engleski

Sub-Nyquist Sampling in Shift-Invariant Spaces

We introduce a novel framework for acquisition of analog signals by combining compressive sensing (CS) and the shift-invariant (SI) reconstruction procedure. We reinterpret the random demodulator as a system that acquires a linear combination of the samples in the conventional SI setting with the box function as the sampling kernel. The SI samples are recovered by solving the CS optimization problem and subsequently filtered by a correction filter in order to obtain expansion coefficients of the signal. The underlying model is inherently infinite dimensional, but the SI property allows for formulation of the problem within finite- dimensional CS. We provide experimental results of the proposed system at the end of the paper.

B-splines, inverse problems, sampling, sparsity

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