2010/08/04 by Nam Yul Yu, Yu, Nam Yul · 2 citations
Computer Science · Engineering · Mathematics · #Blind Source Separation Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1008.0885
openalex publication_date 2010/08/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. This paper studies a K × N partial Fourier measurement matrix for compressed sensing which is deterministically constructed via cyclic difference sets (CDS). Precisely, the matrix is constructed by K rows of the N× N inverse discrete Fourier transform (IDFT) matrix, where each row index is from a (N, K, λ) cyclic difference set. The restricted isometry property (RIP) is statistically studied for the deterministic matrix to guarantee the recovery of sparse signals. A computationally efficient reconstruction algorithm is then proposed from the structure of the matrix. Numerical results show that the reconstruction algorithm presents competitive recovery performance with allowable computational complexity.