Supplementary Material of “ A Novel Sparsity Measure for Tensor Recovery ”

In this supplementary material, we present details of the algorithms for solving the proposed tensor recovery models with folded-concave relaxations, and present more experimental results. 1. Solving tensor tecovery models with foldedconcave relaxations In the maintext, we have described how to solve the proposed tensor recovery models with the trace norm relaxation. Here, we present the strategy for solving the models with folded-concave relaxations. 1.1. Locally linear approximation for the foldedconcave penalties First, we introduce the idea of the locally linear approximation (LLA) for the folded-concave penalties, which is adopted from [10] and [6]. It is easy to verify that the following result holds: Proposition 1 ([6]) Let f(x) be a concave function on (0,∞). Then f(x) ≤ f(x0) + f (x0)(x− x0), (1) with equality if x = x0. Apply this proposition to the folded-concave penalties, we can get the LLAs for them: ψmcp(t) ≤ ψmcp(t0) + ψ′ mcp(t0)(t− t0) , ψ̂mcp(t|t0), (2) and ψscad(t) ≤ ψscad(t0) +ψ′ scad(t0)(t− t0) , ψ̂scad(t|t0), (3) where ψ′ mcp(t0) = ( λ− t0 a )

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