This paper is concerned with nonlinear inverse problems where data and solution are vector valued and, moreover, where the solution is assumed to have a sparse expansion with respect to a preassigned frame. We especially focus on such problems where the different components of the solution exhibit a common or so–called joint sparsity pattern. Joint sparsity means here that the measure (typicall...

Standard compressive sensing results state that to exactly recover an s sparse signal in R, one requires O(s·log p) measurements. While this bound is extremely useful in practice, often real world signals are not only sparse, but also exhibit structure in the sparsity pattern. We focus on group-structured patterns in this paper. Under this model, groups of signal coefficients are active (or ina...

At high rate, a sparse signal is optimally encoded through an adaptive strategy that finds and encodes the signal’s representation in the sparsity-inducing basis. This thesis examines how much the distortion rate (D(R)) performance of a nonadaptive encoder, one that is not allowed to explicitly specify the sparsity pattern, can approach that of an adaptive encoder. Two methods are studied: firs...

This paper addresses the discretisation problem for sparse linear systems. Classical methods usually destroy sparsity patterns of continuous-time systems. We develop an optimisation procedure that yields the best approximation to the discrete-time dynamical matrix with a prescribed sparsity pattern and subject to stability and other constraints. By formulating this problem in an adequate manner...

This paper presents a novel ECG signal measuring approach using compressive sensing method. The signal representing sparsity in any orthogonal basis can be well recovered using minimize L1 norm optimization, while satisfying the RIP condition for the measurement matrix  and orthogonal basis . First, based on this theorem, an analysis for evaluating the sparsity of ECG signal in orthogonal bas...

Traditional tensor decompositions such as the CANDECOMP / PARAFAC (CP) and Tucker decompositions yield higher-order principal components that have been used to understand tensor data in areas such as neuroimaging, microscopy, chemometrics, and remote sensing. Sparsity in high-dimensional matrix factorizations and principal components has been well-studied exhibiting many benefits; less attentio...

Medical imaging is a useful technique for disease diagnosis and it has many applications in the medical field. There are several techniques used for medical imaging. Among them compression sensing (CS) technique has been widely accepted because of the low sample requirement and accurate recovery of image. In this paper, a novel adaptive matching pursuit for compressive sensing of blind sparsity...

We demonstrate that the global fields of temperature, humidity, and geopotential heights admit a nearly sparse representation in the wavelet domain, offering a viable path forward to explore new paradigms of sparsity-promoting data assimilation and compressive recovery of land surface-atmospheric states from space. We illustrate this idea using retrieval products of the Atmospheric Infrared Sou...

Phase-retrieval problems of one-dimensional (1D) signals are known to suffer from ambiguity that hampers their recovery from measurements of their Fourier magnitude, even when their support (a region that confines the signal) is known. Here we demonstrate sparsity-based coherent diffraction imaging of 1D objects using extreme-ultraviolet radiation produced from high harmonic generation. Using s...