Fast optimal and suboptimal algorithms for sparse solutions to linear inverse problems
نویسندگان
چکیده
We present two “fast” approaches to the NP-hard problem of computing a maximally sparse approximate solution to linear inverse problems, also known as best subset selection. The first approach, a heuristic, is an iterative algorithm globally convergent to sparse elements of any given convex, compact S C Wmr. We demonstrate its effectiveness in bandlimited extrapolation and in sparse filter design. The second approach is a polynomial-time greedy sequential backward elimination algorithm. We show that if A has full column rank and c is small enough, then the algorithm will find the sparsest x satifying l]Ax bll 5 c. if such exists.
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