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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
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<meta name="description" content="Project page of QN-Mixer">
<meta property="og:title" content="QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction" />
<meta property="og:description"
content="Project page of the CVPR 2024 paper QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction" />
<meta property="og:url" content="https://towzeur.github.io/QN-Mixer/" />
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<meta name="keywords" content="QN-Mixer,CVPR,CVPR'24,CVPR 2024,CT,Quasi-Newton,MLP-Mixer,Sparse-View,Reconstruction">
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<title>QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction</title>
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}
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<body>
<section class="hero">
<div class="hero-body">
<div class="container is-max-desktop">
<div class="columns is-centered">
<div class="column has-text-centered">
<h1 class="title is-1 publication-title">QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT
Reconstruction</h1>
<div class="is-size-5 publication-authors">
<!-- Paper authors -->
<span class="author-block">
<a href="https://www.linkedin.com/in/ishak-ayad/" target="_blank">Ishak
Ayad</a><sup>1,2,*</sup></span>
<span class="author-block">
<a href="https://www.linkedin.com/in/nicolas-larue-1750a6159/" target="_blank">Nicolas
Larue</a><sup>1,3,*</sup></span>
<span class="author-block">
<a href="https://perso.etis-lab.fr/nguyen-verger/" target="_blank">Maï K. Nguyen</a><sup>1</sup>
</span>
</div>
<div class="is-size-5 publication-authors">
<span class="author-block"><sup>1</sup> ETIS (UMR 8051), CY Cergy Paris University, ENSEA, CNRS, France</span><br>
<span class="author-block"><sup>2</sup> AGM (UMR 8088), CY Cergy Paris University, CNRS, France</span><br>
<span class="author-block"><sup>3</sup> University of Ljubljana, Slovenia</span><br>
<div id="venue">
IEEE Conference on Computer Vision and Pattern Recognition (<b>CVPR</b>), 2024<br><br>
</div>
<span class="eql-cntrb"><small><sup>*</sup>Indicates Equal Contribution</small></span>
</div>
<div class="column has-text-centered">
<!-- ArXiv abstract Link -->
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<a href="https://arxiv.org/abs/2402.17951" target="_blank"
class="external-link button is-normal is-rounded is-dark">
<span class="icon">
<i class="ai ai-arxiv"></i>
</span>
<span>arXiv</span>
</a>
</span>
<!-- Github link -->
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<a href="https://github.com/ishak96" target="_blank"
class="external-link button is-normal is-rounded is-dark">
<span class="icon">
<i class="fab fa-github"></i>
</span>
<span>Code (coming soon)</span>
</a>
</span>
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</div>
</div>
</div>
</div>
</section>
<!-- Teaser video-->
<section class="hero teaser">
<div class="container is-max-desktop">
<div class="hero-body">
<!-- Your gif here -->
<img src="static/images/recon.gif" alt="teaser" />
<h2 class="subtitle has-text-centered">
Our method outperforms existing approaches and achieves state-of-the-art performance in terms of SSIM and
PSNR,
while reducing the number of unrolling iterations required.
</h2>
</div>
</div>
</section>
<!-- End teaser video -->
<!-- Paper abstract -->
<section class="section hero is-light">
<div class="container is-max-desktop">
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<div class="column is-four-fifths">
<h2 class="title is-3">Abstract</h2>
<div class="content has-text-justified">
<p>
Inverse problems span across diverse fields. In medical contexts, computed tomography (CT) plays a crucial
role in reconstructing a patient's internal structure, presenting challenges due to artifacts caused by
inherently ill-posed inverse problems. Previous research advanced image quality via post-processing and
deep unrolling algorithms but faces challenges, such as extended convergence times with ultra-sparse data.
Despite enhancements, resulting images often show significant artifacts, limiting their effectiveness for
real-world diagnostic applications. We aim to explore deep second-order unrolling algorithms for solving
imaging inverse problems, emphasizing their faster convergence and lower time complexity compared to
common first-order methods like gradient descent. In this paper, we introduce QN-Mixer, an algorithm based
on the quasi-Newton approach. We use learned parameters through the BFGS algorithm and introduce
Incept-Mixer, an efficient neural architecture that serves as a non-local regularization term, capturing
long-range dependencies within images. To address the computational demands typically associated with
quasi-Newton algorithms that require full Hessian matrix computations, we present a memory-efficient
alternative. Our approach intelligently downsamples gradient information, significantly reducing
computational requirements while maintaining performance. The approach is validated through experiments on
the sparse-view CT problem, involving various datasets and scanning protocols, and is compared with
post-processing and deep unrolling state-of-the-art approaches. Our method outperforms existing approaches
and achieves state-of-the-art performance in terms of SSIM and PSNR, all while reducing the number of
unrolling iterations required.
</p>
</div>
</div>
</div>
</div>
</section>
<!-- End paper abstract -->
<!-- Problem -->
<section class="section hero is-small">
<div class="container is-max-desktop">
<div class="hero-body">
<h2 class="title is-3">Sparse-View Reconstruction Challenges</h2>
<div id="teaser_container">
<img src="static/images/sparse_view_ct.png" alt="problem" id="teaser_img" />
<p class="content has-text-justified" id="teaser_p">
Computed tomography (CT) is a widely used imaging modality in medical diagnosis and treatment planning,
delivering intricate anatomical details of the human body with precision. Despite its success, CT is
associated with high radiation doses, which can increase the risk of cancer induction.
Adhering to the ALARA principle (As Low As Reasonably Achievable), the medical community emphasizes
minimizing radiation exposure to the lowest level necessary for accurate diagnosis.
Numerous approaches have been proposed to reduce radiation doses while maintaining image quality.
Among these, sparse-view CT emerges as a promising solution, effectively lowering radiation doses by
subsampling the projection data, often referred to as the sinogram.
Nonetheless, reconstructed images using the well-known Filtered Back Projection (FBP) algorithm suffer from
pronounced streaking artifacts, which can lead to misdiagnosis.
The challenge of effectively reconstructing high-quality CT images from sparse-view data is
gaining increasing attention in both the computer vision and medical imaging communities.
</p>
</div>
</div>
</div>
</div>
</section>
<!-- End method overview -->
<section class="section hero is-light">
<div class="container is-max-desktop">
<div class="hero-body">
<h2 class="title is-3">Proposed method</h2>
<img src="static/images/teaser.png" alt="Proposed method" />
<p class="content has-text-justified">
Reconstructed images using the well-known Filtered Back Projection (FBP) algorithm suffer
from pronounced streaking artifacts.
<ol type="a">
<li>Initial deep learning techniques applied FBP reconstructed images as a post-processing task show
promise in artifact removal and structure preservation but face limitations due to constrained receptive
fields, leading to suboptimal results. However, these methods are computationally efficient.
</li>
<li>Deep unrolling algorithms, such as the RegFormer algorithm, have been introduced as an iterative
reconstruction methods.
However, they face issues such as slow convergence and high computational costs. Consequently, there is a
need to explore more efficient
alternatives due to the difficulties in capturing long-range dependencies and the growing computational
demands of modern neural networks.
</li>
<li>The paper introduces a second-order unrolling network called QN-Mixer, which employs a latent
BFGS algorithm to approximate the inverse Hessian matrix with a deep-net learned regularization term.
It outperforms state-of-the-art methods in terms of quantitative metrics while requiring fewer
iterations than first-order unrolling networks.
</li>
</ol>
</p>
</div>
</div>
</div>
</section>
<!-- Method overview -->
<section class="hero is-small">
<div class="hero-body">
<div class="container is-max-desktop">
<h2 class="title is-3">Methodology</h2>
<!-- Your image here -->
<img src="static/images/overview.png" alt="overview" />
<p class="content has-text-justified">
Our method is a new type of unrolling networks, drawing inspiration from the quasi-Newton method.
The figure above illustrates the QN-Mixer architecture. It approximates the inverse Hessian matrix using a
latent BFGS algorithm and incorporates a non-local regularization term, Incept-Mixer, aimed at capturing
non-local relationships. To address the computational challenges associated with full inverse Hessian matrix
approximation, a latent BFGS algorithm is utilized.
</p>
<div style="display: flex; justify-content: center;">
<img src="static/images/Incept-Mixer-1.png" alt="incept-mixer" style="width: 600px; aspect-ratio:same" />
</div>
<p class="content has-text-justified">
Incept-Mixer bloc is crafted by drawing inspiration from both the multi-layer perceptron mixer and the
inception architecture, leveraging the strengths of each: capturing long-range interactions through the
attention-like mechanism of MLP-Mixer and extracting local invariant features from the inception block.
</p>
</div>
</div>
</div>
</section>
<!-- End method overview -->
<!-- Image carousel -->
<section class="hero is-small is-light">
<div class="hero-body">
<div class="container">
<h2 class="title is-3">Visual Comparison</h2>
<div id="results-carousel" class="carousel results-carousel">
<div class="item">
<!-- Your image here -->
<img src="static/images/visual_aapm.png" alt="AAPM" />
<h2 class="subtitle has-text-centered">
Visual comparison on AAPM. (PSNR/SSIM)
</h2>
</div>
<div class="item">
<!-- Your image here -->
<img src="static/images/visual_aapm_2.png" alt="AAPM" />
<h2 class="subtitle has-text-centered">
Visual comparison on AAPM. (PSNR/SSIM)
</h2>
</div>
<div class="item">
<!-- Your image here -->
<img src="static/images/visual_lesion.png" alt="Deeplesion/">
<h2 class="subtitle has-text-centered">
Visual comparison on Deeplesion. (PSNR/SSIM)
</h2>
</div>
<div class="item">
<!-- Your image here -->
<img src="static/images/visual_lesion_2.png" alt="Deeplesion/">
<h2 class="subtitle has-text-centered">
Visual comparison on Deeplesion. (PSNR/SSIM)
</h2>
</div>
</div>
</div>
</div>
</section>
<!-- End image carousel -->
<!--BibTex citation -->
<section class="section" id="BibTeX">
<div class="container is-max-desktop content">
<h2 class="title">BibTeX</h2>
<pre><code>
@inproceedings{ayad2024,
title={QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction},
author={Ayad, Ishak and Larue, Nicolas and Nguyen, Maï K.},
booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
year={2024},
}
</code></pre>
</div>
</section>
<!--End BibTex citation -->
<!--Acknowledgements-->
<section class="section" id="acknowledgements">
<div class="container is-max-desktop content">
<h2 class="title">Acknowledgements</h2>
<p>
This work was granted access to the HPC resources of IDRIS under the allocation 2021-[AD011012741] / 2022-[AD011013915] provided by
GENCI and supported by DIM Math Innov funding.
</p>
</div>
</section>
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