Phase-Preserved Curvelet Thresholding for Image Denoising

Noise corrupts all frequency sub-bands during multiscale representation of any degraded image. Naïve hard thersolding in Curvelet may not be sufficient in suppressing noise in all sub-bands. Threshold also cannot identify signal and noise and thus removes all. This leads to lost image details and unrecovered signal residual in Curvelet coefficients, with ringing artifacts in the reconstructed image. For complex transforms, the indispensable phase information is also removed due to magnitude thresholding. This article mathematically proved, by defining a measure called noise sensitivity to show its immunity to Gaussian noise compared to magnitude. The proposed adaptive Wiener filter in coarser scales aims to recover both lost signals due to hard threshold and preserve corresponding phase for recovering essential image details. Instead of hard thresholding, bilateral filtering (BF) was applied in the finest scale to smooth out the unwanted noisy components. The BF in the finest scale exhibits better localization of edges and also removes granular artifacts that may occur due to Curvelet thresholding (CT). In the final step, reconstructed image is treated with guided image filter to further reduce artifacts near edges and to preserve maximum details of latent image. For testing and validation, the proposed phase-preserved Curvelet thresholding (PPCT) algorithm is investigated under both natural and simulated noise. Results favor the hybrid PPCT technique compared to individual CT and BF method. Moreover, the efficacy of PPCT is comparable to several state-of-the-art methods when signal is more dominating to noise and exhibits better performance at higher noise power.