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4 September 2009 Compressed sensing of autoregressive processes
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Suppose the signal x ∈ Rn is realized by driving a d-sparse signal z ∈ Rn through an arbitrary unknown stable discrete-linear time invariant system H, namely, x(t) = (h * z)(t), where h(·) is the impulse response of the operator H. Is x(·) compressible in the conventional sense of compressed sensing? Namely, can x(t) be reconstructed from sparse set of measurements. For the case when the unknown system H is auto-regressive (i.e. all pole) of a known order it turns out that x can indeed be reconstructed from O(k log(n)) measurements. The main idea is to pass x through a linear time invariant system G and collect O(k log(n)) sequential measurements. The filter G is chosen suitably, namely, its associated Toeplitz matrix satisfies the RIP property. We develop a novel LP optimization algorithm and show that both the unknown filter H and the sparse input z can be reliably estimated. These types of processes arise naturally in Reflection Seismology.
© (2009) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Venkatesh Saligrama and Manqi Zhao "Compressed sensing of autoregressive processes", Proc. SPIE 7446, Wavelets XIII, 744609 (4 September 2009);


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