Vamsidhar Saraswathula

Sasidhar Parvathireddy, Vamsidhar Saraswathula, Rama Krishna Gorthi

In recent times, diffusion models have achieved remarkable performance in image restoration tasks. Their core mechanism relies on the restricted presumption of degradation prior to the additive noise operation. However, the blur model, one of the most widely studied degradation formulations, violates this assumption, as it is inherently based on convolution rather than addition. In this paper, we introduce ConvDiff, a novel diffusion based framework that substitutes the additive operation with convolution for the task of image deblurring. In the forward process, we construct a meaningful trajectory from the clean image to its blurred counterpart by exploiting the frequency domain characteristics of convolution, rather than progressively corrupting the image with additive noise. While the current work instantiates this framework for Gaussian blur, where frequency-domain decomposition yields closed-form and physically valid intermediate states, the underlying principle of constructing degradation trajectories from the blur operator extends naturally to other blur families. This formulation bridges the gap between the mathematical principles of blurring and the iterative design of diffusion-based restoration algorithms, enabling more physically grounded and effective image restoration models.

Vamsidhar Saraswathula, Rama Krishna Gorthi

In this paper, we propose to reformulate the blind image deblurring task to directly learn an inverse of the degradation model represented by a deep linear network. We introduce Deep Identity Learning (DIL), a novel learning strategy that includes a dedicated regularization term based on the properties of linear systems, to exploit the identity relation between the degradation and inverse degradation models. The salient aspect of our proposed framework is it neither relies on a deblurring dataset nor a single input blurry image (e.g. Polyblur, a self-supervised method). This framework detours the typical degradation kernel estimation step involved in most of the existing blind deblurring solutions by the proposition of our Random Kernel Gallery (RKG) dataset. The proposed approach extends our previous Image Super-Resolution (ISR) work, NSSR-DIL, to the image deblurring task. In this work, we updated the regularization term in DIL based on Fourier transform properties of the identity relation, to deliver robust performance across a wide range of degradations. Besides the regularization term, we provide an explicit and compact representation of the learned deep linear network in a matrix form, called Deep Restoration Kernel (DRK) to perform image restoration. Our experiments show that the proposed method outperforms both traditional and deep learning based deblurring methods, with at least an order of 100 lesser computational resources. The D3 model, both LCNN & DRK, can be effortlessly extended to the Image Super-Resolution (ISR) task as well to restore the low-resolution images with fine details. The D3 model and its kernel form representation (DRK) are lightweight yet robust and restore the blurry input in a fraction of a second.