Joint recovery algorithms using difference of innovations for distributed compressed sensing

Distributed compressed sensing is concerned with representing an ensemble of jointly sparse signals using as few linear measurements as possible. Two novel joint reconstruction algorithms for distributed compressed sensing are presented in this paper. These algorithms are based on the idea of using one of the signals as side information; this allows to exploit joint sparsity in a more effective way with respect to existing schemes. They provide gains in reconstruction quality, especially when the nodes acquire few measurements, so that the system is able to operate with fewer measurements than is required by other existing schemes. We show that the algorithms achieve better performance with respect to the state-of-the-art.Comment: Conference Record of the Forty Seventh Asilomar Conference on Signals, Systems and Computers (ASILOMAR), 201

Signal Recovery in Perturbed Fourier Compressed Sensing

In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of measurements. However due to system calibration errors, the system may measure the Fourier transform at frequencies $\{u_i + \delta_i\}_{i=1}^M$ that are different from the base frequencies and where $\{\delta_i\}_{i=1}^M$ are unknown. Ignoring perturbations of this nature can lead to major errors in signal recovery. In this paper, we present a simple but effective alternating minimization algorithm to recover the perturbations in the frequencies \emph{in situ} with the signal, which we assume is sparse or compressible in some known basis. In many cases, the perturbations $\{\delta_i\}_{i=1}^M$ can be expressed in terms of a small number of unique parameters $P \ll M$. We demonstrate that in such cases, the method leads to excellent quality results that are several times better than baseline algorithms (which are based on existing off-grid methods in the recent literature on direction of arrival (DOA) estimation, modified to suit the computational problem in this paper). Our results are also robust to noise in the measurement values. We also provide theoretical results for (1) the convergence of our algorithm, and (2) the uniqueness of its solution under some restrictions.Comment: New theortical results about uniqueness and convergence now included. More challenging experiments now include