Framework For Denoising Research Articles

Game Theory based Framework for Synthetic Aperture Radar Image De-noising and Change Detection

Game Theory based Framework for Synthetic Aperture Radar Image De-noising and Change Detection

TH‐A‐18C‐07: Noise Suppression in Material Decomposition for Dual‐Energy CT

Purpose:A general problem of dual‐energy CT (DECT) is that the decomposition is sensitive to noise in the two sets of dual‐energy projection data, resulting in severely degraded qualities of decomposed images. We have previously proposed an iterative denoising method for DECT. Using a linear decomposition function, the method does not gain the full benefits of DECT on beam‐hardening correction. In this work, we expand the framework of our iterative method to include non‐linear decomposition models for noise suppression in DECT.Methods:We first obtain decomposed projections, which are free of beam‐hardening artifacts, using a lookup table pre‐measured on a calibration phantom. First‐pass material images with high noise are reconstructed from the decomposed projections using standard filter‐backprojection reconstruction. Noise on the decomposed images is then suppressed by an iterative method, which is formulated in the form of least‐square estimation with smoothness regularization. Based on the design principles of a best linear unbiased estimator, we include the inverse of the estimated variance‐covariance matrix of the decomposed images as the penalty weight in the least‐square term. Analytical formulae are derived to compute the variance‐covariance matrix from the measured decomposition lookup table.Results:We have evaluated the proposed method via phantom studies. Using non‐linear decomposition, our method effectively suppresses the streaking artifacts of beam‐hardening and obtains more uniform images than our previous approach based on a linear model. The proposed method reduces the average noise standard deviation of two basis materials by one order of magnitude without sacrificing the spatial resolution.Conclusion:We propose a general framework of iterative denoising for material decomposition of DECT. Preliminary phantom studies have shown the proposed method improves the image uniformity and reduces noise level without resolution loss. In the future, we will perform more phantom studies to further validate the performance of the purposed method.This work is supported by a Varian MRA grant.

RESOLVING SINGLE-LEAD ECG FROM EMG INTERFERENCE IN HOLTER RECORDING BASED ON EEMD

The aim of this study was to propose an electrocardiogram (ECG) de-noising framework based on ensemble empirical mode decomposition (EEMD) to eliminate electromyography (EMG) interference without signal distortion. ECG signals are easily corrupted by EMG, especially in Holter monitor recordings. The frequency component overlapping between EMG and ECG is a challenge in signal processing that remains to be solved. The aim of the present study, therefore, was to resolve ECG signals from recorded segments with EMG noise. Two units were put into our proposed framework; first, modified moving average filter for signal preprocessing to cancel baseline wandering, and second, EEMD to cancel EMG. In order to enhance the de-noising capability (such as signal distortion in traditional EEMD), we developed a novel EEMD signal reconstruction algorithm using a statistical ECG model. We tested the proposed framework using MIT-BIH database, artificial and single-lead recorded real-world noisy signals. Correlation coefficients and ECG morphological features were used to evaluate the performance of the proposed algorithm. Our results showed that the proposed de-noising algorithm successfully resolved ECG signals from baseline wandering and EMG interference without distorting the signal waveform.

An Alternative Variational Framework for Image Denoising

We propose an alternative framework for total variation based image denoising models. The model is based on the minimization of the total variation with a functional coefficient, where, in this case, the functional coefficient is a function of the magnitude of image gradient. We determine the considerations to bear on the choice of the functional coefficient. With the use of an example functional, we demonstrate the effectiveness of a model chosen based on the proposed consideration. In addition, for the illustrative model, we prove the existence and uniqueness of the minimizer of the variational problem. The existence and uniqueness of the solution associated evolution equation are also established. Experimental results are included to demonstrate the effectiveness of the selected model in image restoration over the traditional methods of Perona-Malik (PM), total variation (TV), and the D-α-PM method.

Patch‐Collaborative Spectral Point‐Cloud Denoising

AbstractWe present a new framework for point cloud denoising by patch‐collaborative spectral analysis. A collaborative generalization of each surface patch is defined, combining similar patches from the denoised surface. The Laplace–Beltrami operator of the collaborative patch is then used to selectively smooth the surface in a robust manner that can gracefully handle high levels of noise, yet preserves sharp surface features. The resulting denoising algorithm competes favourably with state‐of‐the‐art approaches, and extends patch‐based algorithms from the image processing domain to point clouds of arbitrary sampling. We demonstrate the accuracy and noise‐robustness of the proposed algorithm on standard benchmark models as well as range scans, and compare it to existing methods for point cloud denoising.

Bayesian denoising framework of phonocardiogram based on a new dynamical model

In this paper, we introduce a model-based Bayesian denoising framework for phonocardiogram (PCG) signals. The denoising framework is founded on a new dynamical model for PCG, which is capable of generating realistic synthetic PCG signals. The introduced dynamical model is based on PCG morphology and is inspired by electrocardiogram (ECG) dynamical model proposed by McSharry et al. and can represent various morphologies of normal PCG signals. The extended Kalman smoother (EKS) is the Bayesian filter that is used in this study. In order to facilitate the adaptation of the denoising framework to each input PCG signal, the parameters are selected automatically from the input signal itself. This approach is evaluated on several PCGs recorded on healthy subjects, while artificial white Gaussian noise is added to each signal, and the SNR and morphology of the outputs of the proposed denoising approach are compared with the outputs of the wavelet denoising (WD) method. The results of the EKS demonstrate better performance than WD over a wide range of PCG SNRs. The new PCG dynamical model can also be employed to develop other model-based processing frameworks such as heart sound segmentation and compression.

Model-based adaptive resolution upconversion of degraded images

Resolution upconversion of a degraded image is an ill-posed inverse problem that is even harder than video superresolution due to lack of redundant observations from reference frames. To overcome this difficulty an adaptive 2D piecewise autoregressive (PAR) model is used to strengthen the constraints on the solution of the inverse problem. The PAR model can be fit to local image waveforms by adjusting its parameters. But estimating the model parameters needs the knowledge of the very original high-resolution pixels to be estimated by the model. We resolve this chicken-and-egg dilemma by adaptive nonlinear least-squares joint estimation of both model parameters and original pixels. This non-linear estimation problem is solved by the method of structured total least-squares, constrained by the degradation function (e.g., the point spread function of a camera plus noises) that forms the observed low-resolution image. As such, this work offers a unified general framework for joint upsampling, deconvolution, and denoising. Moreover, the upsampling can be carried out at an arbitrary scale rather than power of two. Experiments show that the proposed NEARU technique outperforms current methods in both PSNR and subjective visual quality, and its advantage becomes greater for larger scaling factors.

A multiresolution framework for local similarity based image denoising

In this paper, we present a generic framework for denoising of images corrupted with additive white Gaussian noise based on the idea of regional similarity. The proposed framework employs a similarity function using the distance between pixels in a multidimensional feature space, whereby multiple feature maps describing various local regional characteristics can be utilized, giving higher weight to pixels having similar regional characteristics. An extension of the proposed framework into a multiresolution setting using wavelets and scale space is presented. It is shown that the resulting multiresolution multilateral (MRM) filtering algorithm not only eliminates the coarse-grain noise but can also faithfully reconstruct anisotropic features, particularly in the presence of high levels of noise.

Nonlocal means-based denoising for medical images.

Medical images often consist of low-contrast objects corrupted by random noise arising in the image acquisition process. Thus, image denoising is one of the fundamental tasks required by medical imaging analysis. Nonlocal means (NL-means) method provides a powerful framework for denoising. In this work, we investigate an adaptive denoising scheme based on the patch NL-means algorithm for medical imaging denoising. In contrast with the traditional NL-means algorithm, the proposed adaptive NL-means denoising scheme has three unique features. First, we use a restricted local neighbourhood where the true intensity for each noisy pixel is estimated from a set of selected neighbouring pixels to perform the denoising process. Second, the weights used are calculated thanks to the similarity between the patch to denoise and the other patches candidates. Finally, we apply the steering kernel to preserve the details of the images. The proposed method has been compared with similar state-of-art methods over synthetic and real clinical medical images showing an improved performance in all cases analyzed.

A General Framework for Sparsity-Based Denoising and Inversion

Estimating a reliable and stable solution to many problems in signal processing and imaging is based on sparse regularizations, where the true solution is known to have a sparse representation in a given basis. Using different approaches, a large variety of regularization terms have been proposed in literature. While it seems that all of them have so much in common, a general potential function which fits most of them is still missing. In this paper, in order to propose an efficient reconstruction method based on a variational approach and involving a general regularization term (including most of the known potential functions, convex and nonconvex), we deal with i) the definition of such a general potential function, ii) the properties of the associated “proximity operator” (such as the existence of a discontinuity), and iii) the design of an approximate solution of the general “proximity operator” in a simple closed form. We also demonstrate that a special case of the resulting “proximity operator” is a set of shrinkage functions which continuously interpolate between the soft-thresholding and hard-thresholding. Computational experiments show that the proposed general regularization term performs better than <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ℓ</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -penalties for sparse approximation problems. Some numerical experiments are included to illustrate the effectiveness of the presented new potential function.

Image denoising with anisotropic bivariate shrinkage

This paper presents a novel image denoising algorithm based on the modeling of wavelet coefficients with an anisotropic bivariate Laplacian distribution function. The anisotropic bivariate Laplacian model not only captures the child–parent dependency between wavelet coefficients, but also fits the anisotropic property of the variances of wavelet coefficients in different scales of natural images. With this statistical model, we derive a closed-form anisotropic bivariate shrinkage function in the framework of Bayesian denoising and a new image denoising approach with local marginal variance estimation based on this newly derived shrinkage function is proposed in the discrete wavelet transform (DWT) domain. The proposed anisotropic bivariate shrinkage approach is also extended to the dual-tree complex wavelet transform (DT-CWT) domain to further improve the performance of image denoising. To take full advantage of DT-CWT, a more accurate noise variance estimator is proposed and the way the anisotropic bivariate shrinkage function applied to the magnitudes of DT-CWT coefficients is presented. Experiments were carried out in both the DWT and the DT-CWT domain to validate the effectiveness of the proposed method. Using a representative set of standard test images corrupted by additive white Gaussian noise, the simulation results show that the proposed method provides promising results and is competitive with the best wavelet-based denoising results reported in the literature both in terms of peak signal-to-noise ratio (PSNR) and in visual quality.

Fusion of noisy infrared and visible images based on anisotropic bivariate shrinkage

The performance of wavelet-based image fusion can be improved by taking into account the statistical dependencies between wavelet coefficients. This paper focuses on the fusion of noisy infrared and visible images and presents a new image fusion approach based on the modeling of wavelet coefficients with an anisotropic bivariate Laplacian distribution function. The use of the anisotropic bivariate Laplacian model not only captures the dependencies between wavelet coefficients and their parents, but also fits the fact that the variances of wavelet coefficients of natural images are quite different from scale to scale. Based on this statistical model together with the assumption of additive white Gaussian noise, a closed-form anisotropic bivariate shrinkage function is derived within the framework of Bayesian denoising. Then an improved image fusion algorithm is proposed by incorporating the newly derived shrinkage approach into the fusion scheme. The performance of the proposed method was compared with three other methods and was found to perform the best in terms of both visual quality and objective metric Q AB / F n [17] when tested on four representative sets of infrared and visible images corrupted by additive white Gaussian noise.

Synthetic ECG generation and Bayesian filtering using a Gaussian wave-based dynamical model

In this paper, we describe a Gaussian wave-based state space to model the temporal dynamics of electrocardiogram (ECG) signals. It is shown that this model may be effectively used for generating synthetic ECGs as well as separate characteristic waves (CWs) such as the atrial and ventricular complexes. The model uses separate state variables for each CW, i.e. P, QRS and T, and hence is capable of generating individual synthetic CWs as well as realistic ECG signals. The model is therefore useful for generating arrhythmias. Simulations of sinus bradycardia, sinus tachycardia, ventricular flutter, atrial fibrillation and ventricular tachycardia are presented. In addition, discrete versions of the equations are presented for a model-based Bayesian framework for denoising. This framework, together with an extended Kalman filter and extended Kalman smoother, was used for denoising the ECG for both normal rhythms and arrhythmias. For evaluating the denoising performance, the signal-to-noise ratio (SNR) improvement of the filter outputs and clinical parameter stability were studied. The results demonstrate superiority over a wide range of input SNRs, achieving a maximum 12.7 dB improvement. Results indicate that preventing clinically relevant distortion of the ECG is sensitive to the number of model parameters. Models are presented which do not exhibit such distortions. The approach presented in this paper may therefore serve as an effective framework for synthetic ECG generation and model-based filtering of noisy ECG recordings.

Recursive framework for joint inpainting and de-noising of photographic films

We address the problem of inpainting noisy photographs. We present a recursive image recovery scheme based on the unscented Kalman filter (UKF) to simultaneously inpaint identified damaged portions in an image and suppress film-grain noise. Inpainting of the missing observations is guided by a mask-dependent reconstruction of the image edges. Prediction within the UKF is based on a discontinuity-adaptive Markov random field prior that attempts to preserve edges while achieving noise reduction in uniform regions. We demonstrate the capability of the proposed method with many examples.

SURE-Based Non-Local Means

Non-local means (NLM) provides a powerful framework for denoising. However, there are a few parameters of the algorithm-most notably, the width of the smoothing kernel-that are data-dependent and difficult to tune. Here, we propose to use Stein's unbiased risk estimate (SURE) to monitor the mean square error (MSE) of the NLM algorithm for restoration of an image corrupted by additive white Gaussian noise. The SURE principle allows to assess the MSE without knowledge of the noise-free signal. We derive an explicit analytical expression for SURE in the setting of NLM that can be incorporated in the implementation at low computational cost. Finally, we present experimental results that confirm the optimality of the proposed parameter selection.

Wavelet Denoising of Coarsely Quantized Signals

This paper presents a practical wavelet-based approach to denoising coarsely quantized signals. Such signals can arise from the status data collected within large-scale engineering plants employing traditional limit checking fault detection and identification (FDI). Transitioning such plants to more advanced FDI techniques requires that the coarsely quantized data be accurately denoised. As FDI by its nature is concerned with the analysis of nonstationary signals, wavelets offer an appropriate denoising framework. Existing techniques for optimal wavelet denoising presuppose Gaussian noise contamination and, hence, are suboptimal for coarsely quantized signals. In this paper, a secondary correction stage is added to the standard wavelet-denoising process to improve its denoising performance on coarsely quantized signals. This correction stage exploits a priori knowledge of the known coarsely quantized signal dependencies to tune the wavelet thresholds. The effectiveness of the approach is demonstrated through the analysis of real-world data collected from an operational large-scale engineering plant

Robust estimation approach for blind denoising

This work develops a new robust statistical framework for blind image denoising. Robust statistics addresses the problem of estimation when the idealized assumptions about a system are occasionally violated. The contaminating noise in an image is considered as a violation of the assumption of spatial coherence of the image intensities and is treated as an outlier random variable. A denoised image is estimated by fitting a spatially coherent stationary image model to the available noisy data using a robust estimator-based regression method within an optimal-size adaptive window. The robust formulation aims at eliminating the noise outliers while preserving the edge structures in the restored image. Several examples demonstrating the effectiveness of this robust denoising technique are reported and a comparison with other standard denoising filters is presented.