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The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is…
Sparse support recovery (SSR) is an important part of the compressive sensing (CS). Most of the current SSR methods are with the full information measurements. But in practice the amplitude part of the measurements may be seriously…
Compressed sensing (CS) theory considers the restricted isometry property (RIP) as a sufficient condition for measurement matrix which guarantees the recovery of any sparse signal from its compressed measurements. The RIP condition also…
Compressed sensing (CS) demonstrates that sparse signals can be recovered from underdetermined linear measurements. We focus on the joint sparse recovery problem where multiple signals share the same common sparse support sets, and they are…
Within the Compressive Sensing (CS) paradigm, sparse signals can be reconstructed based on a reduced set of measurements. Reliability of the solution is determined by the uniqueness condition. With its mathematically tractable and feasible…
This paper proposes a compressed sensing (CS) framework for the acquisition and reconstruction of frequency-sparse signals with chaotic dynamical systems. The sparse signal is acting as an excitation term of a discrete-time chaotic system…
We consider the problem of recovering fusion frame sparse signals from incomplete measurements. These signals are composed of a small number of nonzero blocks taken from a family of subspaces. First, we show that, by using a-priori…
Compressed sensing (CS) is a powerful tool for reducing the amount of data to be collected while maintaining high spatial resolution. Such techniques work well in practice and at the same time are supported by solid theory. Standard CS…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear…
This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…
This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…
Compressed sensing (CS) is a promising approach to reduce the number of measurements in photoacoustic tomography (PAT) while preserving high spatial resolution. This allows to increase the measurement speed and to reduce system costs.…
The recently proposed modified-compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on…
Recent breakthrough results in compressive sensing (CS) have established that many high dimensional signals can be accurately recovered from a relatively small number of non-adaptive linear observations, provided that the signals possess a…
With the development of numbers of high resolution data acquisition systems and the global requirement to lower the energy consumption, the development of efficient sensing techniques becomes critical. Recently, Compressed Sampling (CS)…
We consider the problem of recovering a signal $\mathbf{x}^* \in \mathbf{R}^n$, from magnitude-only measurements $y_i = |\left\langle\mathbf{a}_i,\mathbf{x}^*\right\rangle|$ for $i=[m]$. Also called the phase retrieval, this is a…
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random…