Related papers: Average Case Recovery Analysis of Tomographic Comp…
This paper tackles algorithmic and theoretical aspects of dictionary learning from incomplete and random block-wise image measurements and the performance of the adaptive dictionary for sparse image recovery. This problem is related to…
Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…
In x-ray computed tomography (CT) it is generally acknowledged that reconstruction methods exploiting image sparsity allow reconstruction from a significantly reduced number of projections. The use of such reconstruction methods is…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
Speeding up the data acquisition is one of the central aims to advance tomographic imaging. On the one hand, this reduces motion artifacts due to undesired movements, and on the other hand this decreases the examination time for the…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
In this paper, we develop a framework to design sensing matrices for compressive sensing applications that lead to good mean squared error (MSE) performance subject to sensing cost constraints. By capitalizing on the MSE of the oracle…
The problem central to sparse recovery and compressive sensing is that of stable sparse recovery: we want a distribution of matrices A in R^{m\times n} such that, for any x \in R^n and with probability at least 2/3 over A, there is an…
Tomography can be used to reveal internal properties of a 3D object using any penetrating wave. Advanced tomographic imaging techniques, however, are vulnerable to both systematic and random errors associated with the experimental…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Compressed sensing (CS) is a valuable technique for reconstructing measurements in numerous domains. CS has not yet gained widespread adoption in scanning tunneling microscopy (STM), despite potentially offering the advantages of lower…
The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…
Magnetic resonance imaging (MRI) is an essential medical tool with inherently slow data acquisition process. Slow acquisition process requires patient to be long time exposed to scanning apparatus. In recent years significant efforts are…
Compressive sensing has been receiving a great deal of interest from researchers in many areas because of its ability in speeding up data acquisition. This framework allows fast signal acquisition and compression when signals are sparse in…
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic…
Many practical sensing applications involve multiple sensors simultaneously acquiring measurements of a single object. Conversely, most existing sparse recovery guarantees in compressed sensing concern only single-sensor acquisition…