Sparsity and uniqueness for some specific under-determined linear systems

@article{Fuchs2005SparsityAU,
  title={Sparsity and uniqueness for some specific under-determined linear systems},
  author={Jean-Jacques Fuchs},
  journal={Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.},
  year={2005},
  volume={5},
  pages={v/729-v/732 Vol. 5}
}
The paper extends some results on sparse representations of signals in redundant bases developed for arbitrary bases to two frequently encountered bases. The general problem is the following: given an n/spl times/m matrix, A, with m>n, and a vector, b=Ax/sub 0/, with x/sub 0/ having q<n nonzero components, find sufficient conditions for x/sub 0/ to be the unique sparsest solution to Ax=Ax/sub 0/. The answer gives an upper-bound on q depending upon A. We consider the cases where A is a… CONTINUE READING
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