Wavelet denoising is a classical and effective approach for reducing noise in images and signals. Suggested in 1994, this approach is carried out by rectifying the coefficients of a noisy image in the transform domain, using a set of scalar shrinkage function (SFs). A plethora of papers deals with the optimal shape of the SFs and the transform used, where it is known that applying the SFs in redundant bases provides improved results. This paper provides a complete picture of the interrelations between the transform used, the optimal shrinkage functions, and the domains in which they are optimized. In particular, we show that for subband optimization, where each SF is optimized independently for a particular band, optimizing the SFs in the spatial domain is always better than or equal to optimizing the SFs in the transform domain. For redundant bases, we provide the expected denoising gain we may achieve, relative to the unitary basis, as a function of the redundancy rate.
Denoising of coefficients in a sparse domain (e.g. wavelet) has been researched extensively because of its simplicity and effectiveness. Literature mainly has focused on designing the best global threshold. However, this paper proposes a new denoising method using bivariate shrinkage function in framelet domain. In the proposed method, maximum aposteriori probability is used for estimate of the denoised coefficient and non-Gaussian bivariate function is applied to model the statistics of framelet coefficients. For every framelet coefficient, there is a corresponding threshold depending on the …
The rise of machine learning in image processing has created a gap between trainable data-driven and classical model-driven approaches: While learning-based models often show superior performance, classical ones are often more transparent. To reduce this gap, we introduce a generic wavelet shrinkage function for denoising which is adaptive to both the wavelet scales as well as the noise standard deviation. It is inferred from trained results of a tightly parametrised function which is inherited from nonlinear diffusion. Our proposed shrinkage function is smooth and compact while only using two…
Qingdao University（青岛大学）；Harbin Institute of Technology（哈尔滨工业大学）；University of Kentucky（肯塔基大学）
It is a challenging task to remove heavy and mixed types of noise from Hyperspectral images (HSIs). In this paper, we propose a novel nonconvex approach to RPCA for HSI denoising, which adopts the log-determinant rank approximation and a novel $\ell_{2,\log}$ norm, to restrict the low-rank or column-wise sparse properties for the component matrices, respectively.For the $\ell_{2,\log}$-regularized shrinkage problem, we develop an efficient, closed-form solution, which is named $\ell_{2,\log}$-shrinkage operator, which can be generally used in other problems. Extensive experiments on both simul…
The generic risk estimator addresses the problem of denoising images corrupted by additive white noise without placing any restriction on the statistical distribution of the noise. In this paper, we discuss an efficient FPGA implementation of this algorithm. We use the undecimated Haar wavelet transform with shrinkage parameters for each sub-band as the denoising function. The computational complexity and memory requirement of the algorithm is first analyzed. To optimize the performance, a combination of convolution and recursion is employed to realize Haar filter bank and gradient descent alg…
Decomposition of digital signals and images into other basis or dictionaries than time or space domains is a very common approach in signal and image processing and analysis. Such a decomposition is commonly obtained using fixed transforms (e.g., Fourier or wavelet) or dictionaries learned from example databases or from the signal or image itself. In this work, we investigate in detail a new approach of constructing such a signal or image-dependent bases inspired by quantum mechanics tools, i.e., by considering the signal or image as a potential in the discretized Schroedinger equation. To ill…
Qingdao University（青岛大学）；Harbin Institute of Technology（哈尔滨工业大学）；University of Electronic Science and Technology of China（电子科技大学）；University of Kentucky（肯塔基大学）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
In this paper, we propose a novel nonconvex approach to robust principal component analysis for HSI denoising, which focuses on simultaneously developing more accurate approximations to both rank and column-wise sparsity for the low-rank and sparse components, respectively. In particular, the new method adopts the log-determinant rank approximation and a novel $\ell_{2,\log}$ norm, to restrict the local low-rank or column-wisely sparse properties for the component matrices, respectively. For the $\ell_{2,\log}$-regularized shrinkage problem, we develop an efficient, closed-form solution, which…
Image denoising aims to restore a clean image from an observed noisy image. The model-based image denoising approaches can achieve good generalization ability over different noise levels and are with high interpretability. Learning-based approaches are able to achieve better results, but usually with weaker generalization ability and interpretability. In this paper, we propose a wavelet-inspired invertible network (WINNet) to combine the merits of the wavelet-based approaches and learningbased approaches. The proposed WINNet consists of K-scale of lifting inspired invertible neural networks (L…
In this paper, we propose an invertible neural network for image denoising (DnINN) inspired by the transform-based denoising framework. The proposed DnINN consists of an invertible neural network called LINN whose architecture is inspired by the lifting scheme in wavelet theory and a sparsity-driven denoising network which is used to remove noise from the transform coefficients. The denoising operation is performed with a single soft-thresholding operation or with a learned iterative shrinkage thresholding network. The forward pass of LINN produces an over-complete representation which is more…
The paper presents an image denoising algorithm by combining a method that is based on directional quasi-analytic wavelet packets (qWPs) with the popular BM3D algorithm. The qWPs and its corresponding transforms are designed in [1]. The denoising algorithm qWP (qWPdn) applies an adaptive localized soft thresholding to the transform coefficients using the Bivariate Shrinkage methodology. The combined method consists of several iterations of qWPdn and BM3D algorithms, where the output from one algorithm updates the input to the other (cross-boosting).The qWPdn and BM3D methods complement each ot…
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Massachusetts Institute of Technology（麻省理工学院）；Tufts School of Medicine（塔夫茨医学院）
Optical coherence tomography angiography (OCTA) is a novel and clinically promising imaging modality to image retinal and sub-retinal vasculature. Based on repeated optical coherence tomography (OCT) scans, intensity changes are observed over time and used to compute OCTA image data. OCTA data are prone to noise and artifacts caused by variations in flow speed and patient movement. We propose a novel iterative maximum a posteriori signal recovery algorithm in order to generate OCTA volumes with reduced noise and increased image quality. This algorithm is based on previous work on probabilistic…
Northwestern Polytechnical University（西北工业大学）；Harbin Institute of Technology（哈尔滨工业大学）；Peng Cheng Laboratory（鹏城实验室）；University of Macau（澳门大学）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳市人工智能与机器人研究院）
Deep convolutional neural networks (CNNs) are used for image denoising via automatically mining accurate structure information. However, most of existing CNNs depend on enlarging depth of designed networks to obtain better denoising performance, which may cause training difficulty. In this paper, we propose a multi-stage image denoising CNN with the wavelet transform (MWDCNN) via three stages, i.e., a dynamic convolutional block (DCB), two cascaded wavelet transform and enhancement blocks (WEBs) and a residual block (RB). DCB uses a dynamic convolution to dynamically adjust parameters of sever…
Compressive sensing is an impressive approach for fast MRI. It aims at reconstructing MR image using only a few under-sampled data in k-space, enhancing the efficiency of the data acquisition. In this study, we propose to learn priors based on undecimated wavelet transform and an iterative image reconstruction algorithm. At the stage of prior learning, transformed feature images obtained by undecimated wavelet transform are stacked as an input of denoising autoencoder network (DAE). The highly redundant and multi-scale input enables the correlation of feature images at different channels, whic…
Institut de Mathématiques de Bordeaux, CNRS, Université de Bordeaux, Bordeaux INP（波尔多数学研究所、法国国家科学研究中心、波尔多大学、波尔多国立理工学院）；University of California, San Diego（加利福尼亚大学圣地亚哥分校）
Patch priors have become an important component of image restoration. A powerful approach in this category of restoration algorithms is the popular Expected Patch Log-Likelihood (EPLL) algorithm. EPLL uses a Gaussian mixture model (GMM) prior learned on clean image patches as a way to regularize degraded patches. In this paper, we show that a generalized Gaussian mixture model (GGMM) captures the underlying distribution of patches better than a GMM. Even though GGMM is a powerful prior to combine with EPLL, the non-Gaussianity of its components presents major challenges to be applied to a comp…
The discrete curvelet transform decomposes an image into a set of fundamental components that are distinguished by direction and size as well as a low-frequency representation. The curvelet representation is approximately sparse; thus, it is a useful sparsifying transformation to be used with compressed sensing. However, the low-frequency portion is seldom sparse. This manuscript presents a method to modify the redundant sparsifying transformation comprised of the wavelet and curvelet transforms to take advantage of this fact with compressed sensing image reconstruction. Instead of relying on …
