Minimization of the q-ratio sparsity with 1 < q ≤∞ for signal recovery

Zhou, ZhiyongDepartment of Statistics, Zhejiang University City College, China (författare)

In this paper, we propose a general scale invariant approach for sparse signal recovery via the minimization of the q-ratio sparsity sq(z) = (||z||1 / ||z||q )q/(q-1) with q ∈ [0 , ∞]. The properties of the q-ratio sparsity measure are studied and illustrated with examples. For the proposed q-ratio sparsity minimization problem with 1 < q ≤∞ , we establish a verifiable exact reconstruction condition and derive its concise error bounds in terms of q-ratio constrained minimal singular values (CMSV). From an algorithmic point of view, we recognize that the proposed problem belongs to the nonlinear fractional programming and investigate two kinds of methods for solving it including the parametric methods and the change of variable method. Numerical experiments are conducted to demonstrate the advantageous performance of the proposed approaches over the state-of-the-art sparse recovery methods.

Yu, Jun,1962-Umeå universitet,Institutionen för matematik och matematisk statistik,Mathematical Statistics(Swepub:umu)juyu0002 (författare)
Department of Statistics, Zhejiang University City College, ChinaInstitutionen för matematik och matematisk statistik (creator_code:org_t)

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