<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-interdisciplinary-mathematics</journal-id>
      <journal-title-group>
        <journal-title>Journal of Interdisciplinary Mathematics</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-012X</issn>
      <issn publication-format="print">0972-0502</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIM-2270</article-id>
      <title-group>
        <article-title>Solving linear inverse problem via mixture regularization</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Kittisuwan</surname>
            <given-names>P.</given-names>
          </name>
          <aff>Department of Telecommunication Engineering, Faculty of Engineering, Rajamangala University of Technology Rattanakosin, Nakhon Pathom, 73000, Thailand</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Siwapornanan</surname>
            <given-names>C.</given-names>
          </name>
          <aff>Department of Applied Science, Faculty of Science and Technology, Rajamangala University of Technology Rattanakosin, Nakhon Pathom, 73000, Thailand</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Akkaraekthalin</surname>
            <given-names>P.</given-names>
          </name>
          <aff>Department of Electrical and Computer Engineering, Faculty of Engineering, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>5</issue>
      <fpage>2045</fpage>
      <lpage>2057</lpage>
      <pub-date date-type="pub">
        <day>27</day>
        <month>08</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>The iterative shrinkage/thresholding algorithm (ISTA) with the regularizer gives good efficiency to solve the linear inverse problem. In fact, the maximum a posteriori (MAP) estimator with the probability density function (PDF) and ISTA with the regularizer are similar, and we imply that PDF is similar to the regularizer. In general cases, the mixture PDF created from many ordinary PDFs gives better efficiency than the ordinary PDF. Consequently, we present the simple method based on the linear combination of various ordinary regularizers to create the mixture regularizer, and also present the simple-mixture regularizer for ISTA to solve the linear inverse problem. Experimental results of the generated and real signals show that our method outperforms the state-of-the-art methods.</p>
      </abstract>
      <kwd-group>
        <kwd>Linear inverse problem</kwd>
        <kwd>Linear combination</kwd>
        <kwd>Non-convex regularizer (penalty function)</kwd>
        <kwd>Iterative shrinkage/thresholding algorithm (ISTA)</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
