Using Supervised Learning to Construct the Best Regularization Term and\n the Best Multiresolution Analysis

2020/09/17 by Saman Khoramian, Khoramian, Saman
Computer Science · Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Numerical methods in inverse problems #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2009.08262

openalex publication_date 2020/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By the recent advances in computer technology leading to the invention of\nmore powerful processors, the importance of creating models using data training\nis even greater than ever. Given the significance of this issue, this work\ntries to establish a connection among Machine Learning, Inverse Problems, and\nApplied Harmonic Analysis. Inspired by methods introduced in [12, 17, 22, 30],\nwhich are connections between Wavelet and Inverse Problems, we offer a model\nwith the capability of learning in terms of an application in signal\nprocessing. In order to reach this model, a bi-level optimization problem will\nhave to be faced. For solving this, a sequence of step functions is presented\nthat its convergence to the solution will be proved. Each of these step\nfunctions derives from several constrained optimization problems on\n mathbbRⁿ that will be introduced here.\n

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