Reconstruction of Ridgelet Coefficients Using Total Variation Minimization

The combination of ordinary wavelet shrinkage with total variation minimization was successfully applied. In this paper, we apply the technique with respect to ridgelet coefficients. Firstly, a translation-invariant ridgelet transform is proposed. And then, an image denoising algorithm, based on ridgelet shrinkage and total variation minimization, is given. This algorithm preserves the important information of image and reduces the noise by thresholding small ridgelet coefficients. By replacing these thresholded coefficients by values minimizing the total variation, the algorithm reduces the pseudo-Gibbs artifacts. Experiment results show that this algorithm yields significantly superior image quality and higher peak signal to noise ratio (PSNR).