Accelerating Plug-and-Play Image Reconstruction via Multi-Stage Sketched Gradients
This addresses computational bottlenecks in medical imaging reconstruction, though it appears incremental as an acceleration scheme for existing methods.
The paper tackles the problem of slow plug-and-play image reconstruction algorithms by proposing a new paradigm using multi-stage sketched gradients for acceleration, with numerical experiments on X-ray fan-beam CT showing remarkable effectiveness and computational free-lunch.
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.