Image Restoration Using Adaptive Region-Wise p-Norm Filter with Local Constraints

Abstract

In this work, we introduce a feature adaptive second-order p-norm filter with local constraints for image restoration and texture preservation. The p-norm value of the filter is chosen adaptively between 1 and 2 in a local region based on the regional image characteristics. The filter behaves like a mean curvature motion (MCM) [A. Marquina and S. Osher, SIAM Journal of Scientific Computing 22, 387–405 (2000)] in the regions where the p-norm value is 1 and switches to a Laplacian filter in the rest of the regions (where the p-norm value is 2). The proposed study considerably reduces stair-case effect and effectively removes noise from images while deblurring them. The noise is assumed as Gaussian distributed (with zero mean and variance [Formula: see text]) and blur is linearly shift invariant (out-of-focus). The filter converges at a faster rate with semi-implicit Crank–Nicholson scheme. The regularization parameter is initialized and updated based on the local image features and therefore this filter preserves edges, structures, textures and fine details present in images very well. The method is applied on different kinds of images with different image characteristics. We show the response of the filter to various kinds of images and numerically quantify the performance in terms of standard statistical measures.