Bilinear Compressed Sensing Under Known Signs via Convex Programming

被引:3
|
作者
Aghasi, Alireza [1 ]
Ahmed, Ali [2 ]
Hand, Paul [3 ,4 ]
Joshi, Babhru [5 ]
机构
[1] Georgia State Univ, J Mack Robinson Coll Business, Atlanta, GA 30302 USA
[2] ITU, Dept Elect Engn, Lahore 54000, Pakistan
[3] Northeastern Univ, Dept Math, Boston, MA 02115 USA
[4] Northeastern Univ, Khoury Coll Comp Sci, Boston, MA 02115 USA
[5] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z4, Canada
基金
美国国家科学基金会;
关键词
Inverse problems; deconvolution; blind source separation; compressed sensing; optimization; PHASE RETRIEVAL; BLIND DECONVOLUTION; SPARSE; ALGORITHMS; RECOVERY;
D O I
10.1109/TSP.2020.3017929
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
We consider the bilinear inverse problem of recovering two vectors, x is an element of R-L and w is an element of R-L, from their entrywise product. We consider the case where x and w have known signs and are sparse with respect to known dictionaries of size K and N, respectively. Here, K andN may be larger than, smaller than, or equal to L. We introduce l(1)-BranchHull, which is a convex program posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved. Under the assumptions that x and w satisfy a comparable-effective-sparsity condition and are S-1 - and S-2-sparsewith respect to a random dictionary, we present a recovery guarantee in a noisy case. We show that l(1)-BranchHull is robust to small dense noise with high probability if the number of measurements satisfy L >= Omega((S-1 + S-2) log(2) (K + N)). Numerical experiments show that the scaling constant in the theorem is not too large. We also introduce variants of l(1)-BranchHull for the purposes of tolerating noise and outliers, and for the purpose of recovering piecewise constant signals. We provide an ADMM implementation of these variants and show they can extract piecewise constant behavior from real images.
引用
收藏
页码:6366 / 6379
页数:14
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