Non-convex Compressed Sensing with the Sum-of-Squares Method
نویسندگان
چکیده
We consider stable signal recovery in `q quasi-norm for 0 < q ≤ 1. In this problem, given a measurement vector y = Ax for some unknown signal vector x ∈ R and a known matrix A ∈ Rm×n, we want to recover z ∈ R with ‖x − z‖q = O(‖x − x‖q) from a measurement vector, where x∗ is the s-sparse vector closest to x in `q quasi-norm. Although a small value of q is favorable for measuring the distance to sparse vectors, previous methods for q < 1 involve `q quasi-norm minimization which is computationally intractable. In this paper, we overcome this issue by using the sum-of-squares method, and give the first polynomial-time stable recovery scheme for a large class of matrices A in `q quasi-norm for any fixed constant 0 < q ≤ 1.
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