Multi-Scale Based Approach for Denoising Real-World Noisy Image Using Curvelet Thresholding: Scope and Beyond

Na \ddot {i} ve simulated additive white Gaussian noise (AWGN) may not fully characterize the complexity of real world noisy images. Owing to optimal sparsity in image representation, we propose a curvelet based model for denoising real-world RGB images. Initially, the image is decomposed in three curvelet scales, namely: the approximation scale (that retains low-frequency information), the coarser scale and the finest scale (that preserves high-frequency components). Coefficients in the approximation and finest scale are estimated using NLM filter, while a scale dependent threshold is adopted for signal estimation in the coarser scale. The reconstructed image in spatial domain is further processed using Guided Image Filter (GIF) to suppress the ringing artifacts due to curvelet thresholding. The proposed approach known as CTuNLM method is extended for color image denoising using uncorrelated YUV color space. Extensive experiments on multi-channel real noisy images are conducted in comparison with eight sate-of-the-art methods. With four encouraging qualitative and quantitative measures including PSNR and SSIM, we found that CTuNLM method achieves better denoising performance in terms of noise reduction and detail preservation. We further examined the potential of proposed approach by focusing only on the Finest scale curvelet Coefficients (FC). Features like small details, edges and textures always add up to improve the overall denoising performance, while minimizing spurious details. We studied "The Curious Case of the Finest Scale" and constructed "Deep Curvelet-Net": an encoder-decoder-based CNN architecture, as a pilot work. The encoder uses multiscale spatial characteristics from noisy FC, while the decoder processes de-noised FC under the supervision of encoder's multiscale spatial attention map. The "Deep Curvelet-Net" links encoder multiscale feature modeling with decoder spatial attention supervision to learn the most essential features for denoising. The CNN-based architecture only estimates FC, while all other CTuNLM stages are left unchanged to produce the denoised output. Results presented in this article validated the design of proposed CNN architecture in curvelet domain and motivated us to search beyond classical thresholding and/or filtering approaches.