The Proximal Map of the Weighted Mean Absolute Error
Lukas Baumg\"artner, Roland Herzog, Stephan Schmidt, Manuel, Wei{\ss}
TL;DR
This paper develops an efficient algorithm for computing the proximal map of the weighted mean absolute error, enabling improved solutions for image denoising and energy minimization problems.
Contribution
It introduces a novel, vectorized algorithm for the proximal map of the weighted mean absolute error, enhancing computational efficiency in optimization tasks.
Findings
Algorithm is efficient and vectorized.
Applied to total-variation image denoising.
Effective in non-smooth energy minimization.
Abstract
We investigate the proximal map for the weighted mean absolute error function. An algorithm for its efficient and vectorized evaluation is presented. As a demonstration, this algorithm is applied as part of a checkerboard algorithm to solve a total-variation image denoising (ROF) problem as well as a non-smooth energy minimization problem.
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Taxonomy
TopicsImage and Signal Denoising Methods · Sparse and Compressive Sensing Techniques · Photoacoustic and Ultrasonic Imaging