Title :
On identifiability in bilinear inverse problems
Author :
Choudhary, Shobhit ; Mitra, U.
Author_Institution :
Ming Hsieh Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA
Abstract :
This paper considers identifiability and recoverability in bilinear inverse problems which is relevant to blind deconvolution and matrix factorization. It is shown that bilinear inverse problems can be posed as rank-1 matrix recovery problems subject to linear constraints. Sufficient conditions for identifiability are developed for the cases when rank-2 matrices are present in the null space of the linear operator. Signal recovery using the nuclear norm heuristic for rank-1 matrix recovery is considered and simple conditions for success are provided.
Keywords :
deconvolution; inverse problems; matrix decomposition; signal restoration; bilinear inverse problem; blind deconvolution; linear operator; matrix factorization; nuclear norm heuristic; rank-1 matrix recovery problem; rank-2 matrices; signal recovery; Deconvolution; Linear matrix inequalities; Null space; Sparse matrices; Standards; Vectors; bilinear inverse problems; identifiability; matrix recovery;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on
Conference_Location :
Vancouver, BC
DOI :
10.1109/ICASSP.2013.6638476
