A basic problem in digital image restoration is the smoothing or blurring of edges due to the averaging effects of most techniques. Filtering results in images that are less noisy but less sharp as well. In order to be able to effectively reduce noise while maintaining a degree of sharpness we define a cost function constrained to reflect a perception-related criterion. In this paper we examine the effects of a modification of the mean squared error (MSE) based on the subjective importance of edges. We have studied both the space-invariant and space-varying filters with standard edge detection operators. The static approach offers a simple and parallel implementation while the adaptive one gives better performance regarding sharpness and subjective quality. We present computer simulations on images of a standard data set with various noise densities and investigate the application of Ll-filters with the perception-constrained cost function. Also an analysis of the robustness of filters is included for cases when a test image is not available.