTHOR]

Objective: Fluorescence molecular tomography (FMT) is an important tool for life science, which can noninvasive real-time three-dimensional (3-D) visualization for fluorescence source location. FMT is widely used in tumor research due to its high-sensitive and low cost. However, the reconstruction of FMT is difficult. Although the reconstruction methods of FMT have developed rapidly in recent years, the morphological reconstruction of FMT is still a challenge problem. Thus, the purpose of this study is to realize the morphological reconstruction performance of FMT in glioma research. Methods: In this study, group sparsity was used as a new priori information for FMT. Besides sparsity, group sparsity also takes the group structure of the fluorescent sources, which can maintain the morphological information of the sources. Fused LASSO method (FLM) was proved it can efficiently model the group sparsity prior. Thus, we utilize FLM to reconstruct the morphological information of glioma. Furthermore, to reduce the influence of the high scattering of skull, we modified the FLM for improving the accuracy of morphological reconstruction. Results: Glioma numerical simulation model and in vivo glioma model were established to evaluate the performance of morphological reconstruction of the proposed method. The results demonstrated that the proposed method was efficient to reconstruct the morphological information of glioma. Conclusion: Group sparsity priori can effectively improve the morphological accuracy of FMT reconstruction. Significance: Group sparsity can maintain the morphological information of fluorescent sources effectively, which has great application potential in FMT. The group sparsity based methods can realize the morphological reconstruction, which is of great practical significance in tumor research. [ABSTRACT FROM AUTHOR]

This paper presents a deep learning algorithm for tomographic reconstruction (GANrec). The algorithm uses a generative adversarial network (GAN) to solve the inverse of the Radon transform directly. It works for independent sinograms without additional training steps. The GAN has been developed to fit the input sinogram with the model sinogram generated from the predicted reconstruction. Good quality reconstructions can be obtained during the minimization of the fitting errors. The reconstruction is a self‐training procedure based on the physics model, instead of on training data. The algorithm showed significant improvements in the reconstruction accuracy, especially for missing‐wedge tomography acquired at less than 180° rotational range. It was also validated by reconstructing a missing‐wedge X‐ray ptychographic tomography (PXCT) data set of a macroporous zeolite particle, for which only 51 projections over 70° could be collected. The GANrec recovered the 3D pore structure with reasonable quality for further analysis. This reconstruction concept can work universally for most of the ill‐posed inverse problems if the forward model is well defined, such as phase retrieval of in‐line phase‐contrast imaging. [ABSTRACT FROM AUTHOR]

In the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead to the unique reconstruction of all possible signals, even in combination with certain practically feasible random masks. To avoid this difficulty, the analysis is often restricted to measurement ensembles (or masks) that satisfy a small-ball probability condition, in order to ensure that the reconstruction is unique. This paper shows a complementary result: for random Bernoulli measurements, there is still a large class of signals that can be reconstructed uniquely, namely, those signals that are non-peaky. In fact, this result is much more general: it holds for random measurements sampled from any subgaussian distribution \mathcal D , without any small-ball conditions. This is demonstrated in two ways: 1) a proof of stability and uniqueness and 2) a uniform recovery guarantee for the PhaseLift algorithm. In all of these cases, the number of measurements $m$ approaches the information-theoretic lower bound. Finally, for random Bernoulli measurements with erasures, it is shown that PhaseLift achieves uniform recovery of all signals (including peaky ones). [ABSTRACT FROM PUBLISHER]

Microwave inverse scattering is an exploratory imaging modality with potential for several clinical breast imaging applications, including density evaluation, cancer detection, and treatment monitoring. However, conventional regularization techniques used to solve the ill-posed inverse problem typically result in blurred boundaries between tissue structures exhibiting dielectric contrast, thereby limiting the effective resolution. We present a method to improve microwave breast imaging resolution that incorporates a priori information about the boundaries between different tissues in the breast into the inverse scattering algorithm. This spatial prior information can be derived from another imaging modality, such as magnetic resonance imaging. Our method exploits the fact that the dielectric properties within a tissue type exhibit low to moderate variability by favoring solutions to the inverse scattering problem, which have small variations in dielectric properties within each tissue region. The amount of variation tolerated in each regions is controlled by a spatial prior constraint parameter. We demonstrate the feasibility of the method by imaging detailed, anatomically inspired numerical 3-D breast phantoms. The performance in the presence of different levels of noise and for different choices of the constraint parameter is evaluated. We also demonstrate the robustness of the algorithm with respect to errors in the spatial prior information. [ABSTRACT FROM AUTHOR]

This paper describes a fast-forward electromagnetic solver (FFS) for the image reconstruction algorithm of our microwave tomography system. Our apparatus is a preclinical prototype of a biomedical imaging system, designed for the purpose of early breast cancer detection. It operates in the 3–6-GHz frequency band using a circular array of probe antennas immersed in a matching liquid; it produces image reconstructions of the permittivity and conductivity profiles of the breast under examination. Our reconstruction algorithm solves the electromagnetic (EM) inverse problem and takes into account the real EM properties of the probe antenna array as well as the influence of the patient’s body and that of the upper metal screen sheet. This FFS algorithm is much faster than conventional EM simulation solvers. In comparison, in the same PC, the CST solver takes ~45 min, while the FFS takes ~1 s of effective simulation time for the same EM model of a numerical breast phantom. [ABSTRACT FROM PUBLISHER]

The Fly Algorithm was initially developed for 3-D robot vision applications. It consists in solving the inverse problem of shape reconstruction from projections by evolving a population of 3-D points in space (the ‘flies’), using an evolutionary optimisation strategy. Here, in its version dedicated to tomographic reconstruction in medical imaging, the flies are mimicking radioactive photon sources. Evolution is controlled using a fitness function based on the discrepancy of the projections simulated by the flies with the actual pattern received by the sensors. The reconstructed radioactive concentration is derived from the population of flies, i.e. a collection of points in the 3-D Euclidean space, after convergence. ‘Good’ flies were previously binned into voxels. In this paper, we study which flies to include in the final solution and how this information can be sampled to provide more accurate datasets in a reduced computation time. We investigate the use of density fields, based on Metaballs and on Gaussian functions respectively, to obtain a realistic output. The spread of each Gaussian kernel is modulated in function of the corresponding fly fitness. The resulting volumes are compared with previous work in terms of normalised-cross correlation. In our test-cases, data fidelity increases by more than 10% when density fields are used instead of binning. Our method also provides reconstructions comparable to those obtained using well-established techniques used in medicine (filtered back-projection and ordered subset expectation-maximisation). [ABSTRACT FROM AUTHOR]

In optoacoustic tomography, detectors with relatively large areas are often employed to achieve high detection sensitivity. However, spatial-averaging effects over large detector areas may lead to attenuation of high acoustic frequencies and, subsequently, loss of fine features in the reconstructed image. Model-based reconstruction algorithms improve image resolution in such cases by correcting for the effect of the detector's aperture on the detected signals. However, the incorporation of the detector's geometry in the optoacoustic model leads to a significant increase of the model matrix memory cost, which hinders the application of inversion and analysis tools such as singular value decomposition (SVD). We demonstrate the use of the wavelet-packet framework for optoacoustic systems with finite-aperture detectors. The decomposition of the model matrix in the wavelet-packet domain leads to sufficiently smaller model matrices on which SVD may be applied. Using this methodology over an order of magnitude reduction in inversion time is demonstrated for numerically generated and experimental data. Additionally, our framework is demonstrated for the analysis of inversion stability and reveals a new, nonmonotonic dependency of the system condition number on the detector size. Thus, the proposed framework may assist in choosing the optimal detector size in future optoacoustic systems. [ABSTRACT FROM AUTHOR]

A new method of near-field electromagnetic holography of subsurface dielectric targets is developed and studied in experiments with the multifrequency microwave system. It is based on the solution of the near-field inverse scattering problem obtained by data of multifrequency measurements of the two-dimensional (2-D) scattered field distribution with the source–receiver system that is located above the surface of a medium with buried dielectric targets. The solution, obtained initially in the lateral k-space representation, can be used to derive tomograms of distributed inhomogeneities or to determine the geometric shape of solid targets with sharp boundaries for further visualization as holography images with a subwavelength resolution. Such a holography method is studied in detail, including the formation of scattered field and signal for various samples in various media, achievable resolution, and effects of multiple scattering. [ABSTRACT FROM PUBLISHER]

Electrical resistance tomography (ERT) and electrical capacitance tomography (ECT) are two established process tomography techniques that can be applied into various indsutries. ERT can monitor the electrical conductivity changes in the process whereas ECT can detect the electrical dielectric materials. Due to their high-speed and low cost features, they are particularly attractive to industrial applications which require real time conditional monitoring. For the past decades, 2D linear back projection (LBP) has been the standard technique for both commercialised ERT and ECT systems because of its simplicity and fast reconstruction speed. In this paper, ITS Plc has released a 'Reconstruction Tool-Suite' software that allows industrial users to utilise different reconstruction algorithms to further understand their processes. Different algorithms are integrated into this software package including the single step Tikhonov method and the iterative Landweber method. In the latest version of the software, the full-field 3D tomography reconstruction scheme is also included, which allows the users to perform 3D reconstruction for their processes. A series of experiments are conducted to validate the pros and cons of different methods. [ABSTRACT FROM AUTHOR]

We consider the problem of constructing a penalty function associated with a given monotone function. We provide a construction that allows the monotone function to be discontinuous or bounded. We show that, although the penalty may be non-convex, it is weakly convex. We briefly discuss the implications for iterative solutions of linear inverse problems. [ABSTRACT FROM AUTHOR]

Single-photon avalanche diodes (SPADs) can be integrated into large pixel arrays. The aim of this paper is to present a view on how these imagers change the paradigm of wide-field near-infrared imaging (NIRI). Thanks to the large number of pixels that they offer and to their advanced time-resolved measurement capabilities, new approaches in the image reconstruction can be applied. A SPAD imager was integrated in a NIRI setup to demonstrate how it can improve spatial resolution in reconstructed images. The SPAD imager has a time resolution of 97 ps and a picosecond laser source with an average output power of 3 mW was employed. The large amount of data produced by this new setup could not directly be analyzed with state-of-the art image reconstruction algorithms. Therefore a new theoretical framework was developed. Simulations show that millimetric resolution is achievable with this setup. Experimental results have demonstrated that a resolution of at least 5 mm is possible with the current setup. A discussion about how different characteristics of the SPAD imagers affect the NIRI measurements is presented and possible future improvements are introduced. [ABSTRACT FROM PUBLISHER]

This communication investigates a bi-static scattering measurement system for mm-Wave imaging purposes in the W-band (75–110 GHz). The main benefit of using millimeter waves is the high resolution provided by short wavelengths (2.7 to 4 mm). The specific interest in the W-band stems from the increasing number of applications. The system provides multi-frequency, multi-view (multiple receiver positions) data at a single incidence, as the emitter is fixed. In the context of future imaging applications, we seek high accuracy in the measurements. For this, we compare the experimental results obtained from two PEC cylinders with the analytic solution. Raw measurement data have been calibrated during post-processing in order to account for misalignment errors and noise of the measurement system. Therefore the large cylinder is used as the reference target for deriving the calibration coefficients and the small cylinder is used as a test object. Averaged values of the signal-to-noise ratio over the W-band are 15.5 dB and 10 dB for the large and the small cylinder, respectively. Measurement results are used for the first time in W-band for quantitative imaging. [ABSTRACT FROM PUBLISHER]

Compressed sensing can substantially reduce the number of samples required for conventional signal acquisition at the expense of an additional reconstruction procedure. It also provides robust reconstruction when using quantized measurements, including in the one-bit setting. In this paper, our goal is to design a framework for binary compressed sensing that is adapted to images. Accordingly, we propose an acquisition and reconstruction approach that complies with the high dimensionality of image data and that provides reconstructions of satisfactory visual quality. Our forward model describes data acquisition and follows physical principles. It entails a series of random convolutions performed optically followed by sampling and binary thresholding. The binary samples that are obtained can be either measured or ignored according to predefined functions. Based on these measurements, we then express our reconstruction problem as the minimization of a compound convex cost that enforces the consistency of the solution with the available binary data under total-variation regularization. Finally, we derive an efficient reconstruction algorithm relying on convex-optimization principles. We conduct several experiments on standard images and demonstrate the practical interest of our approach. [ABSTRACT FROM AUTHOR]

A novel inverse fast multipole method (FMM) application for accelerating inverse problem solution is presented. The idea is based on the multipole expansion properties of the scattered fields and reconstructed equivalent currents, which allow an easy inversion of the FMM operators, resulting in a forward solution of the inverse problem, i.e., without matrix inversion or cost function minimization. In addition, this technique allows the use of reconstruction domain discretization larger than half a wavelength and overcomes the restriction of having the entire target enclosed by a reconstruction domain, features that also contribute to the reduction of calculation time. Two 3D application examples are presented, highlighting the achieved inverse FMM speed-up with respect to previous inverse scattering methods for geometry reconstruction. [ABSTRACT FROM PUBLISHER]

In fluorescence molecular tomography, the highly scattering property of biological tissues leads to an ill-posed inverse problem and reduces the accuracy of detection and localization of fluorescent targets. Regularization technique is usually utilized to obtain a stable solution. Conventional Tikhonov regularization is based on singular value decomposition (SVD) and L-curve strategy, which attempts to find a tradeoff between the residual norm and image norm. It is computationally demanding and may fail when there is no optimal turning point in the L-curve plot. In this letter, a neighborhood regularization method is presented. It achieves a reliable solution by computing the geometric mean of multiple regularized solutions. These solutions correspond to different regularization parameters with neighbor orders of magnitude. The main advantages lie in three aspects. First, it can produce comparable or better results in comparison with the conventional Tikhonov regularization with L-curve routine. Second, it replaces the time-consuming SVD computation with a trace-based pseudoinverse strategy, thus greatly reducing the computational cost. Third, it is robust and practical even when the L-curve technique fails. Results from numerical and phantom experiments demonstrate that the proposed method is easy to implement and effective in improving the quality of reconstruction. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a simple and robust algorithm for compressive sensing (CS) signal reconstruction based on the weighted median (WM) operator. The proposed approach addresses the reconstruction problem by solving a l0-regularized least absolute deviation (l0-LAD) regression problem with a tunable regularization parameter, being suitable for applications where the underlying contamination follows a statistical model with heavier-than-Gaussian tails. The solution to this regularized LAD regression problem is efficiently computed, under a coordinate descent framework, by an iterative algorithm that comprises two stages. In the first stage, an estimation of the sparse signal is found by recasting the reconstruction problem as a parameter location estimation for each entry in the sparse vector leading to the minimization of a sum of weighted absolute deviations. The solution to this one-dimensional minimization problem turns out to be the WM operator acting on a shifted-and-scaled version of the measurement samples with weights taken from the entries in the measurement matrix. The resultant estimated value is then passed to a second stage that identifies whether the corresponding entry is relevant or not. This stage is achieved by a hard threshold operator with adaptable thresholding parameter that is suitably tuned as the algorithm progresses. This two-stage operation, WM operator followed by a hard threshold operator, adds the desired robustness to the estimation of the sparse signal and, at the same time, ensures the sparsity of the solution. Extensive simulations demonstrate the reconstruction capability of the proposed approach under different noise models. We compare the performance of the proposed approach to those yielded by state-of-the-art CS reconstruction algorithms showing that our approach achieves a better performance for different noise distributions. In particular, as the distribution tails become heavier the performance gain achieved by the proposed approach increases significantly. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an one-dimensional inverse problem in diffusion based optical tomography using iteratively regularized Gauss–Newton (IRGN) algorithm for ill-posed nonlinear problems. We devise a stable reconstruction algorithm for the inverse problem using iterative regularization with Armijo–Goldstein–Wolf (AGW) type line search strategy. We demonstrate the efficacy of the IRGN combined with AGW by reconstructing the scattering parameter relevant to the inverse problem in optical tomography. [Copyright &y& Elsevier]