Accelerating Plug-and-Play Image Reconstruction via Multi-Stage Sketched Gradients

TL;DR

This paper introduces a multi-stage sketched gradient approach to accelerate plug-and-play image reconstruction, reducing computational complexity through dimensionality reduction and demonstrating significant improvements in X-ray CT applications.

Contribution

It presents a novel multi-stage sketched gradient method that accelerates PnP algorithms by combining dimensionality reduction with gradient approximation, applicable to various existing methods.

Findings

Significant reduction in computational complexity for PnP algorithms.

Effective application to X-ray fan-beam CT reconstruction.

Compatibility with existing PnP/RED methods enhances versatility.

Abstract

In this work we propose a new paradigm for designing fast plug-and-play (PnP) algorithms using dimensionality reduction techniques. Unlike existing approaches which utilize stochastic gradient iterations for acceleration, we propose novel multi-stage sketched gradient iterations which first perform downsampling dimensionality reduction in the image space, and then efficiently approximate the true gradient using the sketched gradient in the low-dimensional space. This sketched gradient scheme can also be naturally combined with PnP-SGD methods for further improvement on computational complexity. As a generic acceleration scheme, it can be applied to accelerate any existing PnP/RED algorithm. Our numerical experiments on X-ray fan-beam CT demonstrate the remarkable effectiveness of our scheme, that a computational free-lunch can be obtained using this dimensionality reduction in the image space.