Related papers: Spectral Compressed Sensing via Projected Gradient…
Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…
In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x \in \mathbb{R}^n$ given access to…
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…
Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using…
The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.…
We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter…
This paper concerns dictionary learning, i.e., sparse coding, a fundamental representation learning problem. We show that a subgradient descent algorithm, with random initialization, can provably recover orthogonal dictionaries on a natural…
In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…
An architecture for hardware realization of a system for sparse signal reconstruction is presented. The threshold based reconstruction method is considered, which is further modified in this paper to reduce the system complexity in order to…
Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not…
Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a…
We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…
We consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of…
Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…
Efficient algorithms for the sparse solution of under-determined linear systems $Ax = b$ are known for matrices $A$ satisfying suitable assumptions like the restricted isometry property (RIP). Without such assumptions little is known and…
The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engineering. Whereas classical compressed sensing algorithms do…
The discrete curvelet transform decomposes an image into a set of fundamental components that are distinguished by direction and size as well as a low-frequency representation. The curvelet representation is approximately sparse; thus, it…
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…