Total Variations for Hue, Saturation, and Value of a Color Image (CSIAM Transactions on Applied Mathematics, 2024)
In this paper, we develop total variations for hue, saturation, and value ofa color image, and we propose a novel hue-saturation-value total variation model forcolor image restoration. We first refine the hue formulation of a color image to makeit mathematically and applicationally meaningful by assigning different hue valuesto different colors. We then develop the proposed hue-saturation-value total variation based on the conception of hue/saturation/value gradient. We investigate thedual formulation and the properties of the proposed hue-saturation-value total variation, and we finally propose a color image restoration model which is formulatedby combing the proposed hue-saturation-value total variation regularization with thedata-fitting term between the objective color image and the observed color image. Wedevelop an efficient alternating iterative algorithm to solve the proposed optimizationmodel 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 modelis better than that of other testing methods in terms of visual quality, peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and S-CIELAB color error.