Improving Image Restoration with Soft-Rounding

Several important classes of images such as text, barcode and pattern images have the property that pixels can only take a distinct subset of values. This knowledge can benefit the restoration of such images, but it has not been widely considered in current restoration methods. In this work, we describe an effective and efficient approach to incorporate the knowledge of distinct pixel values of the pristine images into the general regularized least squares restoration framework. We introduce a new regularizer that attains zero at the designated pixel values and becomes a quadratic penalty function in the intervals between them. When incorporated into the regularized least squares restoration framework, this regularizer leads to a simple and efficient step that resembles and extends the rounding operation, which we term as soft-rounding. We apply the soft-rounding enhanced solution to the restoration of binary text/barcode images and pattern images with multiple distinct pixel values. Experimental results show that soft-rounding enhanced restoration methods achieve significant improvement in both visual quality and quantitative measures (PSNR and SSIM). Furthermore, we show that this regularizer can also benefit the restoration of general natural images.Comment: 9 pages, 6 figure

On the filtering effect of iterative regularization algorithms for linear least-squares problems

Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to provide the fastest methods for the reconstruction of the solution, involving choices of adaptive parameters and scaling matrices. However, in presence of an ill-conditioned model and real data, the need of a regularized solution instead of the least-squares one changed the point of view in favour of iterative algorithms able to combine a fast execution with a stable behaviour with respect to the restoration error. In this paper we want to analyze some classical and recent gradient approaches for the linear least-squares problem by looking at their way of filtering the singular values, showing in particular the effects of scaling matrices and non-negative constraints in recovering the correct filters of the solution