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Fast and Robust Compressive Sensing Method Using Mixed Hadamard Sensing Matrix

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1 Author(s)
Shishkin, S.L. ; United Technol. Res. Center, East Hartford, CT, USA

The paper presents a novel class of sensing matrix that provides great speed-up of virtually any compressed sensing (CS) algorithm. It combines separable structure and maximal incoherence with any fixed basis. The former enables fast matrix-vector computation which is the most computationally expensive part of most CS algorithms; the latter guarantees a good restricted isometry property bound and high quality of CS recovery. Even greater speed-up is achieved by using Hadamard or Fourier matrixes in the construction. The construction of the sensing matrix is incorporated in a Split Bregman method of total variation minimization. The resulting algorithm is not only much faster than any published CS method; it also demonstrates high quality CS recovery of images with the number of measurements as low as 5% of the number of pixels, in the presence of high measurement noise (up to 20% of measurement standard deviation).

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Emerging and Selected Topics in Circuits and Systems, IEEE Journal on  (Volume:2 ,  Issue: 3 )