QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction

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.