Color Image and Multispectral Image Denoising Using Block Diagonal Representation

Abstract

Filtering images of more than one channel is challenging in terms of both efficiency and effectiveness. By grouping similar patches to utilize the self-similarity and sparse linear approximation of natural images, recent nonlocal and transformdomain methods have been widely used in color and multispectral image (MSI) denoising. Many related methods focus on the modeling of group level correlation to enhance sparsity, which often resorts to a recursive strategy with a large number of similar patches. The importance of the patch level representation is understated. In this paper, we mainly investigate the influence and potential of representation at patch level by considering a general formulation with block diagonal matrix. We further show that by training a proper global patch basis, along with a local principal component analysis transform in the grouping dimension, a simple transform-threshold-inverse method could produce very competitive results. Fast implementation is also developed to reduce computational complexity. Extensive experiments on both simulated and real datasets demonstrate its robustness, effectiveness and efficiency.

Weighted t-Schatten-p Norm Minimization for Real Color Image Denoising

“…In this section, we first evaluate the denoising performance of the proposed method on one synthetic and two public realistic image datasets, and then we compare it with nine representative methods, including color block-matching 3D filtering (CBM3D) [7], multi-channel weighted nuclear norm minimization (MCWNNM) [38], guided image denoisng (GID) [36], trilateral weighted sparse coding (TWSC) [37], multi-channel weighted Schatten-p norm minimization (MCWSNM) combining WSNM in [35] and MCWNNM in [38] for color images denoising, color multi-spectral t-SVD (CMSt-SVD) [18], denoising convolutional neural networks (DnCNN) [42], fast and flexible denoising network (FFDNet) [43] and weighted tensor nuclear norm minimization (WTNNM) [20]. All the denoising results of compared methods are obtained via the source codes released from the authors' website by fine-tuned parameters.…”

A Modified Higher-Order Singular Value Decomposition Framework With Adaptive Multilinear Tensor Rank Approximation for Three-Dimensional Magnetic Resonance Rician Noise Removal

“…The proposed method exhibited a state-of-the-art performance in Rician noise removal with excellent fine detail preservation, which even outperformed several existing classical denoising methods (RSNLMMSE, BM4D, PRI-NLM3D, and HOSVD-R). Further, the capability to effectively capture the sparsity of multidimensional dataset would enable our work to be extended to several other domains, such as hyperspectral images (43,44), color images (45), and video (46).…”

A Comprehensive Comparison of Multi-Dimensional Image Denoising Methods

“…A simple and effective method is to model the sparsity with certain thresholding techniques [43], [101] to attenuate the noise. For example, the hard-thresholding technique is adopted by the BM3D family and some state-of-the-art tensor-based methods [19], [77], which attempts to shrink the coefficients T (G n ) in the transform-domain [8] under a threshold τ via…”

“…Interestingly, from the traditional Gaussian denoisers [14] with matrix and tensor representations to recently developed approaches using different deep neural network (DNN) architectures [15], nearly all the newly proposed methods claim to outperform the BM3D family [6], [11], [13], [16], [17]. However, some recent studies [18], [19] come to a different conclusion, and it is observed that many methods are normally verified based on a limited number (often less than three) of datasets, and the parameters of BM3Dbased methods may not be fine-tuned with certain noise estimation techniques [20], [21]. With a large number of existing methods [22] and outstanding survey papers [7], [8], [14], [15], [23], [24], [25], [26], [27], there still lacks a thorough comparison for the multi-dimensional image denoising tasks.…”