Stein unbiased risk estimate as a model selection estimator

Abstract EN

To restore a low-rank structure from a noisy matrix, many recent authors has used and studied truncated singular value decomposition.

So thus, according to these studies, the image can be better estimated by shrinking the singular values as well.

In this paper, we are interested in the performance of the model proposed by Candès (2012) for other thresholding function (Minimax Concave Penalty (MCP)), and under the assumption that the distribution of data matrix Y belongs to an elliptically distribution family which extends the Gaussian case.

Under this distributional context, we propose to apply stein unbiased risk estimate (SURE) improved by S.

Canu and D.

Fourdrinier (2017), in order to select the best thresholding function between MCP and Soft-thresholding, and the optimal shrinking parameter λ from the data Y.

Numerical results reveal that the risk estimate SURE is good, the minima are reached for the same λ (λ∗ =λ ̂= 5218.

4) and the difference between the estimated (SURE) and the usual (Mean Square Error (MSE)) risks is small, and that the risk of MCP is lower than the one of Soft.