arXiv subjects

Saman Khoramian

Publications and source records attributed to Saman Khoramian.

3 recordsLinked to original sources

arXiv2023

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

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

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arXiv2022

Generalizations of the Hilbert-Weierstrass Theorem and Tonelli-Morrey Theorem: the Regularity of Solutions of Differential Equations and Optimal Control Problems

Two Theorems attributed to Hilbert-Weierstrass and Tonelli-Morrey respectively are two classical studies for the regularity discussion around the solutions of some problems in the realm of Calculus of Variations. Now, since differential equations and optimal control problems with high-order have been growing in the literature, addressing the regularity issues for these problems should be paid more attention. In this regard, here, a generalization for the regularity theorems will be presented. It is desired that these theorems will be useful for researchers to prove the regularity properties of differential equations or optimal control problems.

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arXiv2019

An iterative thresholding algorithm for linear inverse problems with mixed multi-constraints and its applications

In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved. In this regard, we will conclude the findings of many papers (most of which are on image processing) from this generalization. It is hoped that the approach proposed in this paper will be a suitable reference for some applied works where multi-frames, multi-wavelets, or multi-constraints are present in linear inverse problems.

math.OC↗