Guixian Xu

In this work, we propose a new paradigm of iterative model-based reconstruction algorithms for providing real-time solution for zooming-in and refining a region of interest in medical and clinical tomographic images. This algorithmic framework is tailored for a clinical need in medical imaging practice that after a reconstruction of the full tomographic image, the clinician may believe that some critical parts of the image are not clear enough, and may wish to see clearer these regions of interest. A naive approach (which is highly not recommended) would be to perform the global reconstruction of a higher resolution image, which has two major limitations: first, it is computationally inefficient, and second, the image regularization is still applied globally, which may over-smooth some local regions. Furthermore, if one wishes to fine-tune the regularization parameter for local parts, it would be computationally infeasible in practice for the case of using global reconstruction. Our new iterative approaches for such tasks are based on jointly utilizing the measurement information, efficient up-sampling/down-sampling across image spaces, and locally adjusted image prior for efficient and high-quality post-processing. The numerical results in low-dose X-ray CT image local zoom-in demonstrate the effectiveness of our approach.

We propose a new operator sketching paradigm for designing efficient iterative data-driven reconstruction (IDR) schemes, such as plug-and-play algorithms and deep unrolling networks. These IDR schemes are the state-of-the-art solutions for imaging inverse problems. However, for high-dimensional imaging tasks, such as X-ray CT, PET and MRI imaging, these IDR schemes typically become inefficient in terms of computation, due to the need to compute the high-dimensional forward and adjoint operators multiple times. In this work, we introduce a universal dimensionality reduction framework for accelerating IDR schemes in solving imaging inverse problems, based on leveraging the sketching techniques from stochastic optimization. Using this framework, we derive several accelerated IDR schemes, including the plug-and-play multistage sketched gradient (PnP-MS2G) and sketching-based primal–dual (LSPD and SkLSPD) deep unrolling networks. Meanwhile, to fully accelerate PnP schemes when the denoisers are computationally expensive, we further propose novel stochastic lazy denoising schemes (Lazy-PnP and Lazy-PnP-EQ), leveraging the ProxSkip scheme in optimization and equivariant image denoisers, to significantly enhance the practicality and efficiency of PnP algorithms. We provide theoretical analysis for recovery guarantees of instances of the proposed framework. Our numerical experiments on natural image processing and tomographic image reconstruction demonstrate the remarkable effectiveness of our sketched IDR schemes.

We propose a new operator-sketching paradigm for designing efficient iterative data-driven reconstruction (IDR) schemes, such as plug-and-play algorithms and deep unrolling networks. These IDR schemes are the state-of-the-art solutions for imaging inverse problems. However, for high-dimensional imaging tasks, such as X-ray CT, PET and MRI imaging, these IDR schemes typically become inefficient both in terms of computation, due to the need to compute the high-dimensional forward and adjoint operators multiple times. In this work, we introduce a universal dimensionality reduction framework for accelerating IDR schemes in solving imaging inverse problems, based on leveraging the sketching techniques from stochastic optimization. Using this framework, we derive several accelerated IDR schemes, including the plug-and-play multi-stage sketched gradient (PnP-MS2G) and sketching-based primal-dual (LSPD and Sk-LSPD) deep unrolling networks. Meanwhile, to fully accelerate PnP schemes when the denoisers are computationally expensive, we further propose novel stochastic lazy denoising schemes (Lazy-PnP and Lazy-PnP-EQ), leveraging the ProxSkip scheme in optimization and equivariant image denoisers, to significantly enhance the practicality and efficiency of PnP algorithms. We provide theoretical analysis for recovery guarantees of instances of the proposed framework. Our numerical experiments on natural image processing and tomographic image reconstruction demonstrate the remarkable effectiveness of our sketched IDR schemes.