Problem Of Denoising Research Articles

Neighborhood Matching for Curved Domains with Application to Denoising in Diffusion MRI.

In this paper, we introduce a strategy for performing neighborhood matching on general non-Euclidean and non-flat domains. Essentially, this involves representing the domain as a graph and then extending the concept of convolution from regular grids to graphs. Acknowledging the fact that convolutions are features of local neighborhoods, neighborhood matching is carried out using the outcome of multiple convolutions at multiple scales. All these concepts are encapsulated in a sound mathematical framework, called graph framelet transforms (GFTs), which allows signals residing on non-flat domains to be decomposed according to multiple frequency subbands for rich characterization of signal patterns. We apply GFTs to the problem of denoising of diffusion MRI data, which can reside on domains defined in very different ways, such as on a shell, on multiple shells, or on a Cartesian grid. Our non-local formulation of the problem allows information of diffusion signal profiles of drastically different orientations to be borrowed for effective denoising.

An Integrated De-Speckling Approach for Medical Ultrasound Images Based on Wavelet and Trilateral Filter

Speckle noise is a granular artifact in medical ultrasound images. It causes serious problems and hinders the development of automatic diagnosis technology. A novel and integrated approach is proposed to address the de-noising problem by using wavelet transformation and trilateral filter. Firstly, a dynamic additive model is developed to account for the medical ultrasound signal with speckle noise.Secondly, in accordance with the statistical property of the additive model, an adaptive wavelet shrinkage algorithm is applied to the noisy medical signal. Particularly, the algorithm is significant to the high-frequency component of the speckle noise in the wavelet domain. Thirdly, but most importantly, the low-frequency component of the speckle noise is suppressed by a trilateral filter. It simultaneously reduces the speckle and impulse noise in real set data. Finally, a lot of experiments are conducted on both synthetic images and real clinical ultrasound images for authenticity. Experimental results show the proposed method not only guarantees noise reduction, but also performswell on edge sharpening and offers greater flexibility. Compared with other existingmethods, experimental results show that the proposed algorithm demonstrates an excellent de-noising performance, offers great flexibility and substantially sharpens the desirable edge.

Fast Bayesian JPEG Decompression and Denoising With Tight Frame Priors.

JPEG decompression can be understood as an image reconstruction problem similar to denoising or deconvolution. Such problems can be solved within the Bayesian maximum a posteriori probability framework by iterative optimization algorithms. Prior knowledge about an image is usually described by the l1 norm of its sparse domain representation. For many problems, if the sparse domain forms a tight frame, optimization by the alternating direction method of multipliers can be very efficient. However, for JPEG, such solution is not straightforward, e.g., due to quantization and subsampling of chrominance channels. Derivation of such solution is the main contribution of this paper. In addition, we show that a minor modification of the proposed algorithm solves simultaneously the problem of image denoising. In the experimental section, we analyze the behavior of the proposed decompression algorithm in a small number of iterations with an interesting conclusion that this mode outperforms full convergence. Example images demonstrate the visual quality of decompression and quantitative experiments compare the algorithm with other state-of-the-art methods.

Greedy double sparse dictionary learning for sparse representation of speech signals

This paper proposes a greedy double sparse (DS) dictionary learning algorithm for speech signals, where the dictionary is the product of a predefined base dictionary, and a sparse matrix. Exploiting the DS structure, we show that the dictionary can be learned efficiently in the coefficient domain rather than the signal domain. It is achieved by modifying the objective function such that all the matrices involved in the coefficient domain are either sparse or near-sparse, thus making the dictionary update stage fast. The dictionary is learned on frames extracted from a speech signal using a hierarchical subset selection approach. Here, each dictionary atom is a training speech frame, chosen in accordance to its energy contribution for representing all other training speech frames. In other words, dictionary atoms are encouraged to be close to the training signals that uses them in their decomposition. After each atom update the modified residual serves as the new training data, thus the information learned by the previous atoms guides the update of subsequent dictionary atoms. In addition, we have shown that for a suitable choice of the base dictionary, storage efficiency of the DS dictionary can be further improved. Finally, the efficiency of the proposed method is demonstrated for the problem of speech representation and speech denoising.

Blind Image Denoising via Dependent Dirichlet Process Tree.

Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This paper addresses this problem and proposes a novel blind image denoising algorithm to recover the clean image from noisy one with the unknown noise model. To model the empirical noise of an image, our method introduces the mixture of Gaussian distribution, which is flexible enough to approximate different continuous distributions. The problem of blind image denoising is reformulated as a learning problem. The procedure is to first build a two-layer structural model for noisy patches and consider the clean ones as latent variable. To control the complexity of the noisy patch model, this work proposes a novel Bayesian nonparametric prior called "Dependent Dirichlet Process Tree" to build the model. Then, this study derives a variational inference algorithm to estimate model parameters and recover clean patches. We apply our method on synthesis and real noisy images with different noise models. Comparing with previous approaches, ours achieves better performance. The experimental results indicate the efficiency of the proposed algorithm to cope with practical image denoising tasks.

An Integrated De-speckling Approach for Medical Ultrasound Images Based on Wavelet and Trilateral Filter

Speckle noise is a granular artifact in medical ultrasound images. It causes serious problems and hinders the development of automatic diagnosis technology. In this paper, a novel and integrated approach is proposed to address the de-noising problem by using wavelet transformation and trilateral filter. Firstly, a dynamic additive model is developed to account for the medical ultrasound signal with speckle noise. Secondly, in accordance with the statistical property of the additive model, an adaptive wavelet shrinkage algorithm is applied to the noisy medical signal. Particularly, the algorithm is significant to the high-frequency component of the speckle noise in the wavelet domain. Thirdly, but most importantly, the low-frequency component of the speckle noise is suppressed by a trilateral filter. It simultaneously reduces the speckle and impulse noise in real set data. Finally, a lot of experiments are conducted on both synthetic images and real clinical ultrasound images for authenticity. Compared with other existing methods, experimental results show that the proposed algorithm demonstrates an excellent de-noising performance, offers great flexibility and substantially sharpens the desirable edge.

Multispectral Photoacoustic Imaging Artifact Removal and Denoising Using Time Series Model-Based Spectral Noise Estimation.

The aim of this study is to solve a problem of denoising and artifact removal from in vivo multispectral photoacoustic imaging when the level of noise is not known a priori. The study analyzes Wiener filtering in Fourier domain when a family of anisotropic shape filters is considered. The unknown noise and signal power spectral densities are estimated using spectral information of images and the autoregressive of the power 1 ( AR(1)) model. Edge preservation is achieved by detecting image edges in the original and the denoised image and superimposing a weighted contribution of the two edge images to the resulting denoised image. The method is tested on multispectral photoacoustic images from simulations, a tissue-mimicking phantom, as well as in vivo imaging of the mouse, with its performance compared against that of the standard Wiener filtering in Fourier domain. The results reveal better denoising and fine details preservation capabilities of the proposed method when compared to that of the standard Wiener filtering in Fourier domain, suggesting that this could be a useful denoising technique for other multispectral photoacoustic studies.

Off-the-Grid Line Spectrum Denoising and Estimation With Multiple Measurement Vectors

Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is the spectrally-sparse signal, which is composed of a small number of spectral atoms with arbitrary frequencies on the unit interval. In this paper we study the problem of line spectrum denoising and estimation with an ensemble of spectrally-sparse signals composed of the same set of continuous-valued frequencies from their partial and noisy observations. Two approaches are developed based on atomic norm minimization and structured covariance estimation, both of which can be solved efficiently via semidefinite programming. The first approach aims to estimate and denoise the set of signals from their partial and noisy observations via atomic norm minimization, and recover the frequencies via examining the dual polynomial of the convex program. We characterize the optimality condition of the proposed algorithm and derive the expected convergence rate for denoising, demonstrating the benefit of including multiple measurement vectors. The second approach aims to recover the population covariance matrix from the partially observed sample covariance matrix by motivating its low-rank Toeplitz structure without recovering the signal ensemble. Performance guarantee is derived with a finite number of measurement vectors. The frequencies can be recovered via conventional spectrum estimation methods such as MUSIC from the estimated covariance matrix. Finally, numerical examples are provided to validate the favorable performance of the proposed algorithms, with comparisons against several existing approaches.

Random Mixed Field Model for Mixed-Attribute Data Restoration

Noisy and incomplete data restoration is a critical preprocessing step in developing effective learning algorithms, which targets to reduce the effect of noise and missing values in data. By utilizing attribute correlations and/or instance similarities, various techniques have been developed for data denoising and imputation tasks. However, current existing data restoration methods are either specifically designed for a particular task, or incapable of dealing with mixed-attribute data. In this paper, we develop a new probabilistic model to provide a general and principled method for restoring mixed-attribute data. The main contributions of this study are twofold: a) a unified generative model, utilizing a generic random mixed field (RMF) prior, is designed to exploit mixed-attribute correlations; and b) a structured mean-field variational approach is proposed to solve the challenging inference problem of simultaneous denoising and imputation. We evaluate our method by classification experiments on both synthetic data and real benchmark datasets. Experiments demonstrate, our approach can effectively improve the classification accuracy of noisy and incomplete data by comparing with other data restoration methods.

A New Nonlinear Diffusion Equation Model for Noisy Image Segmentation

Image segmentation and image denoising are two important and fundamental topics in the field of image processing. Geometric active contour model based on level set method can deal with the problem of image segmentation, but it does not consider the problem of image denoising. In this paper, a new diffusion equation model for noisy image segmentation is proposed by incorporating some classical diffusion equation denoising models into the segmental process. An assumption about the connection between the image intensity and level set function is given firstly. Some classical denoising models are employed to describe the evolution of level set function secondly. The final nonlinear diffusion equation model for noisy image segmentation is built thirdly. Then image segmentation and image denoising are combined in a united framework. The segmental results can be presented by level set function. Experimental results show that the new model has the advantage of noise resistance and is superior to traditional segmentation model.

Simultaneously Removing Noise and Increasing Resolution of Seismic Data Using Waveform Shaping

We propose a novel method for simultaneously removing random noise and increasing the resolution of seismic data. We formulate the problem of simultaneous denoising and increasing resolution as an inverse problem and solve it using the shaping regularization framework. The resolution of seismic data is increased by shaping the estimated seismic wavelet into a user-defined wavelet that is easier for interpretation. The random noise is removed by a simple FK thresholding step in the shaping regularization framework. There are two shaping processes here: 1) shaping the estimated wavelet to a more ideal wavelet; and 2) shaping the inverted model to a more admissible model during the iterations. We use a wedge synthetic model and land poststack seismic data to demonstrate the performance of the proposed approach. It is the first time that a simultaneous resolution enhancement and noise attenuation framework is proposed to process poststack seismic data.

Solution of inverse problem for de-noising Raman spectral data with total variation using majorisation-minimisation algorithm

Inverse problems is a vibrant field of applied mathematics in which one tries to know the cause when effect is known or output is known and input is estimated. It is widely used in many fields of science and engineering such as signal de-noising, reconstruction, in-painting, compressed sensing, deconvolution, etc. The inverse problem of de-noising is defined as an optimisation problem. The solution of this optimisation problem is obtained using majorisation-minimisation MM algorithm. This approach is very effective in de-noising one-dimensional signal. In this article, majorisation-minimisation algorithm is used for de-noising Raman spectral data of Sr

Sharp MSE Bounds for Proximal Denoising

Denoising has to do with estimating a signal $$\mathbf {x}_0$$x0 from its noisy observations $$\mathbf {y}=\mathbf {x}_0+\mathbf {z}$$y=x0+z. In this paper, we focus on the structured denoising where the signal $$\mathbf {x}_0$$x0 possesses a certain structure and $$\mathbf {z}$$z has independent normally distributed entries with mean zero and variance $$\sigma ^2$$ź2. We employ a structure-inducing convex function $$f(\cdot )$$f(·) and solve $$\min _\mathbf {x}\{\frac{1}{2}\Vert \mathbf {y}-\mathbf {x}\Vert _2^2+\sigma {\lambda }f(\mathbf {x})\}$$minx{12źy-xź22+źźf(x)} to estimate $$\mathbf {x}_0$$x0, for some $$\lambda >0$$ź>0. Common choices for $$f(\cdot )$$f(·) include the $$\ell _1$$l1 norm for sparse vectors, the $$\ell _1-\ell _2$$l1-l2 norm for block-sparse signals and the nuclear norm for low-rank matrices. The metric we use to evaluate the performance of an estimate $$\mathbf {x}^*$$xź is the normalized mean-squared error $$\text {NMSE}(\sigma )=\frac{{\mathbb {E}}\Vert \mathbf {x}^*-\mathbf {x}_0\Vert _2^2}{\sigma ^2}$$NMSE(ź)=Eźxź-x0ź22ź2. We show that NMSE is maximized as $$\sigma \rightarrow 0$$źź0 and we find the exact worst-case NMSE, which has a simple geometric interpretation: the mean-squared distance of a standard normal vector to the $${\lambda }$$ź-scaled subdifferential $${\lambda }\partial f(\mathbf {x}_0)$$źźf(x0). When $${\lambda }$$ź is optimally tuned to minimize the worst-case NMSE, our results can be related to the constrained denoising problem $$\min _{f(\mathbf {x})\le f(\mathbf {x}_0)}\{\Vert \mathbf {y}-\mathbf {x}\Vert _2\}$$minf(x)≤f(x0){źy-xź2}. The paper also connects these results to the generalized LASSO problem, in which one solves $$\min _{f(\mathbf {x})\le f(\mathbf {x}_0)}\{\Vert \mathbf {y}-{\mathbf {A}}\mathbf {x}\Vert _2\}$$minf(x)≤f(x0){źy-Axź2} to estimate $$\mathbf {x}_0$$x0 from noisy linear observations $$\mathbf {y}={\mathbf {A}}\mathbf {x}_0+\mathbf {z}$$y=Ax0+z. We show that certain properties of the LASSO problem are closely related to the denoising problem. In particular, we characterize the normalized LASSO cost and show that it exhibits a phase transition as a function of number of observations. We also provide an order-optimal bound for the LASSO error in terms of the mean-squared distance. Our results are significant in two ways. First, we find a simple formula for the performance of a general convex estimator. Secondly, we establish a connection between the denoising and linear inverse problems.

Bayesian Inference for Neighborhood Filters With Application in Denoising.

Range-weighted neighborhood filters are useful and popular for their edge-preserving property and simplicity, but they are originally proposed as intuitive tools. Previous works needed to connect them to other tools or models for indirect property reasoning or parameter estimation. In this paper, we introduce a unified empirical Bayesian framework to do both directly. A neighborhood noise model is proposed to reason and infer the Yaroslavsky, bilateral, and modified non-local means filters by joint maximum a posteriori and maximum likelihood estimation. Then, the essential parameter, range variance, can be estimated via model fitting to the empirical distribution of an observable chi scale mixture variable. An algorithm based on expectation-maximization and quasi-Newton optimization is devised to perform the model fitting efficiently. Finally, we apply this framework to the problem of color-image denoising. A recursive fitting and filtering scheme is proposed to improve the image quality. Extensive experiments are performed for a variety of configurations, including different kernel functions, filter types and support sizes, color channel numbers, and noise types. The results show that the proposed framework can fit noisy images well and the range variance can be estimated successfully and efficiently.

L1 norm constrained migration of blended data with the FISTA algorithm

Blended acquisition significantly improves the seismic acquisition efficiency. However, the direct imaging of blended data is not satisfactory due to the crosstalk contamination. Assuming that the distribution of subsurface reflectivity is sparse, in this paper, we formulate the seismic imaging problem of blended data as a Basis Pursuit denoise (BPDN) problem. Based on compressed sensing, we propose a L1 norm constrained migration method applying to the direct imaging of blended data. The Fast Iterative Shrinkage-Thresholding Algorithm, which is stable and computationally efficient, is implemented in our method. Numerical tests on the theoretical models show that the crosstalk introduced by blended sources is effectively attenuated and the migration quality has been improved enormously.

A Comparative Study on the Development of Binary Object Extraction System using Different Self Organizing Neural Network

Accurately Extraction of a binary object from a noisy perspective has been a daunting task in the field of pattern recognition. Several techniques have been tried to optimally solve the problem of denoising of object over the decades. In this paper, different binary object extraction methods are reviewed which are basically guided by different SelfOrganizing Neural Networks (SONN) architectures as BiDirectional Self Organizing Neural Network (BDSONN), multi-Layer Self Organizing neural Network (MLSONN) and quantum version of MLSONN (QMLSONN). The result shows that QMLSONN outperforms over other network architectures in terms of time and also it restores shape of the object with great accuracy.

Image De-nosing with Morphological Component Analysis

In this paper, we investigate the problem of image de-noising. Here, the theory of morphological component analysis is employed to separate the image to be de-noised into some layers with different morphological components. In this paper, images are decomposed into two parts: smooth and textural parts. As noise only exists in the textural parts, we utilize bilateral filter to smooth textural parts. Finally, the smooth parts and the filtered textual parts are combined to get the image free of noise. The algorithm is tested experimentally, and the results show that it is superior to other state-of-art algorithms.

New De-noising Method for Speech Signal Based on Wavelet Entropy and Adaptive Threshold

Aiming at the problem of speech signal de-noising, this paper presents an adaptive threshold denoising method based on wavelet entropy. The method decomposes speech signal with noise by wavelet transform, and calculates wavelet entropy of the decomposed signal in each wavelet sub-interval. It combines the wavelet entropy with adaptive threshold to determine the threshold of high frequency coe‐cients. Compromised index threshold function is proposed to denoise the speech signal, and then the denoised signal is reconstructed. Finally, the paper compares the de-noising performance of the proposed threshold method, minimaxi threshold method, sqtwolog threshold method, and rigrsure threshold method. The simulation results show that when the input Signal-to-noise Ratio (SNR) is 7 dB, the output SNR with the proposed threshold de-noising method is the largest, and the input and output SNR curve is higher than what the other three kinds of threshold de-noising methods have, which proves that this method has better de-noising performance.

Denoising, deconvolving, and decomposing photon observations

The analysis of astronomical images is a non-trivial task. The D3PO algorithm addresses the inference problem of denoising, deconvolving, and decomposing photon observations. Its primary goal is the simultaneous but individual reconstruction of the diffuse and point-like photon flux given a single photon count image, where the fluxes are superimposed. In order to discriminate between these morphologically different signal components, a probabilistic algorithm is derived in the language of information field theory based on a hierarchical Bayesian parameter model. The signal inference exploits prior information on the spatial correlation structure of the diffuse component and the brightness distribution of the spatially uncorrelated point-like sources. A maximum a posteriori solution and a solution minimizing the Gibbs free energy of the inference problem using variational Bayesian methods are discussed. Since the derivation of the solution is not dependent on the underlying position space, the implementation of the D3PO algorithm uses the NIFTY package to ensure applicability to various spatial grids and at any resolution. The fidelity of the algorithm is validated by the analysis of simulated data, including a realistic high energy photon count image showing a 32 x 32 arcmin^2 observation with a spatial resolution of 0.1 arcmin. In all tests the D3PO algorithm successfully denoised, deconvolved, and decomposed the data into a diffuse and a point-like signal estimate for the respective photon flux components.

Night Vision Image De-noising of Apple Harvesting Robots Based on the Wavelet Fuzzy Threshold

In this paper, the de-noising problem of night vision images is studied for apple harvesting robots working at night. The wavelet threshold method is applied to the de-noising of night vision image...