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Statistical Compressive Sensing of Analog Signals in B-Spline Function Spaces

In this paper, we assume that the observed signal lies in a B-spline function space. B-splines, which belong to the class of functions that generate shift-invariant (SI) subspaces, fit into the compressive sensing framework and provide sparse solutions for various real-world signals. Thus, we propose signal acquisition with the system for sub-Nyquist sampling of sparse signals in SI spaces. Additionally, we assume that SI samples obtained by the proposed system follow a Gaussian distribution, so that we can use the statistical compressive sensing measurement and reconstruction strategy. The proposed setting allows for sampling of sparse signals with a much lower sampling rate in contrast to the high- rate sampling in the standard SI setting ; in addition with efficient linear reconstruction which extremely reduces the computational complexity of signal recovery.

B-splines ; inverse problems ; sampling ; sparsity

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