Exploring Implicit Neural Representations in Image Deconvolution with Non-Sparse Kernels

In recent years, Implicit Neural Representations (INRs) have emerged as a powerful and widely studied technique, offering promising results in areas such as 3D scene reconstruction from 2D images (NeRF). They have also shown significant potential in solving various inverse problems, including deblurring, super-resolution, and image reconstruction. This paper investigates the capacity of INRs for non-blind image deconvolution, operating without the need for any external training datasets. State-of-the art blind or semi-blind methods achieve suboptimal results on non-sparse smoothing kernels widely encountered in medical imaging. We propose a self-supervised framework for this task, where the kernel and the image are estimated separatelly. For the blur kernel we employ a compact network and Fourier features encoding, whereas for the image we use hash encoding, better suited for reproducing sharp details. To facilitate comparisons, we are conducting this study on natural images convolved with Gaussian filters. The implemented framework demonstrates promising results for both image and kernel deconvolution, outperforming several existing self-supervised methods.