Improving image deblurring

In this paper, we present a new model to improve image deblurring for the Helsinki Deblur Challenge, promoted by the Finnish Inverse Problems Society in the year of 2021. The challenge consisted in deblurring photographs of random strings of text with varying levels of blur caused by misfocusing the camera. This problem is usually referred to in the literature as out-of-focus deblur. A set of blurred and sharp images was available and also images of dots and other technical targets (horizontal and vertical lines) with the same camera settings. From the observation that the convolution of the sharp images with a uniform disk, which is commonly used as the point spread function (PSF) for the out-of-focus deblur problem, resulted in a image different from the observed blurred images, we observed a pattern that could be modeled as a contrast map. By multiplying this map to the observed images it was possible to significantly improve the image deblurring algorithms, specially for high levels of blur. This map was obtained from the blurred and sharp images that were available. Also, we propose a new deblurring function to be used with the fixed point Regularization by Denoise (RED) algorithm and the results were compared with the Least Absolute Shrinkage and Selection Operator (LASSO) algorithm.