Publication

Optimization Of Compound Regularization Parameters Based On Stein'S Unbiased Risk Estimate

Xin Liu, Hanjie Pan
2017
Conference Papers

Abstract

Recently, the type of compound regularizers has become a popular choice for signal reconstruction. The estimation quality is generally sensitive to the values of multiple regularization parameters. In this work, based on BDF algorithm, we develop a data-driven optimization scheme based on minimization of Stein's unbiased risk estimate (SURE) statistically equivalent to mean squared error (MSE). We propose a recursive evaluation of SURE to monitor the MSE during BDF iteration; the optimal values of the multiple parameters are then identified by the minimum SURE. Monte-Carlo simulation is applied to compute SURE for large-scale data. We exemplify the proposed method with image deconvolution. Numerical experiments show that the proposed method leads to highly accurate estimates of regularization parameters and nearly optimal restoration performance.

Official source

https://infoscience.epfl.ch/entities/publication/63d17adb-5b95-4f36-9439-e70ccb909e4f

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Xin Liu, Hanjie Pan
2017
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/63d17adb-5b95-4f36-9439-e70ccb909e4f

About this result

Related concepts (32)

Regularization (mathematics)

In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting. Although regularization procedures can be divided in many ways, the following delineation is particularly helpful: Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem.

Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.

Ridge regression

Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also known as Tikhonov regularization, named for Andrey Tikhonov, it is a method of regularization of ill-posed problems. It is particularly useful to mitigate the problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters.

Related publications (32)

Optimization Of Compound Regularization Parameters Based On Stein'S Unbiased Risk Estimate

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