  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.
