کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4628454 | 1631830 | 2013 | 16 صفحه PDF | دانلود رایگان |
The uniqueness of sparsest solutions of underdetermined linear systems plays a fundamental role in compressed sensing theory. Several new algebraic concepts, including the sub-mutual coherence, scaled mutual coherence, coherence rank, and sub-coherence rank, are introduced in this paper in order to develop new and improved sufficient conditions for the uniqueness of sparsest solutions. The coherence rank of a matrix with normalized columns is the maximum number of absolute entries in a row of its Gram matrix that are equal to the mutual coherence. The main result of this paper claims that when the coherence rank of a matrix is low, the mutual-coherence-based uniqueness conditions for the sparsest solution of a linear system can be improved. Furthermore, we prove that the Babel-function-based uniqueness can be also improved by the so-called sub-Babel function. Moreover, we show that the scaled-coherence-based uniqueness conditions can be developed, and that the right-hand-side vector b of a linear system, the support overlap of solutions, and the range property of a transposed matrix can be also integrated into the criteria for the uniqueness of the sparsest solution of an underdetermined linear system.
Journal: Applied Mathematics and Computation - Volume 224, 1 November 2013, Pages 58–73