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Approximation Theory of Total Variation Minimization for Data Completion

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arxiv 2207.07473 v1 pith:FRKNOUAR submitted 2022-07-15 math.AP cs.NAmath.NAmath.STstat.TH

Approximation Theory of Total Variation Minimization for Data Completion

classification math.AP cs.NAmath.NAmath.STstat.TH
keywords restorationdataerrorminimizationunderlyingapproximationestimateguarantee
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in the framework of compressed sensing, there are few works on the restoration guarantee of the restoration from partial observations. This paper is to analyze the error of TV based restoration from random entrywise samples. In particular, we estimate the error between the underlying original data and the approximate solution that interpolates (or approximates with an error bound depending on the noise level) the given data that has the minimal TV seminorm among all possible solutions. Finally, we further connect the error estimate for the discrete model to the sparse gradient restoration problem and to the approximation to the underlying function from which the underlying true data comes.

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  1. Exponential-Family Tensor Completion via Nonconvex Dual Total-Variation Regularization

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    Introduces nonconvex dual-TV regularizers based on transformed L1 for exponential-family tensor completion and proves error bounds of order O(n3 rt (max sk^2) log / n) that approach minimax rates up to O(max sk^2 / ma...