2009/09/15 by Yin Xiang, Xiang, Yin, LianLin Li +3
Computer Science · Engineering · #68P30 #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Microwave Imaging and Scattering Analysis #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.0909.2737
openalex publication_date 2009/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A different compressive sensing framework, convolution with white noise waveform followed by subsampling at fixed (not randomly selected) locations, is studied in this paper. We show that its recoverability for sparse signals depends on the coherence (denoted by mu) between the signal representation and the Fourier basis. In particular, an n-dimensional signal which is S-sparse in such a basis can be recovered with a probability exceeding 1-delta from any fixed m~O(mu2*S*log(n/delta)^(3/2)) output samples of the random convolution.