Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement Vectors

While single measurement vector (SMV) models have been widely studied in signal processing, there is a surging interest in addressing the multiple measurement vectors (MMV) problem. In the MMV setting, more than one measurement vector is available and the multiple signals to be recovered share some commonalities such as a common support. Applications in which MMV is a naturally occurring phenomenon include online streaming, medical imaging, and video recovery. This work presents a stochastic iterative algorithm for the support recovery of jointly sparse corrupted MMV. We present a variant of the Sparse Randomized Kaczmarz algorithm for corrupted MMV and compare our proposed method with an existing Kaczmarz type algorithm for MMV problems. We also showcase the usefulness of our approach in the online (streaming) setting and provide empirical evidence that suggests the robustness of the proposed method to the distribution of the corruption and the number of corruptions occurring.Comment: 13 pages, 6 figure

Method for coregistration of optical measurements of breast tissue with histopathology : the importance of accounting for tissue deformations

For the validation of optical diagnostic technologies, experimental results need to be benchmarked against the gold standard. Currently, the gold standard for tissue characterization is assessment of hematoxylin and eosin (H&E)-stained sections by a pathologist. When processing tissue into H&E sections, the shape of the tissue deforms with respect to the initial shape when it was optically measured. We demonstrate the importance of accounting for these tissue deformations when correlating optical measurement with routinely acquired histopathology. We propose a method to register the tissue in the H&E sections to the optical measurements, which corrects for these tissue deformations. We compare the registered H&E sections to H&E sections that were registered with an algorithm that does not account for tissue deformations by evaluating both the shape and the composition of the tissue and using microcomputer tomography data as an independent measure. The proposed method, which did account for tissue deformations, was more accurate than the method that did not account for tissue deformations. These results emphasize the need for a registration method that accounts for tissue deformations, such as the method presented in this study, which can aid in validating optical techniques for clinical use. (C) The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License

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

Application of the Reduced Basis Method to Hyperspectral Diffuse Optical Tomography

Diffuse optical tomography (DOT), which uses low-energy laser light in the visible to near infrared range, has become a popular alternative to traditional medical imaging techniques such as x-ray, because it is non-ionizing and cost effective. Since DOT is especially effective in reconstructing images of soft tissue, where light penetrates more easily, one of its main applications is in breast cancer detection. Hyperspectral DOT (hyDOT) uses hundreds of optical wavelengths in the imaging process in order to improve the resolution of the image by adding new information. We develop a reduced basis method approach to solve the forward problem in hyDOT, which is to determine the measurements on the boundary of the tissue given information about the light source on the boundary, the location of any tumors, and the values of the absorption and diffusion coefficients. Our work on the forward problem is motivated by the image reconstruction problem in hyDOT which is computationally expensive because any algorithm requires solving the forward problem hundreds, if not thousands, of times. We show how the reduced basis method greatly improves the computational burden of the forward problem and thus, improves the efficiency of the reconstruction problem

Compressed sensing in fluorescence microscopy.

Compressed sensing (CS) is a signal processing approach that solves ill-posed inverse problems, from under-sampled data with respect to the Nyquist criterium. CS exploits sparsity constraints based on the knowledge of prior information, relative to the structure of the object in the spatial or other domains. It is commonly used in image and video compression as well as in scientific and medical applications, including computed tomography and magnetic resonance imaging. In the field of fluorescence microscopy, it has been demonstrated to be valuable for fast and high-resolution imaging, from single-molecule localization, super-resolution to light-sheet microscopy. Furthermore, CS has found remarkable applications in the field of mesoscopic imaging, facilitating the study of small animals' organs and entire organisms. This review article illustrates the working principles of CS, its implementations in optical imaging and discusses several relevant uses of CS in the field of fluorescence imaging from super-resolution microscopy to mesoscopy

Advances in Hyperspectral and Multispectral Optical Spectroscopy and Imaging of Tissue

The purpose of this SI is to provide an overview of recent advances made in the methods used for tissue imaging and characterization, which benefit from using a large range of optical wavelengths. Guerouah et al. has contributed a profound study of the responses of the adult human brain to breath-holding challenges based on hyperspectral near-infrared spectroscopy (hNIRS). Lange et al. contributed a timely and comprehensive review of the features and biomedical and clinical applications of supercontinuum laser sources. Blaney et al. reported the development of a calibration-free hNIRS system that can measure the absolute and broadband absorption and scattering spectra of turbid media. Slooter et al. studied the utility of measuring multiple tissue parameters simultaneously using four optical techniques operating at different wavelengths of light—optical coherence tomography (1300 nm), sidestream darkfield microscopy (530 nm), laser speckle contrast imaging (785 nm), and fluorescence angiography (~800 nm)—in the gastric conduit during esophagectomy. Caredda et al. showed the feasibility of accurately quantifying the oxy- and deoxy-hemoglobin and cytochrome-c-oxidase responses to neuronal activation and obtaining spatial maps of these responses using a setup consisting of a white light source and a hyperspectral or standard RGB camera. It is interest for the developers and potential users of clinical brain and tissue optical monitors, and for researchers studying brain physiology and functional brain activity

Deep-tissue optical imaging of near cellular-sized features

Detection of biological features at the cellular level with sufcient sensitivity in complex tissue remains a major challenge. To appreciate this challenge, this would require fnding tens to hundreds of cells (a 0.1 mm tumor has ~125 cells), out of ~37 trillion cells in the human body. Near-infrared optical imaging holds promise for high-resolution, deep-tissue imaging, but is limited by autofuorescence and scattering. To date, the maximum reported depth using second-window near-infrared (NIR-II: 1000–1700 nm) fuorophores is 3.2 cm through tissue. Here, we design an NIR-II imaging system, “Detection of Optically Luminescent Probes using Hyperspectral and difuse Imaging in Near-infrared” (DOLPHIN), that resolves these challenges. DOLPHIN achieves the following: (i) resolution of probes through up to 8 cm of tissue phantom; (ii) identifcation of spectral and scattering signatures of tissues without a priori knowledge of background or autofuorescence; and (iii) 3D reconstruction of live whole animals. Notably, we demonstrate noninvasive real-time tracking of a 0.1 mm-sized fuorophore through the gastrointestinal tract of a living mouse, which is beyond the detection limit of current imaging modalities.Untied States. National Cancer Institute. Cancer Center Support (Grant P30-CA14051)United States. National Cancer Institute. Center for Cancer Nanotechnology Excellence (Grant 5-U54-CA151884-03

Adaptive Basis Scan by Wavelet Prediction for Single-Pixel Imaging

International audienceSingle pixel camera imaging is an emerging paradigm that allows high-quality images to be provided by a device only equipped with a single point detector. A single pixel camera is an experimental setup able to measure the inner product of the scene under view –the image– with any user-defined pattern. Post-processing a sequence of point measurements obtained with different patterns permits to recover spatial information, as it has been demonstrated by state-of-the art approaches belonging to the compressed sensing framework. In this paper, a new framework for the choice of the patterns is proposed together with a simple and efficient image recovery scheme. Our goal is to overcome the computationally demanding 1-minimization of compressed sensing. We propose to choose patterns among a wavelet basis in an adaptive fashion, which essentially relies onto the prediction of the significant wavelet coefficients' location. More precisely, we adopt a multiresolution strategy that exploits the set of measurements acquired at coarse scales to predict the set of measurements to be performed at a finer scale. Prediction is based on a fast cubic interpolation in the image domain. A general formalism is given so that any kind of wavelets can be used, which enables one to adjust the wavelet to the type of images related to the desired application. Both simulated and experimental results demonstrate the ability of our technique to reconstruct biomedical images with improved quality compared to CS-based recovery. Application to real-time fluorescence imaging of biological tissues could benefit from the proposed method