The Phase Transition of Matrix Recovery from Gaussian Measurements Matches the Minimax MSE of Matrix Denoising

By Gavish Matan, Donoho David, and Montanari Andrea
Working Paper Stanford University (2013)

  • Matan Gavish

    Stanford University

    USA

Created

November 5, 2013

Last update

November 5, 2013

Software

Matlab

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83

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3818

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98

Description

The program provided calculates the asymptotic minimax MSE, and the asymptotic minimax tuning threshold, of matrix denoising by Singular Value Thresholding: lim_{N->\infty} inf_lambda sup_{rank(X)<= M*rho} MSE ||Xhat_lambda - X||^2_F /MN ... Here: (*) Xhat_lambda is the Singular Value Thresholding denoiser (applying soft thresholding with threshold lambda to each singular value of the data) (*) rho is the asymptotic rank fraction (*) M/N -> beta (the asymptotic aspect ratio) (*) X is an M-by-N matrix, M<=N (*) ||.||_F denotes the Frobenius matrix norm (sum of squares of matrix entries)

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