The potential of compressive sensing (CS) has spurred great interest in the research community and is a fast growing area of research. However, research translating CS theory into practical hardware and demonstrating clear and significant benefits with this hardware over current, conventional imaging techniques has been limited. This article helps researchers to find those niche applications wh...

When 3-D models of environments need to be transmitted or stored, they should be compressed efficiently to increase the capacity of the communication channel or the storage medium. We propose a novel compression technique based on compressive sensing, applied to sparse representations of 3-D range measurements. We develop a novel algorithm to generate sparse innovations between consecutive rang...

In compressed sensing, one wishes to acquire an approximately sparse high-dimensional signal x ∈ R via m n noisy linear measurements, then later approximately recover x given only those measurement outcomes. Various guarantees have been studied in terms of the notion of approximation in recovery, and some isolated folklore results are known stating that some forms of recovery are stronger than ...

In this paper, we address the theoretical limitations in reconstructing sparse signals (in a known complete basis) using compressed sensing framework. We also divide the CS to non-blind and blind cases. Then, we compute the Bayesian Cramer-Rao bound for estimating the sparse coefficients while the measurement matrix elements are independent zero mean random variables. Simulation results show a ...

images of the two simultaneously excited slices. Displayed are (a) the conventional reconstruction of the CAIPIRINHA acquisition using GRAPPA and (b) the reconstruction of the incoherently undersampled CAIPIRINHA acquisition using the proposed combination of Compressed Sensing and GRAPPA. (c) Difference between a) and b) magnified by a factor of 10. Accelerated Simultaneous Multi-slice Cardiac ...

Synopsis We investigate the feasibility of using 2-D self-navigation for respiratory gating for free-breathing whole-heart 3-D CINE imaging, where respirationinduced cardiac motion may be more easily detected than in commonly used 1-D self-navigation methods. We compare self-navigation images, derived gating signals and resulting 3-D CINE images of the 1-D and 2-D methods and nd that respirator...

In this note, we summarize the results we recently proved in [14] on the theoretical performance guarantees of the decoders ∆p. These decoders rely on ` minimization with p ∈ (0, 1) to recover estimates of sparse and compressible signals from incomplete and inaccurate measurements. Our guarantees generalize the results of [2] and [16] about decoding by `p minimization with p = 1, to the setting...

The goal of sparse recovery is to recover the (approximately) best k-sparse approximation x̂ of an n-dimensional vector x from linear measurements Ax of x. We consider a variant of the problem which takes into account partial knowledge about the signal. In particular, we focus on the scenario where, after the measurements are taken, we are given a set S of size s that is supposed to contain most...

Over the recent years, a new *linear* method for compressing high-dimensional data (e.g., images) has been discovered. For any high-dimensional vector x, its *sketch* is equal to Ax, where A is an m x n matrix (possibly chosen at random). Although typically the sketch length m is much smaller than the number of dimensions n, the sketch contains enough information to recover an *approximation* t...

We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via l1-l1 and l1-l2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruc...