  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.
