Detection of time-varying support via rank evolution approach for effective joint sparse recovery

Abstract

Efficient recovery of sparse signals from few linear projections is a primary goal in a number of applications, most notably in a recently-emerged area of compressed sensing. The multiple measurement vector (MMV) joint sparse recovery is an extension of the single vector sparse recovery problem to the case when a set of consequent measurements share the same support. In this contribution we consider a modification of the MMV problem where the signal support can change from one block of data to another and the moment of change is not known in advance. We propose an approach for the support change detection based on the sequential rank estimation of a windowed block of the measurement data. We show that under certain conditions it allows for an unambiguous determination of the moment of change, provided that the consequent data vectors are incoherent to each other

Frequency Subsampling of Ultrasound Nondestructive Measurements: Acquisition, Reconstruction, and Performance

“…• The problem of estimating the model order s max to set n f before carrying out the reconstruction is hard to overcome in a CS setting. There is a large literature on sparsity order estimation with various advantages and drawbacks, see [46], [47], [48], [49]. Often a satisfactory method for model order selection depends very much on the specific applications' side constraints.…”

Estimating Sparsity Level for Enabling Compressive Sensing of Wireless Channels and Spectra in 5G and Beyond

“…Another source of inferring the sparsity level is linking it to signal rank estimation. Examples include the multiple mea-surement vector problem [21], in stationary environments [22] and block-stationary signals [23]. However, these approaches assume stationarity in the support and temporal variations of the sparse representation coefficients which are not necessarily valid.…”

Sparsity Order Estimation From a Single Compressed Observation Vector

“…A link between sparsity order estimation and rank estimation was put forward in [22] for the multiple measurement vector (MMV) problem, which we have also studied in our own prior work, both for the stationary case [9], [11] as well as the case of time-varying support for block-stationary signals [10]. However, these approaches require a certain stationarity in the support patterns as well as a temporal variation in the coefficients of the sparse representation to create linearly independent observations.…”