Joint Bilateral Filter for Signal Recovery from Phase Preserved Curvelet Coefficients for Image Denoising

Abstract

Thresholding of Curvelet Coefficients, for image denoising, drains out subtle signal component in noise subspace. In effect, it also produces ringing artifacts near edges. We found that the noise sensitivity of Curvelet phases — in contrast to their magnitude — reduces with higher noise level. Thus, we preserved the phase of the coefficients below threshold at coarser scale and estimated the corresponding magnitude by Joint Bilateral Filtering (JBF) technique. In contrast to the traditional hard thresholding, the coefficients in the finest scale is estimated using Bilateral Filtering (BF). The proposed filtering approach in the finest scale exhibits better connectedness among the edges, while removing the granular artifacts in the denoised image due to hard thresholding. Finally, the use of Guided Image Filter (GIF) on the Curvelet-based reconstructed image (initial denoised image in spatial domain) ensures the preservation of small image information with sharper edges and textures detail in the final denoised image. The lower noise sensitivity of Curvelet phase at higher noise strength accelerates the performance of proposed method over several state-of-the-art techniques and provides comparable outcome at lower noise levels.