Total Variations for Hue, Saturation, and Value of a Color Image

Abstract

In this paper, we develop total variations for hue, saturation, and value of a color image, and we propose a novel hue-saturation-value total variation model for color image restoration. We first refine the hue formulation of a color image to make it mathematically and applicationally meaningful by assigning different hue values to different colors. We then develop the proposed hue-saturation-value total variation based on the conception of hue/saturation/value gradient. We investigate the dual formulation and the properties of the proposed hue-saturation-value total variation, and we finally propose a color image restoration model which is formulated by combing the proposed hue-saturation-value total variation regularization with the data-fitting term between the objective color image and the observed color image. We develop an efficient alternating iterative algorithm to solve the proposed optimization model in practice, and we give the convergence analysis of the proposed algorithm. Numerical examples are presented to demonstrate that the performance of the proposed hue-saturation-value total variation and the proposed color restoration model is better than that of other testing methods in terms of visual quality, peak signal-tonoise ratio (PSNR), structural similarity index (SSIM), and S-CIELAB color error.