SINCO: A Novel structural regularizer for image compression using implicit neural representations

Implicit neural representations (INR) have been recently proposed as deep learning (DL) based solutions for image compression. An image can be compressed by training an INR model with fewer weights than the number of image pixels to map the coordinates of the image to corresponding pixel values. While traditional training approaches for INRs are based on enforcing pixel-wise image consistency, we propose to further improve image quality by using a new structural regularizer. We present structural regularization for INR compression (SINCO) as a novel INR method for image compression. SINCO imposes structural consistency of the compressed images to the groundtruth by using a segmentation network to penalize the discrepancy of segmentation masks predicted from compressed images. We validate SINCO on brain MRI images by showing that it can achieve better performance than some recent INR methods

Convergence of Nonconvex PnP-ADMM with MMSE Denoisers

Plug-and-Play Alternating Direction Method of Multipliers (PnP-ADMM) is a widely-used algorithm for solving inverse problems by integrating physical measurement models and convolutional neural network (CNN) priors. PnP-ADMM has been theoretically proven to converge for convex data-fidelity terms and nonexpansive CNNs. It has however been observed that PnP-ADMM often empirically converges even for expansive CNNs. This paper presents a theoretical explanation for the observed stability of PnP-ADMM based on the interpretation of the CNN prior as a minimum mean-squared error (MMSE) denoiser. Our explanation parallels a similar argument recently made for the iterative shrinkage/thresholding algorithm variant of PnP (PnP-ISTA) and relies on the connection between MMSE denoisers and proximal operators. We also numerically evaluate the performance gap between PnP-ADMM using a nonexpansive DnCNN denoiser and expansive DRUNet denoiser, thus motivating the use of expansive CNNs

A Plug-and-Play Image Registration Network

Deformable image registration (DIR) is an active research topic in biomedical imaging. There is a growing interest in developing DIR methods based on deep learning (DL). A traditional DL approach to DIR is based on training a convolutional neural network (CNN) to estimate the registration field between two input images. While conceptually simple, this approach comes with a limitation that it exclusively relies on a pre-trained CNN without explicitly enforcing fidelity between the registered image and the reference. We present plug-and-play image registration network (PIRATE) as a new DIR method that addresses this issue by integrating an explicit data-fidelity penalty and a CNN prior. PIRATE pre-trains a CNN denoiser on the registration field and "plugs" it into an iterative method as a regularizer. We additionally present PIRATE+ that fine-tunes the CNN prior in PIRATE using deep equilibrium models (DEQ). PIRATE+ interprets the fixed-point iteration of PIRATE as a network with effectively infinite layers and then trains the resulting network end-to-end, enabling it to learn more task-specific information and boosting its performance. Our numerical results on OASIS and CANDI datasets show that our methods achieve state-of-the-art performance on DIR

Block Coordinate Plug-and-Play Methods for Blind Inverse Problems

Plug-and-play (PnP) prior is a well-known class of methods for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image denoisers. While PnP methods have been extensively used for image recovery with known measurement operators, there is little work on PnP for solving blind inverse problems. We address this gap by presenting a new block-coordinate PnP (BC-PnP) method that efficiently solves this joint estimation problem by introducing learned denoisers as priors on both the unknown image and the unknown measurement operator. We present a new convergence theory for BC-PnP compatible with blind inverse problems by considering nonconvex data-fidelity terms and expansive denoisers. Our theory analyzes the convergence of BC-PnP to a stationary point of an implicit function associated with an approximate minimum mean-squared error (MMSE) denoiser. We numerically validate our method on two blind inverse problems: automatic coil sensitivity estimation in magnetic resonance imaging (MRI) and blind image deblurring. Our results show that BC-PnP provides an efficient and principled framework for using denoisers as PnP priors for jointly estimating measurement operators and images

FLAIR: A Conditional Diffusion Framework with Applications to Face Video Restoration

Face video restoration (FVR) is a challenging but important problem where one seeks to recover a perceptually realistic face videos from a low-quality input. While diffusion probabilistic models (DPMs) have been shown to achieve remarkable performance for face image restoration, they often fail to preserve temporally coherent, high-quality videos, compromising the fidelity of reconstructed faces. We present a new conditional diffusion framework called FLAIR for FVR. FLAIR ensures temporal consistency across frames in a computationally efficient fashion by converting a traditional image DPM into a video DPM. The proposed conversion uses a recurrent video refinement layer and a temporal self-attention at different scales. FLAIR also uses a conditional iterative refinement process to balance the perceptual and distortion quality during inference. This process consists of two key components: a data-consistency module that analytically ensures that the generated video precisely matches its degraded observation and a coarse-to-fine image enhancement module specifically for facial regions. Our extensive experiments show superiority of FLAIR over the current state-of-the-art (SOTA) for video super-resolution, deblurring, JPEG restoration, and space-time frame interpolation on two high-quality face video datasets.Comment: 32 pages, 27 figure