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            <h1 class="title is-1 publication-title">Domain Expansion via Network Adaptation for Solving Inverse Problems</h1>
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                <a href="mailto: nyism001@ucr.edu" target="_blank">Nebiyou Yismaw</a><sup>1</sup>,</span>
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                  <a href="https://engineering.wustl.edu/faculty/Ulugbek-Kamilov.html" target="_blank">Ulugbek S. Kamilov</a><sup>2</sup>,</span>
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                    <a href="https://intra.ece.ucr.edu/~sasif/" target="_blank">M. Salman Asif</a><sup>1</sup>
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                      <small>1. University of California Riverside</small>
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                      <small>2. Washington University in St. Louis</small>
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        Fig. 1: Artifact removal (AR) networks trained on MRI scans (fastMRI AR) and face images (celebA AR) suffer from performance degradation under domain shifts, resulting in poor reconstruction quality (as indicated by PSNR and SSIM values under each image). Our proposed network (Modulated AR) adapts fastMRI AR for face image reconstruction by learning rank-one factors (modulations). The network stores shared and domain-specific modulations separately. During inference, it applies the correct modulation according to the specified domain. Our proposed network retains the performance of fastMRI AR on MR images and achieves competitive reconstruction quality with celebA AR on face images.
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        <h2 class="title is-3">Abstract</h2>
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            Deep learning-based methods deliver state-of-the-art performance for solving inverse problems that arise in computational imaging. These methods can be broadly divided into two groups: (1) learn a network to map  measurements to the signal estimate, which is known to be fragile; (2) learn a prior for the signal to use in an optimization-based recovery. Despite the impressive results from the latter approach, many of these methods also lack robustness to shifts in data distribution, measurements, and noise levels. Such domain shifts result in a performance gap and in some cases introduce undesired artifacts in the estimated signal. In this paper, we explore the qualitative and quantitative effects of various domain shifts and propose a flexible and parameter efficient framework that  adapt pretrained networks to such shifts. We demonstrate the effectiveness of our method for a number of natural image, MRI, and CT reconstructions tasks under domain, measurement model, and noise-level shifts. Our experiments demonstrate that our method provides significantly better performance and parameter efficiency compared to existing domain adaptation techniques.
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        <h2 class="title is-3"> Impact of Domain Shift</h2>

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              Fig. 2: Examples of image reconstruction under domain shifts. We use two artifact removal (AR) network trained for fastMRI and celebA images in deep unrolled framework. Second and third columns show both images reconstructed with fastMRI AR and celebA AR, respectively. Reconstruction quality degrades with domain shifts (PSNR and SSIM reported under each image). Our proposed network adaptation method, where we adapt celebA AR to recover an MR image (top row) and fastMRI AR to recover a celebA image (bottom row).
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        <h2 class="title is-3">Learning rank-1 factors for domain adaptation</h2>

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                 Fig. 3: Overview of our factorized network that uses modulated convolutions for domain adaptation. Our network follows the DNCNN architecture that leverages modulated convolution for domain adaptation. After trained on the source domain, the network learns low-rank modulations for each domain while keeping the base network parameters frozen. Using a domain identifier, the network selects the appropriate low-rank factors during inference and applies them to the pretrained network through element-wise multiplication.
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        <h2 class="title is-3">Domain, forward model, and noise level adaptation</h2>
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          We performed a number of experiments to analyze the effects of shifts in different parts of the inverse problem.
          The shifts can occur in the data distribution \( \mathbf{x} \), the forward model \( \mathbf{A} \), and the measurement
          noise \( \eta \). we start with a fixed base network, which we refer to as Base AR, and learn domain-specific rank-one modulations.
          Base AR is trained to reconstruct MR images from \( 4\times\) radially sub-sampled Fourier measurements without any measurement noise.
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          Fig. 4: Sample ground truth images in the first column and reconstruction of these images using three AR networks trained on Face, MR, and CT images in the subsequent three columns .
          Our modulated AR, shown in the last column effectively removes this artifacts and closes the performance gap.
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          Fig. 5:  Reconstruction results under sampling pattern shifts. AR trained on radial pattern performs poorly when tested on Cartesian sampled patterns. Our Modulated AR applies low-rank modulations to adapt Radial AR to Cartesian samples.
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         Fig. 6:  Examples of image reconstruction under sampling ratio shifts. Our Modulated AR shows an average superior performance when compared to the 4×, 8×, and 10× AR networks.
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      <h2 class="title is-4">Noise level shift adaptation</h2>
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        Fig. 7: Visual results of models trained at specific noise levels and our modulated network under measurement level. The last row shows the $20\times$amplified residual of the reconstructed image under no measurement noise.
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      <pre><code>@misc{yismaw2023domain,
      title={Domain Expansion via Network Adaptation for Solving Inverse Problems},
      author={Nebiyou Yismaw and Ulugbek S. Kamilov and M. Salman Asif},
      year={2023},
      eprint={2310.06235},
      archivePrefix={arXiv},
      primaryClass={eess.IV}
}</code></pre>
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