Mismatch and resolution in compressive imaging

Highly coherent sensing matrices arise in discretization of continuum problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold as well as in using highly coherent, redundant dictionaries as sparsifying operators. Algorithms (BOMP, BLOOMP) based on techniques of band exclusion and local optimization are proposed to enhance Orthogonal Matching Pursuit (OMP) and deal with such coherent sensing matrices. BOMP and BLOOMP have provably performance guarantee of reconstructing sparse, widely separated objects {\em independent} of the redundancy and have a sparsity constraint and computational cost similar to OMP's. Numerical study demonstrates the effectiveness of BLOOMP for compressed sensing with highly coherent, redundant sensing matrices.Comment: Figure 5 revise

Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization

We present a reconstruction method involving maximum-likelihood expectation maximization (MLEM) to model Poisson noise as applied to fluorescence molecular tomography (FMT). MLEM is initialized with the output from a sparse reconstruction-based approach, which performs truncated singular value decomposition-based preconditioning followed by fast iterative shrinkage-thresholding algorithm (FISTA) to enforce sparsity. The motivation for this approach is that sparsity information could be accounted for within the initialization, while MLEM would accurately model Poisson noise in the FMT system. Simulation experiments show the proposed method significantly improves images qualitatively and quantitatively. The method results in over 20 times faster convergence compared to uniformly initialized MLEM and improves robustness to noise compared to pure sparse reconstruction. We also theoretically justify the ability of the proposed approach to reduce noise in the background region compared to pure sparse reconstruction. Overall, these results provide strong evidence to model Poisson noise in FMT reconstruction and for application of the proposed reconstruction framework to FMT imaging

Sparsity-driven sparse-aperture ultrasound imaging

We propose an image formation algorithm for ultrasound imaging based on sparsity-driven regularization functionals. We consider data collected by synthetic transducer arrays, with the primary motivating application being nondestructive evaluation. Our framework involves the use of a physical optics-based forward model of the observation process; the formulation of an optimization problem for image formation; and the solution of that problem through efficient numerical algorithms. Our sparsity-driven, model-based approach achieves the preservation of physical features while suppressing spurious artifacts. It also provides robust reconstructions in the case of sparse observation apertures. We demonstrate the effectiveness of our imaging strategy on real ultrasound data

Exploiting flow dynamics for super-resolution in contrast-enhanced ultrasound

Ultrasound localization microscopy offers new radiation-free diagnostic tools for vascular imaging deep within the tissue. Sequential localization of echoes returned from inert microbubbles with low-concentration within the bloodstream reveal the vasculature with capillary resolution. Despite its high spatial resolution, low microbubble concentrations dictate the acquisition of tens of thousands of images, over the course of several seconds to tens of seconds, to produce a single super-resolved image. %since each echo is required to be well separated from adjacent microbubbles. Such long acquisition times and stringent constraints on microbubble concentration are undesirable in many clinical scenarios. To address these restrictions, sparsity-based approaches have recently been developed. These methods reduce the total acquisition time dramatically, while maintaining good spatial resolution in settings with considerable microbubble overlap. %Yet, non of the reported methods exploit the fact that microbubbles actually flow within the bloodstream. % to improve recovery. Here, we further improve sparsity-based super-resolution ultrasound imaging by exploiting the inherent flow of microbubbles and utilize their motion kinematics. While doing so, we also provide quantitative measurements of microbubble velocities. Our method relies on simultaneous tracking and super-localization of individual microbubbles in a frame-by-frame manner, and as such, may be suitable for real-time implementation. We demonstrate the effectiveness of the proposed approach on both simulations and {\it in-vivo} contrast enhanced human prostate scans, acquired with a clinically approved scanner.Comment: 11 pages, 9 figure

Convolutional Sparse Kernel Network for Unsupervised Medical Image Analysis

The availability of large-scale annotated image datasets and recent advances in supervised deep learning methods enable the end-to-end derivation of representative image features that can impact a variety of image analysis problems. Such supervised approaches, however, are difficult to implement in the medical domain where large volumes of labelled data are difficult to obtain due to the complexity of manual annotation and inter- and intra-observer variability in label assignment. We propose a new convolutional sparse kernel network (CSKN), which is a hierarchical unsupervised feature learning framework that addresses the challenge of learning representative visual features in medical image analysis domains where there is a lack of annotated training data. Our framework has three contributions: (i) We extend kernel learning to identify and represent invariant features across image sub-patches in an unsupervised manner. (ii) We initialise our kernel learning with a layer-wise pre-training scheme that leverages the sparsity inherent in medical images to extract initial discriminative features. (iii) We adapt a multi-scale spatial pyramid pooling (SPP) framework to capture subtle geometric differences between learned visual features. We evaluated our framework in medical image retrieval and classification on three public datasets. Our results show that our CSKN had better accuracy when compared to other conventional unsupervised methods and comparable accuracy to methods that used state-of-the-art supervised convolutional neural networks (CNNs). Our findings indicate that our unsupervised CSKN provides an opportunity to leverage unannotated big data in medical imaging repositories.Comment: Accepted by Medical Image Analysis (with a new title 'Convolutional Sparse Kernel Network for Unsupervised Medical Image Analysis'). The manuscript is available from following link (https://doi.org/10.1016/j.media.2019.06.005