Adaptive sampling for fast sparsity pattern recovery
2011
In this paper we propose a low complexity adaptive algorithm
for lossless compressive sampling and reconstruction of
sparse signals. Consider a sparse non-negative real signal x
containing only ? << ? non-zero values. The sampling process
obtains ? measurements by a linear projection y = Ax
and, in order to minimize the complexity, we quantize them
to binary values. We also define the measurement matrix A
to be binary and sparse, enabling the use of a simple message
passing algorithm over a graph. We show how to adaptively
construct this matrix in a multi-stage process that sequentially
reduces the search space until the sparsity pattern is
perfectly recovered. As verified by simulation results, the
process requires ?(?) operations and ?(? log(?/?)) samples
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