The Projected GSURE for Automatic Parameter Tuning in Iterative Shrinkage Methods

TL;DR

This paper introduces a novel projected GSURE method for automatic parameter tuning in iterative shrinkage algorithms, improving image deblurring and zooming performance across various degradation operators.

Contribution

It develops a new parameter selection approach using projected GSURE, applicable to any degradation operator, with an efficient greedy scheme for real-time tuning.

Findings

Outperforms conventional parameter selection methods

Handles ill-posed and rectangular degradation operators

Provides extensive empirical validation

Abstract

Linear inverse problems are very common in signal and image processing. Many algorithms that aim at solving such problems include unknown parameters that need tuning. In this work we focus on optimally selecting such parameters in iterative shrinkage methods for image deblurring and image zooming. Our work uses the projected Generalized Stein Unbiased Risk Estimator (GSURE) for determining the threshold value lambda and the iterations number K in these algorithms. The proposed parameter selection is shown to handle any degradation operator, including ill-posed and even rectangular ones. This is achieved by using GSURE on the projected expected error. We further propose an efficient greedy parameter setting scheme, that tunes the parameter while iterating without impairing the resulting deblurring performance. Finally, we provide extensive comparisons to conventional methods for parameter selection, showing the superiority of the use of the projected GSURE.