QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction
Ishak Ayad, Nicolas Larue, Maï K. Nguyen
TL;DR
This work tackles sparse-view CT reconstruction by formulating it as a regularized inverse problem and introducing QN-Mixer, a second-order unrolling network that integrates a latent BFGS update with a non-local regularizer. The key innovations are a latent space BFGS update to approximate the inverse Hessian, and Incept-Mixer, a non-local regularization block that captures long-range dependencies via a fusion of Inception and MLP-Mixer concepts. Empirical results on the AAPM and DeepLesion datasets show state-of-the-art PSNR and SSIM, improved data efficiency, and faster convergence with significantly fewer unrolled iterations, along with robust performance in OOD and limited-angle scenarios. The approach offers a principled path to faster, more accurate iterative reconstructions in CT, with potential applicability to a broader class of inverse problems, while also highlighting memory considerations and avenues for future expansion to larger Hessians and unsupervised training.
Abstract
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.