In digital signal processing, signals are traditionally acquired
according to the Nyquist-Shannon sampling theorem. Based on it, the
information is preserved, if the signal is sampled at a sampling rate that
is at least twice its highest frequency. However, in many applications the
requirements this imposes on the hardware become prohibitive due to the
physical limitations of the analog-to-digital converters for example.
Recently, a new sampling paradigm has emerged under the name of Compressive
Sampling (CS) that allows to alleviate the aforementioned problems by
exploiting prior information of the signal to be sampled. It has been
demonstrated that for certain type of signals it is possible to signicantly
decrease the sampling rate without loss of information. The signals for
which this is possible are called sparse or compressible signals since they
can be represented by only a few conceits in some basis representation. In
this work we consider a so-called Multiple Measurement Vector (MMV) CS
signal model in which a collection of several input vectors are jointly
sparse, i.e., they share the same sparsity pattern such that the positions
of their non-zero elements are constant over time. However, in practical
applications the sparsity pattern might change from time to time.
Therefore, we extend a classical MMV, which we further refer to as MMV with
static support, to a quasi-static MMV where the strictly joint structure of
the static MMV is preserved for some number of vectors only. We demonstrate
that the application of the joint sparse recovery to the quasi-static MMV
lead to a signicant deterioration of the reconstruction performance due to
the model mismatch. Therefore, we propose an approach that allows to rest
estimate the moment of the sparsity pattern change from compressed
measurements themselves, then split the quasi-static MMV into consecutive
static MMVs and solve joint sparse recovery for each of them individually.
The proposed approach is based on the rank estimation of a sliding window
of measurement data with adaptive choice of the window size. Our numerical
results suggest that the proposed approach allows to signicantly improve
reconstruction performance in a wide SNR range.