Efficient Plug-and-Play method for Dynamic Imaging Via Kalman Smoothing

TL;DR

This paper introduces a plug-and-play method combining Kalman smoothing with deep neural network denoisers for dynamic imaging, enhancing efficiency and expressivity in state-space model-based reconstruction.

Contribution

It develops a novel PnP algorithm based on KS-ADMM that integrates deep learning denoisers, improving computational efficiency in dynamic imaging tasks.

Findings

Improved computational efficiency over standard PnP-ADMM for large timesteps

Enhanced expressivity by integrating deep neural network denoisers

Effective in 2D+t imaging simulations

Abstract

State-space models (SSM) are common in signal processing, where Kalman smoothing (KS) methods are state-of-the-art. However, traditional KS techniques lack expressivity as they do not incorporate spatial prior information. Recently, [1] proposed an ADMM algorithm that handles the state-space fidelity term with KS while regularizing the object via a sparsity-based prior with proximity operators. Plug-and-Play (PnP) methods are a popular type of iterative algorithms that replace proximal operators encoding prior knowledge with powerful denoisers such as deep neural networks. These methods are widely used in image processing, achieving state-of-the-art results. In this work, we build on the KS-ADMM method, combining it with deep learning to achieve higher expressivity. We propose a PnP algorithm based on KS-ADMM iterations, efficiently handling the SSM through KS, while enabling the use of powerful denoising networks. Simulations on a 2D+t imaging problem show that the proposed PnP-KS-ADMM algorithm improves the computational efficiency over standard PnP-ADMM for large numbers of timesteps.