Recently, it has been shown that incoherence is an unrealistic assumption for compressed sensing when applied to infinite-dimensional inverse problems. Instead, the key property that permits efficient recovery in such problems is so-called asymptotic incoherence. The purpose of this paper is to study this new concept, and its implications towards the design of optimal sampling strategies. In pa...

Random equivalent sampling (RES) can composite a waveform with high equivalent sampling rate from multiple low speed sampling sequences. In practical application, the performance of RES signal reconstruction would be degraded by the non-uniform distribution of sampling time. Compressed sensing (CS) theory is adopted to reconstruct RES samples, which could mitigate the inherent coherence of samp...

Many of the applications of compressed sensing have been based on variable density sampling, where certain sections of the sampling coefficients are sampled more densely. Furthermore, it has been observed that these sampling schemes are dependent not only on sparsity but also on the sparsity structure of the underlying signal. This paper extends the result of (Adcock, Hansen, Poon and Roman, ar...

We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are sparse when multiplied with a discrete Fourier transform matrix. Ultimately, these considerations improve previous sampling requirements for deterministic s...

The extensive use of discrete transforms such as the Discrete Cosine Transform in image and video coding suggests the investigation on ltering before down sampling (FBDS) and ltering after up sampling (FAUS) methods directly acting on the transform domain [1, 2]. On the other hand, Transform Domain Filtering (TDF) was recently introduced as an important tool for implementing linear ltering and ...

Quantized maximum a posteriori (Q-MAP) is a recently-proposed Bayesian compressed sensing algorithm that, given the source distribution, recovers X from its linear measurements Y m = AX, where A ∈ R denotes the known measurement matrix. On the other hand, Lagrangian minimum entropy pursuit (L-MEP) is a universal compressed sensing algorithm that aims at recovering X from its linear measurements...

Compressed sensing theory indicates that selecting a few measurements independently at random is a near optimal strategy to sense sparse or compressible signals. This is infeasible in practice for many acquisition devices that acquire samples along continuous trajectories. Examples include magnetic resonance imaging (MRI), radio-interferometry, mobile-robot sampling, ... In this paper, we propo...

Abstract In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted isometry property of these matrices are given to evaluate their capacity as compressive sensing matrices. In general, compressed sensing requires ran...

We introduce Xampling, a design methodology for sub-Nyquist sampling of continuous-time analog signals. The main principles underlying this framework are the ability to capture a broad signal model, low sampling rate, efficient analog and digital implementation and lowrate baseband processing. The main hypothesis of Xampling is that in order to break through the Nyquist barrier, one has to comb...

We introduce Xampling, a design methodology for sub-Nyquist sampling of continuous-time analog signals. The main principles underlying this framework are the ability to capture a broad signal model, low sampling rate, efficient analog and digital implementation and lowrate baseband processing. The main hypothesis of Xampling is that in order to break through the Nyquist barrier, one has to comb...