Title :
Convolutional Compressed Sensing Using Decimated Sidelnikov Sequences
Author :
Nam Yul Yu ; Lu Gan
Author_Institution :
Dept. of Electr. & Comput. Eng., Lakehead Univ., Thunder Bay, ON, Canada
Abstract :
In many applications of compressed sensing, the data acquisition involves convolution by a filter followed by subsampling. In this letter, we propose to construct a filter with real-valued coefficients by taking the discrete Fourier transform of a decimated binary Sidelnikov sequence. With a random subsampler, we prove that stable recovery can be guaranteed if a signal is sparse in the canonical or the FFT basis. Besides, simulation results also show that if a deterministic subsampler is used, the proposed system can offer similar reconstruction performance as that of a random Gaussian operator for a wide range of signal length.
Keywords :
Gaussian processes; compressed sensing; convolution; data acquisition; discrete Fourier transforms; fast Fourier transforms; signal reconstruction; signal sampling; FFT; convolutional compressed sensing; data acquisition; decimated binary Sidelnikov sequence; deterministic subsampler; discrete Fourier transform; filter construction; random Gaussian operator; real-valued coefficients; signal reconstruction; subsampling; Coherence; Compressed sensing; Convolution; Gallium nitride; Simulation; Sparse matrices; Vectors; Coherence; Sidelnikov sequences; convolutional compressed sensing; restricted isometry property;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2014.2311659