In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable to natural non-Gaussian distributions without further assumptions, as can be demonstrated by simple counter-examples involving extremely sparse signals. We s...

Compressive hyperspectral imaging is based on the fact that hyperspectral data is highly redundant. However, there is no symmetry between the compressibility of the spatial and spectral domains, and that should be taken into account for optimal compressive hyperspectral imaging system design. Here we present a study of the influence of the ratio between the compression in the spatial and spectr...

The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this literature, the structure is represented by sparsity in a well-chosen basis. We show how to achieve guarantees similar to standard compressed sensing but without emp...

Abstract. A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani and Sochen. In this paper, we first revisit closed formulae of the finite split oscillator dictionary S by a simple proof. Then we study the non-split tori of the group SL(2, Fp). Finally, An explicit algorithm for computing the finite non...

We proposed a weighted l minimization: min , ‖x‖ + λ‖f‖ s.t.Ax+ f= b to recover a sparse vector x and the corrupted noise vector f from a linear measurement b = Ax + f when the sensing matrix A is an m × n row i.i.d subgaussian matrix. Our first result shows that the recovery is possible when the fraction of corrupted noise is smaller than a positive constant, provided that ‖x‖ ≤ O(n/ln (n/‖x ∗...

We develop methods to efficiently reconstruct the topology and line parameters of a power grid from the measurement of nodal variables. We propose two compressed sensing algorithms that minimize the amount of necessary measurement resources by exploiting network sparsity, symmetry of connections and potential prior knowledge about the connectivity. The algorithms are reciprocal to established s...

Endogenous Sparse Recovery

Compressed sensing is the theory and practice of subNyquist sampling of sparse signals of interest. Perfect reconstruction may then be possible with significantly fewer than the Nyquist required number of data. In this work, we consider a video system where acquisition is performed via framewise pure compressed sensing. The burden of quality video sequence reconstruction falls, then, solely on ...

The central idea of compressed sensing is to exploit the fact that most signals of interest are sparse in some domain and use this to reduce the number of measurements to encode. However, if the sparsity of the input signal is not precisely known, but known to lie within a specified range, compressed sensing as such cannot exploit this fact and would need to use the same number of measurements ...

Currently many types of microscopy are limited, in terms of spatial and temporal resolution, by hardware (e.g., camera framerate, data transfer rate, data storage capacity). The obvious approach to solve the resolution problem is to develop better hardware. An alternative solution, which additionally benefits from improved hardware, is to apply compressive sensing (CS) [1]. CS approaches have b...