Denoising Task Research Articles

A Fully Conservative Parallel Numerical Algorithm with Adaptive Spatial Grid for Solving Nonlinear Diffusion Equations in Image Processing

In this paper we present simple yet efficient parallel program implementation of grid-difference method for solving nonlinear parabolic equations, which satisfies both fully conservative property and second order of approximation on non-uniform spatial grid according to geometrical sanity of a task. The proposed algorithm was tested on Perona–Malik method for image noise ltering task based on differential equations. Also in this work we propose generalization of the Perona–Malik equation, which is a one of diffusion in complex-valued region type. This corresponds to the conversion to such types of nonlinear equations like Leontovich–Fock equation with a dependent on the gradient field according to the nonlinear law coefficient of diffraction. This is a special case of generalization of the Perona–Malik equation to the multicomponent case. This approach makes noise removal process more flexible by increasing its capabilities, which allows achieving better results for the task of image denoising.

Dilated Residual Networks with Symmetric Skip Connection for image denoising

Due to the fast inference and good performance, convolutional neural network (CNN) has been widely applied in image denoising. Some new approaches, such as residual learning and batch normalization are quite effective at accelerating the training process as well as improving accuracy. The batch normalization has been proved to handle Gaussian denoising effectively and efficiently, and can further boost the denoising performance of networks. However, it still leaves much space to improve. In this paper, we attempt to introduce a novel network structure without batch normalization, namely Dilated Residual Networks with Symmetric Skip Connection (DSNet), which depends on a combination of symmetric skip connection and dilated convolution. The advantage of this novel approach is computationally efficient in training, because the layers and the parameters of our networks are less than the previous network structure. Our network structure is more feasible for the task of image denoising, especially Gaussian noise. Our extensive experiments demonstrate that the proposed method can not only outperform the state-of-the-art methods in terms of both accuracy and speed, but also be efficiently implemented by benefiting from GPU computing.

An Iterative Robust Kernel-Based Regression Method for Simultaneous Single Image Super-Resolution and Denoising

In this paper, we present a uniform mathematical framework based on a robust kernel-based regression for the task of simultaneous single-image super-resolution and denoising. The given model is formulated as a convex $\ell _{1}$ sparse optimization problem, which can be efficiently solved by the alternating direction method of multipliers (ADMM). Especially, the proposed method is applied to image patches to reduce computational time. Additionally, an iterative strategy is also incorporated into the approach to refine more image details. The extensive experiments on simulated natural images with additional sparse noise and real time-of-flight (ToF) images demonstrate the ability of simultaneously removing sparse noise and enhancing image resolution.

Robust spike-and-slab deep Boltzmann machines for face denoising

The robust Gaussian restricted Boltzmann machine can effectively learn the structure of noise to achieve better results in the face denoising task. The robust Gaussian restricted Boltzmann machine model contains two types of the restricted Boltzmann machine (RBM) model, where a general RBM is used to model the structure of the noise and a Gaussian RBM is used to model the clean data. The spike-and-slab RBM shows better learning abilities than the Gaussian RBM in real images modeling. In addition, the deep Boltzmann machine (DBM) shows powerful image reconstruction ability. To model the real images better, we first stack the spike-and-slab RBM and the RBM to create the spike-and-slab DBM. And then, we utilize the spike-and-slab DBM instead of the Gaussian RBM to model the density of the clean data in the Robust Gaussian RBM, and the proposed method is named as the robust spike-and-slab DBM which can obtain clearer denoising images. Finally, in order to obtain better denoising results, we make use of the learned spike-and-slab DBM model and the mean field method to multi-inference the denoising data learned from the robust spike-and-slab DBM. Experimental results show that the robust spike-and-slab DBM is an effective neural network denoising method.

A Directed Graph Fourier Transform With Spread Frequency Components

We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low, medium, and high frequencies we seek a digraph (D)GFT such that the orthonormal frequency components are as spread as possible in the graph spectral domain. To that end, we advocate a two-step design whereby we 1) find the maximum directed variation (i.e., a novel notion of frequency on a digraph) a candidate basis vector can attain and 2) minimize a smooth spectral dispersion function over the achievable frequency range to obtain the desired spread DGFT basis. Both steps involve non-convex, orthonormality-constrained optimization problems, which are efficiently tackled via a feasible optimization method on the Stiefel manifold that provably converges to a stationary solution. We also propose a heuristic to construct the DGFT basis from Laplacian eigenvectors of an undirected version of the digraph. We show that the spectral-dispersion minimization problem can be cast as supermodular optimization over the set of candidate frequency components, whose orthonormality can be enforced via a matroid basis constraint. This motivates adopting a scalable greedy algorithm to obtain an approximate solution with quantifiable worst-case spectral dispersion. We illustrate the effectiveness of our DGFT algorithms through numerical tests on synthetic and real-world networks. We also carry out a graph-signal denoising task, whereby the DGFT basis is used to decompose and then low pass filter temperatures recorded across the United States.

The deep kernelized autoencoder

Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel machines have experienced great success by operating via inner-products in a theoretically well-defined reproducing kernel Hilbert space, hence capturing topological properties of input data. In this paper, we enhance the autoencoder's ability to learn effective data representations by aligning inner products between codes with respect to a kernel matrix. By doing so, the proposed kernelized autoencoder allows learning similarity-preserving embeddings of input data, where the notion of similarity is explicitly controlled by the user and encoded in a positive semi-definite kernel matrix. Experiments are performed for evaluating both reconstruction and kernel alignment performance in classification tasks and visualization of high-dimensional data. Additionally, we show that our method is capable to emulate kernel principal component analysis on a denoising task, obtaining competitive results at a much lower computational cost.

Nonlocal Similarity Based Nonnegative Tucker Decomposition for Hyperspectral Image Denoising

Compared with color or grayscale images, hyperspectral images deliver more informative representation of ground objects and enhance the performance of many recognition and classification applications. However, hyperspectral images are normally corrupted by various types of noises, which have a serious impact on the subsequent image processing tasks. In this paper, we propose a novel hyperspectral image denoising method based on tucker decomposition to model the nonlocal similarity across the spatial domain and global similarity along the spectral domain. In this method, 3-D full band patches extracted from a hyperspectral image are grouped to form a third-order tensor by utilizing the nonlocal similarity in a proper window size. In this way, the task of image denoising is transformed into a high-order tensor approximation problem, which can be solved by nonnegative tucker decomposition. Instead of a traditional alternative least square based tucker decomposition, we propose a hierarchical least square based nonnegative tucker decomposition method to reduce the computational cost and improve the denoising effect. In addition, an iterative denoising strategy is adopted to achieve better denoising outcome in practice. Experimental results on three datasets show that the proposed method outperforms several state-of-the-art methods and significantly enhances the quality of the corrupted hyperspectral image.

Restoration by Compression

In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods were suggested only for the Gaussian denoising task, leaving more complicated restoration problems without a generally constructive approach. Here we present practical methods for complexity-regularized restoration of signals, accommodating degradations caused by a known linear operator of an arbitrary form. Our iterative procedure, obtained using the alternating direction method of multipliers (ADMM) approach, addresses the restoration task as a sequence of simpler problems involving L2-regularized estimations and rate-distortion optimizations (considering the squared-error criterion). Further, we replace the rate-distortion optimizations with an arbitrary standardized compression technique and thereby restore the signal by leveraging underlying models designed for compression. Additionally, we propose a shift-invariant complexity regularizer, measuring the bit-cost of all the shifted forms of the estimate, extending our method to use averaging of decompressed outputs gathered from compression of shifted signals. On the theoretical side, we present an analysis of complexity-regularized restoration of a cyclo-stationary Gaussian signal from deterioration by a linear shift-invariant operator and an additive white Gaussian noise. The theory shows that optimal complexity-regularized restoration relies on an elementary restoration filter and compression spreading reconstruction quality unevenly based on the energy distribution of the degradation filter. Nicely, these ideas are realized also in the proposed practical methods. The presented experiments show good results for image deblurring and inpainting using the JPEG2000 and HEVC compression standards.

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.

Robust Nonlinear Regression: A Greedy Approach Employing Kernels With Application to Image Denoising

We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of the associated unknown parameters. Due to the presence of outliers, common techniques such as the Kernel Ridge Regression (KRR) or the Support Vector Regression (SVR) turn out to be inadequate. Instead, we employ sparse modeling arguments to explicitly model and estimate the outliers, adopting a greedy approach. The proposed robust scheme, i.e., Kernel Greedy Algorithm for Robust Denoising (KGARD), is inspired by the classical Orthogonal Matching Pursuit (OMP) algorithm. Specifically, the proposed method alternates between a KRR task and an OMP-like selection step. Theoretical results concerning the identification of the outliers are provided. Moreover, KGARD is compared against other cutting edge methods, where its performance is evaluated via a set of experiments with various types of noise. Finally, the proposed robust estimation framework is applied to the task of image denoising, and its enhanced performance in the presence of outliers is demonstrated.

Regularization Method for Solving Denoising and Inpainting Task Using Stacked Sparse Denoising Autoencoders

This article offers a regularization method for training stacked sparse denoising autoencoders aimed at designing model description of objects used for image denoising and inpainting. The offered regularization method allows increasing the generalizing ability of model description, which results in greater stability of denoising methods using it with regard to variation of the noise type. This makes the offered method vital for the tasks where noise or image distortion types cannot be known beforehand. Response speed of the offered algorithm enables to use it for dataflow processing. Absence of the need to formalize the physical nature of noises allows applying the approach to processing images received from various sensors, including sensors beyond the visible spectrum, multispectral and other sensors. The article shows the results of applying the offered regularization method in the denoising and inpainting task as exemplified by FERET face image base.

Joint Optimization of Masks and Deep Recurrent Neural Networks for Monaural Source Separation

Monaural source separation is important for many real world applications. It is challenging because, with only a single channel of information available, without any constraints, an infinite number of solutions are possible. In this paper, we explore joint optimization of masking functions and deep recurrent neural networks for monaural source separation tasks, including monaural speech separation, monaural singing voice separation, and speech denoising. The joint optimization of the deep recurrent neural networks with an extra masking layer enforces a reconstruction constraint. Moreover, we explore a discriminative criterion for training neural networks to further enhance the separation performance. We evaluate the proposed system on the TSP, MIR-1K, and TIMIT datasets for speech separation, singing voice separation, and speech denoising tasks, respectively. Our approaches achieve 2.30--4.98 dB SDR gain compared to NMF models in the speech separation task, 2.30--2.48 dB GNSDR gain and 4.32--5.42 dB GSIR gain compared to existing models in the singing voice separation task, and outperform NMF and DNN baselines in the speech denoising task.

Color video denoising using epitome and sparse coding

Denoising is a process that remove noise from a signal. In this paper, we present a unified framework to deal with video denoising problems by adopting a two-steps process, namely the video epitome and sparse coding. First, the video epitome will summarize the video contents and remove the redundancy information to generate a single compact representation to describe the video content. Second, employing the single compact representation as an input, the sparse coding will generate a visual dictionary for the video sequence by estimating the most representative basis elements. The fusion of these two methods have resulted an enhanced, compact representation for the denoising task. Experiments on the publicly available datasets have shown the effectiveness of our proposed system in comparison to the state-of-the-art algorithms in the video denoising task.

ICA of Noisy Music Audio Mixtures Based on Iterative Shrinkage Denoising and FastICA Using Rational Nonlinearities

Blind source separation (BSS) has an extensive application prospect in many fields, and independent component analysis (ICA) is a very effective tool for solving the BSS problem. Noisy BSS/ICA, as it approaches the reality, is frequently considered in many practical applications. In this paper, we mainly discuss the "sensor" noise, adding Gaussian white noise to the music audio mixtures. To solve noisy BSS/ICA problem, we deploy denoising pre-processing before performing FastICA. Rather than traditional wavelet shrinkage, we employ a more advanced shrinkage denoising algorithm, parallel coordinate descent (PCD) iterative shrinkage based on redundant dictionary, to accomplish the denoising task. Since the classical nonlinearities (tanh and gauss) used in FastICA are not the optimal ones due to their slow computational speed, we propose two novel rational nonlinearities that have faster computational speed and almost the same or better separation performance comparing with the classical ones. As they originate from Pade approximant of tanh and gauss, but the coefficients are adjusted, we name them Variant Tanh Pade (VTP) and Variant Gauss Pade (VGP), respectively.

Self-Learning Based Image Decomposition With Applications to Single Image Denoising

Decomposition of an image into multiple semantic components has been an effective research topic for various image processing applications such as image denoising, enhancement, and inpainting. In this paper, we present a novel self-learning based image decomposition framework. Based on the recent success of sparse representation, the proposed framework first learns an over-complete dictionary from the high spatial frequency parts of the input image for reconstruction purposes. We perform unsupervised clustering on the observed dictionary atoms (and their corresponding reconstructed image versions) via affinity propagation, which allows us to identify image-dependent components with similar context information. While applying the proposed method for the applications of image denoising, we are able to automatically determine the undesirable patterns (e.g., rain streaks or Gaussian noise) from the derived image components directly from the input image, so that the task of single-image denoising can be addressed. Different from prior image processing works with sparse representation, our method does not need to collect training image data in advance, nor do we assume image priors such as the relationship between input and output image dictionaries. We conduct experiments on two denoising problems: single-image denoising with Gaussian noise and rain removal. Our empirical results confirm the effectiveness and robustness of our approach, which is shown to outperform state-of-the-art image denoising algorithms.

On-line decision tree-based insulation assessment employing mathematical morphology filters for HV cables

In this paper a new approach is given for insulation assessment of HV cables based on investigating the void size and/or remained insulation thickness (RIT), while the void is considered as the partial discharge source. The proposed decision tree based algorithm has well kept its capability in classifying the void size under different conditions of geometrical properties of the void such as size, depth and location; cable characteristics such as age and temperature; and also environmental noise. The procedure includes four stages which are, signal de-noising, PD detection, feature generation and compensation and finally void classification. In the first stage, the prerequisite task of de-noising is performed by a filter based on Mathematical Morphology (MM). PD detection stage is carried out based on mathematical morphology functions, too. In the feature generation stage, a compensation procedure is employed, in order to diminish the effect of pulse propagation along the cable on the PD features used for classification. Finally, in the last stage, void classification is done by Decision tree. Simulation results have shown high accuracy of the proposed insulation assessment method. In addition, in the stages of noise reduction and PD detection, performances of the algorithms are examined by experimental data which is recorded in the field.