<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-information-and-optimization-sciences</journal-id>
      <journal-title-group>
        <journal-title>Journal of Information and Optimization Sciences</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0103</issn>
      <issn publication-format="print">0252-2667</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIOS-2234</article-id>
      <title-group>
        <article-title>Secure and optimized ViT–Trans GAN architecture: A mathematical modeling approach for encrypted MRI brain image reconstruction</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Sharma</surname>
            <given-names>Priyanka</given-names>
          </name>
          <aff>Department of Computer Science and Engineering, Poornima University, Jaipur, Rajasthan, 303905, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Keswani</surname>
            <given-names>Bright</given-names>
          </name>
          <aff>Department of Computer Science and Engineering, Poornima University, Jaipur, Rajasthan, 303905, India</aff>
        </contrib>
      </contrib-group>
      <volume>47</volume>
      <issue>8</issue>
      <fpage>2917</fpage>
      <lpage>2929</lpage>
      <pub-date date-type="pub">
        <day>31</day>
        <month>08</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>The growing use of Magnetic Resonance Imaging (MRI) in brain disorder diagnosis requires reliable methods for both data security and image quality preservation during transmission and storage. To address these challenges, this study proposes a secure image reconstruction framework based on a hybrid Vision Transformer and TransGAN (ViT–TransGAN) model for encrypted MRI brain images. The proposed architecture exploits the long-range dependency learning capability of Vision Transformers along with the generative strength of TransGAN to effectively recover meaningful structural details from encrypted inputs. A mathematical formulation is employed to represent the encryption process, reconstruction mechanism, and optimization objectives, contributing to stable model training and improved reconstruction accuracy. The effectiveness of the proposed method is validated using standard MRI brain datasets, and its performance is compared with existing convolutional neural network and GAN-based approaches. Experimental results demonstrate noticeable improvements in reconstruction quality measured by It is found that proposed ViT+ TransGAN achieves 11.74 of MSE, 40.09 of PSNR, 0.7774 of SSIM, 0.167 of FSIM, -0.9657 of NRMSE, 0.9181 of VIF, 0.8846 of DSC for degradation. Moreover, 13.04 of MSE, 37.20 of PSNR, 0.8691 of SSIM, 0.164 of FSIM, -1.4517 of NRMSE, 0.9642 of VIF and 0.8815 of DSC for reconstructiona.</p>
      </abstract>
      <kwd-group>
        <kwd>Vision transformer</kwd>
        <kwd>Generator</kwd>
        <kwd>Discriminator</kwd>
        <kwd>Reconstruction</kwd>
        <kwd>Degradation</kwd>
        <kwd>Noise</kwd>
        <kwd>Gaussian</kwd>
        <kwd>Artefacts</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>
