Conventional Denoising Research Articles

Denoising of Fetal Phonocardiogram Signal by Wavelet Transformation

Auscultation is still one of the most basic analytical tools used to determine the fetal heart’s functional state as well as the first fetal well-being measure. It is called fetal phonocardiography (fPCG) in its modern form. The technique of fPCG is passive and can be used to track long-term. Robust signal processing techniques are required to denoise the signals in order to improve the diagnostic capabilities of fPCG. A linear filter is used to eliminate distortion and interference from the fPCG signals through conventional denoising techniques. This paper searched for optimal configuration of the wavelet based denoising system. Based on the experimental results, can be conclude that the signal should be decomposed on six levels. From this it can be seen that the lowest MSE (mean square error) value is the use of coiflets three with SURE threshold algorithm with hard threshold parameters.

High-ISO Long-Exposure Image Denoising Based on Quantitative Blob Characterization.

Blob detection and image denoising are fundamental, sometimes related tasks in computer vision. In this paper, we present a computational method to quantitatively measure blob characteristics using normalized unilateral second-order Gaussian kernels. This method suppresses non-blob structures while yielding a quantitative measurement of the position, prominence and scale of blobs, which can facilitate the tasks of blob reconstruction and blob reduction. Subsequently, we propose a denoising scheme to address high-ISO long-exposure noise, which sometimes spatially shows a blob appearance, employing a blob reduction procedure as a cheap preprocessing for conventional denoising methods. We apply the proposed denoising methods to real-world noisy images as well as standard images that are corrupted by real noise. The experimental results demonstrate the superiority of the proposed methods over state-of-the-art denoising methods.

Desert seismic signal denoising by 2D compact variational mode decomposition

AbstractNoise suppression and effective signal recovery are very important for seismic signal processing. The random noise in desert areas has complex characteristics due to the complex geographical environment; noise characteristics such as non-stationary, non-linear and low frequency. These make it difficult for conventional denoising methods to remove random noise in desert seismic records. To address the problem, this paper proposes a two-dimensional compact variational mode decomposition (2D-CVMD) algorithm for desert seismic noise attenuation. This model decomposes the complex desert seismic data into an finite number of intrinsic mode functions with specific directions and vibration characteristics. The algorithm introduces binary support functions, which can detect the edge region of the signal in each mode by penalizing the support function through the L1 and total variation (TV) norm. Finally, the signal can be reconstructed by the support functions and the decomposed modes. We apply the 2D-CVMD algorithm to synthetic and real seismic data. The results show that the 2D-CVMD algorithm can not only suppress desert low-frequency noise, but also recover the weak effective signal.

Simultaneous denoising of multicomponent microseismic data by joint sparse representation with dictionary learning

Microseismic data usually have a low signal-to-noise ratio, necessitating the application of an effective denoising method. Most conventional denoising methods treat each component of multicomponent data separately, e.g., denoising methods with sparse representation. However, microseismic data are often acquired with a 3C receiver, especially in borehole monitoring cases. Independent denoising ignores the relative amplitudes and vector relationships between different components. We have developed a new simultaneous denoising method for 3C microseismic data based on joint sparse representation. The three components are represented by different dictionary atoms; the dictionary can be fixed or adaptive depending on the dictionary learning method that is used. Our method adds an extra time consistency constraint with simultaneous transformation of 3C data. The joint sparse optimization problem is solved using the extended orthogonal matching pursuit. Synthetic microseismic data with a double-couple source mechanism and two field downhole microseismic data were used for testing. Independent denoising of 1C data with the fixed dictionary method and simultaneous denoising of 3C data with the fixed dictionary and dictionary learning (3C-DL) methods were compared. The results indicate that among the three methods, the 3C-DL method is the most effective in suppressing random noise, preserving weak signals, and restoring polarization information; this is achieved by combining the time consistency constraint and dictionary learning.

GAM-Based Mooring Alignment for SINS Based on An Improved CEEMD Denoising Method.

To solve the self-alignment problem of the Strapdown Inertial Navigation System (SINS), a novel adaptive filter based on Complementary Ensemble Empirical Mode Decomposition (CEEMD) is proposed. The Gravitational Apparent Motion (GAM) is used in the coarse alignment, and the problem of obtaining the attitude matrix between the body frame and the navigation frame is attributed to obtaining the matrix between the initial body frame and the current navigation frame using two gravitational apparent motion vectors at different moments. However, the accuracy and time of this alignment method always suffer from the measurement noise of sensors. Thus, a novel adaptive filter based on CEEMD using an -norm to calculate the similarity measure between the Probability Density Function (PDF) of each Intrinsic Mode Function (IMF) and the original signal is proposed to denoise the measurements of the accelerometer. Furthermore, the advantage of this filter is verified by comparing with other conventional denoising methods, such as PDF-based EMD (EMD-PDF) and the Finite Impulse Response (FIR) digital low-pass filter method. The results of the simulation and experiments indicate that the proposed method performs better than the conventional methods in both alignment time and alignment accuracy.

Use of a Tracer-Specific Deep Artificial Neural Net to Denoise Dynamic PET Images

Application of kinetic modeling (KM) on a voxel level in dynamic PET images frequently suffers from high levels of noise, drastically reducing the precision of parametric image analysis. In this paper, we investigate the use of machine learning and artificial neural networks to denoise dynamic PET images. We train a deep denoising autoencoder (DAE) using noisy and noise-free spatiotemporal image patches, extracted from the simulated images of [11C]raclopride, a dopamine D2 receptor agonist. The DAE-processed dynamic and corresponding parametric images (simulated and acquired) are compared with those obtained with conventional denoising techniques, including temporal and spatial Gaussian smoothing, iterative spatiotemporal smoothing/deconvolution, and the highly constrained backprojection processing (HYPR). The simulated (acquired) parametric image non-uniformity was 7.75% (19.49%) with temporal and 5.90% (14.50%) with spatial smoothing, 5.82% (16.21%) with smoothing/deconvolution, 5.49% (13.38%) with HYPR, and 3.52% (11.41%) with DAE. The DAE also produced the best results in terms of the coefficient of variation of voxel values and structural similarity index. Denoising-induced bias in the regional mean binding potential was 7.8% with temporal and 26.31% with spatial smoothing, 28.61% with smoothing/deconvolution, 27.63% with HYPR, and 14.8% with DAE. When the test data did not match the training data, erroneous outcomes were obtained. Our results demonstrate that a deep DAE can provide a substantial reduction in the voxel-level noise compared with the conventional spatiotemporal denoising methods while introducing a similar or lower amount of bias. The better DAE performance comes at the cost of lower generality and requiring appropriate training data.

A hybrid learning-based framework for seismic denoising

Noise attenuation has been a long-standing problem in seismic data processing. It presents unique challenges on land due to a complex near surface coupled with unavoidable environmental noise sources. In many cases, weak signals are embedded in much stronger noise, which makes conventional methods less effective at extracting those signals. In addition, conventional methods may lack adaptability to various noise types and patterns. Machine learning has shown great promise in solving geophysical problems including seismic data processing and interpretation. Here, we propose a novel method that is applicable to attenuating both incoherent noise, such as environmental noise, and coherent noise, such as ground roll and scattered noise, under a unified learning-based framework. This framework takes advantage of conventional methods to build the initial models and then employs dictionary learning and sparse inversion to invert both signal and noise simultaneously. The proposed method augments conventional methods by leveraging learning to recover residual weak signals from strong noise. We have applied this hybrid learning-based method successfully to some of the most difficult data areas where conventional denoising methods underperformed. Synthetic and real data examples demonstrate the effectiveness of the method for various noise types.

Seismic data denoising for complex structure using BM3D and local similarity

BM3D (Block Matching and 3D collaborative filtering) is an effective algorithm for random noise attenuation. It can create the denoised data with high signal-to-noise ratio. Different from the conventional denoising methods that apply just one set of fixed parameters to the whole section, BM3D denoises the digital image (seismic data) patch by patch. This method utilizes the redundant information on similar patches to obtain the final denoised results, thus getting the more obvious effect than the conventional ones. However, when applied to the seismic data with complex structure, it may do some harm to the details of structure and lower the fidelity of reflected signal due to the average effect and some threshold operations in the transform domain. To overcome this problem, we introduce the local similarity into BM3D method, which provides a standard on how similar it is between signal and noise. With this novel method (called BM3DL), we can recover the leaking signal energy from the noisy section and add it back to the denoised result. The synthetic models and real data examples show that this combined method can improve the signal-to-noise ratio of denoised section and keep the fidelity of structure effectively.

Low-Frequency Noise Suppression Method Based on Improved DnCNN in Desert Seismic Data

High-quality seismic data are the basis for stratigraphic imaging and interpretation, but the existence of random noise can greatly affect the quality of seismic data. At present, most understanding and processing of random noise still stay at the level of Gaussian white noise. With the reduction of resource, the acquired seismic data have lower signal-to-noise ratio and more complex noise natures. In particular, the random noise in the desert area has the characteristics of low frequency, non-Gaussian, nonstationary, high energy, and serious aliasing between effective signal and random noise in the frequency domain, which has brought great difficulties to the recovery of seismic events by conventional denoising methods. To solve this problem, an improved feed-forward denoising convolution neural network (DnCNN) is proposed to suppress random noise in desert seismic data. DnCNN has the characteristics of automatic feature extraction and blind denoising. According to the characteristics of desert noise, we modify the original DnCNN from the aspects of patch size, convolution kernel size, network depth, and training set to make it suitable for low-frequency and non-Gaussian desert noise suppression. Both simulation and practical experiments prove that the improved DnCNN has obvious advantages in terms of desert noise and surface wave suppression as well as effective signal amplitude preservation. In addition, the improved DnCNN, in contrast to existing methods, has considerable potential to benefit from large data sets. Therefore, we believe that it can open a new direction in the area of seismic data processing.

High-field mr diffusion-weighted image denoising using a joint denoising convolutional neural network.

Low signal-to-noise ratio (SNR) has been a major limiting factor for the application of higher-resolution diffusion-weighted imaging (DWI). Most of the conventional denoising models suffer from the drawbacks of shallow feature extraction and hand-crafted parameter tuning. Although multiple studies have shown the promising applications of image denoising using convolutional neural networks (CNNs), none of them have considered denoising multiple b-value DWIs using a multichannel CNN model. To present a joint denoising CNN (JD-CNN) model to improve the SNR of multiple b-value DWI. Retrospective technical development. Twenty healthy rats and two rats with clinically confirmed focal cortical dysplasia were included to evaluate the performance of the proposed method. 11.7T MRI, a multiple b-values DWI sequence. The total variation (TV) and BM3D denoising methods were also performed on the same dataset for comparison. Peak SNR (PSNR) and normalized mean square error (NMSE) were calculated for the assessment of image qualities. A paired Student's t-test was conducted to compare the diffusion parameter measurements between different approaches. P < 0.01 was considered statistically significant. Simulation results showed substantial improvement of image quality after JD-CNN denoising (PSNR of original image: 23.15 ± 1.77; PSNR of denoised image: 42.94 ± 2.12). The proposed method outperforms the state-of-the-art methods on high b-value DWIs in terms of PSNR (TV: 33.51 ± 0.83, BM3D: 35.12 ± 0.94, JD-CNN: 46.52 ± 0.98). In addition, the NMSE of the estimated apparent diffusion coefficient (ADC) reduces from 0.72 ± 0.13 to 0.45 ± 0.06 (P < 0.01) with the application of the JD-CNN model. The proposed method is able to remove noise with a wide range of noise levels in multiple b-value DWI and improve the diffusion parameter estimation. This shows potential clinical promise. 2 Technical Efficacy Stage: 2 J. Magn. Reson. Imaging 2019;50:1937-1947.

Regularized pseudo-phase imaging for inspecting and sensing nanoscale features.

Recovering tiny nanoscale features using a general optical imaging system is challenging because of poor signal to noise ratio. Rayleigh scattering implies that the detectable signal of an object of size d illuminated by light of wavelength λ is proportional to d6/λ4, which may be several orders of magnitude weaker than that of additive and multiplicative perturbations in the background. In this article, we solve this fundamental issue by introducing the regularized pseudo-phase, an observation quantity for polychromatic visible light microscopy that seems to be more sensitive than conventional intensity images for characterizing nanoscale features. We achieve a significant improvement in signal to noise ratio without making any changes to the imaging hardware. In addition, this framework not only retains the advantages of conventional denoising techniques, but also endows this new measurand (i.e., the pseudo-phase) with an explicit physical meaning analogous to optical phase. Experiments on a NIST reference material 8820 sample demonstrate that we can measure nanoscale defects, minute amounts of tilt in patterned samples, and severely noise-polluted nanostructure profiles with the pseudo-phase framework even when using a low-cost bright-field microscope.

Desert seismic random noise reduction based on LDA effective signal detection

At present, the seismic exploration of mineral resources such as unknown oil fields and natural gas fields has become the focus and difficulty. The Tarim Oilfield located in the desert area of northwest China has many uncertainties due to complicated geological structure and resource burial conditions. And the seismic record collected carries various noises, especially random noise with complex features, including non-stationary, non-Gaussian, nonlinear and low frequency. The seismic events are contaminated by random noise. Also the effective signal of desert seismic record is in the same frequency band as the random noise. These situations have brought great difficulties in denoising by conventional methods. In this paper, a noise reduction framework based on linear discriminant analysis effective signal detection in desert seismic record is proposed to solve this problem. At first, the method utilizes the difference between the effective signals and the noise in the low-dimensional space. The seismic data are divided into the effective signal cluster and the noise cluster. Then, the effective signal is extracted to realize the position of the seismic events. Finally, the conventional filter is matched to obtain better denoising results. The framework is applied to synthetic desert seismic records and real desert seismic records. The experimental results show that denoising capability after detecting effective signals is obviously better than those of conventional denoising methods. The accuracy of the seismic effective signal detection is higher, and the seismic events’ continuity is maintained better.

Catenary image denoising method using lifting wavelet-based contourlet transform with cycle shift-invariance

In the catenary status detection system based on the image processing, quality of the captured catenary image is critical. In order to obtain a high quality image for further analysis, this paper proposes a new catenary image denoising method based on lifting wavelet-based contourlet transform with cycle shift-invariance (LWBCTCS). In this method, the lifting wavelet is first constructed based on wavelet transform (WT). Then, to decrease the redundancy of contourlet transform (CT), the lifting wavelet-based contourlet transform (LWBCT) is built by using the lifting wavelet to replace the Laplacian pyramid (LP) transform of CT. Finally, the LWBCT with the cycle shift-invariance (LWBCTCS) algorithm is combined to reduce the pseudo-Gibbs phenomena of LWBCT. The proposed method not only has the virtues of multi-scale and multi-direction, but also reduces the visual artifacts in the denoised image. The results of comparative experiments with captured catenary image show that the proposed method can achieve satisfactory denoising performance, in particular, for catenary image with abundant texture and detail outline information. It not only eliminates noise but also preserves the textures and details simultaneously. Besides, comprehensive consideration of the denoising performance shows that the proposed algorithm in terms of the signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR) and mean squared error (MSE) is stable than those conventional denoising algorithms, including WT, CT, curvelet transform (CV) and BLS-GSM methods. The visual quality as well as quantitative metrics is superior than those conventional denoising methods.

Efficient and Robust Non-Local Means Denoising Methods for Biomedical Images

Denoising is an important step to improve image quality and to increase the performance of image analysis. However, conventional partial differential equation based image denoising methods, especially total variation functional minimization techniques, do not work very well on biomedical images such as magnetic resonance images (MRI), ultrasound, and X-ray images. These images present small structures with signals barely detectable above the noise level which involve more complex noise and unclear edges. The recently developed non-local means (NLM) filtering method can treat these types of images better. The standard NLM filter uses the weighted averages of similar patches present in the image. Since the NLM filter is anon-local averaging method, it is very accurate in removing noise but has computational complexity. We develop efficient and optimized NLM based methods and their associate numerical algorithms. The new methods are still accurate enough and moreeffi-cient than the original NLM filter. Numerical results show that the new methods compare favorably to the conventional denoising methods.

Optimal VMD-Based Signal Denoising for Laser Radar via Hausdorff Distance and Wavelet Transform

Laser radar echo signals are easily contaminated by noise, such as background light and electronic noise, and this noise is an obstacle for the subsequent signal detection. However, the conventional denoising methods cannot achieve satisfactory effects when the signal-to-noise-ratio (SNR) is ultralow. In this paper, a novel denoising method for laser radar echo signals based on the parameter-optimal variational mode decomposition (VMD) combined with the Hausdorff distance (HD) and wavelet transform (WT) is proposed. Compared with conventional VMD-based methods, the proposed method utilizes a newly developed grasshopper optimization algorithm (GOA) to obtain the optimal combination of parameters for the VMD. Then, the HD is applied to select the relevant modes and then uses the basis function to reconstruct the signal. In addition, the relevant modes are further processed by the WT denoising method, which allows the reconstructed signal to obtain a higher SNR. The simulation and experimental results show the feasibility, effectiveness and robustness of the proposed method compared to three other available denoising techniques. The proposed method could promote the distance measurement performance of laser radars in harsh environments.

Integrated multi-echo denoising strategy improves identification of inherent language laterality.

Although increasingly used in both neuroscience and clinical studies, a major challenge facing resting-state FMRI (rs-FMRI) still lies in isolating BOLD signal fluctuations resulting from neuronal activity from noise. In this study, we investigated the effect of a newly proposed denoising approach, integrated multi-echo rs-FMRI analysis, on language mapping. Multiband multi-echo rs-FMRI data were acquired, along with language task FMRI that identified language areas in the left hemisphere of 12 subjects. The language laterality and specificity of the language mapping given by seed-based correlation analysis were compared among the rs-FMRI data sets pre-processed using 3 different approaches: multi-echo data with integrated multi-echo independent component analysis, denoising that uses the TE-dependency of each signal component to judge its origin, and multi-echo and single-echo data with conventional denoising. The laterality index was automatically computed without setting any threshold to minimize the arbitrariness and to ensure the generality of the result. A repeated measures analysis of variance followed by post hoc tests showed that optimal combination of the 3-echo data succeeded in increasing the correlation within the targeted language system. With the physically principled multi-echo denoising approach, the integrated strategy further succeeded in revealing areas of synchronization more specific to the language system compared with conventional denoising approach, which eventually improved the identification of the laterality of the system. By successfully reducing non-specific correlations spreading over the brain, integrated multi-echo approach improved language mapping and identification of the laterality of the system using rs-FMRI.

Noise removal in medical mammography images using fast non-local means denoising algorithm for early breast cancer detection: a phantom study

Denoising plays a crucial role in the field of medical imaging in regard to the improvement of image quality. In this study, a fast nonlocal means (FNLM) denoising algorithm which utilizes neighborhood filtering is proposed and implemented for early breast cancer detection based on medical mammography. For comparison with conventional denoising methods, the Wiener filter and total variation (TV) denoising algorithm were used. The temporal resolution, coefficient of variation (COV), and contrast to noise ratio (CNR) were evaluated for three exposure conditions: (a) various tube voltages at fixed 40 mAs, (b) various tube currents at fixed 28 kVp, and (c) auto exposure control mode. The results showed that the proposed FNLM denoising algorithm can achieve a similar temporal resolution to the Wiener filter and may efficiently reduce image noise by using COV and CNR values in mammography.

Quantitative estimation of nonlinearity parameter of noised lamb waves using a chaotic oscillator

Because of the difficulty in quantifying weak nonlinear Lamb waves in strong noises, the second harmonic generated by material nonlinearity or microcontact crack is detected using the Duffing-Van der Pol oscillator (DVPO), and its relative intensity is quantified based on the periodic trajectory area exponent (PTAE) of the oscillator output. In this paper, the windowed harmonic is amplified by different magnification factors and then fed into the DVPO. The linear fitting relationship between the amplification factor and the PTAE is established, from which the absolute amplitude of the second harmonic is estimated. The simulations on aluminum plates with different sizes of contact microcracks validate that the PTAE can quantify the intensity of the second harmonic generated by contact microcracks. Moreover, the experimental data of aluminum plate also demonstrate that the proposed method can more accurately quantify the material nonlinearity in a noisy environment than other conventional denoising methods.

Random noise attenuation of non-uniformly sampled 3D seismic data along two spatial coordinates using non-equispaced curvelet transform

The attenuation of random noise is important for improving the signal to noise ratio (SNR). However, the precondition for most conventional denoising methods is that the noisy data must be sampled on a uniform grid, making the conventional methods unsuitable for non-uniformly sampled data. In this paper, a denoising method capable of regularizing the noisy data from a non-uniform grid to a specified uniform grid is proposed. Firstly, the denoising method is performed for every time slice extracted from the 3D noisy data along the source and receiver directions, then the 2D non-equispaced fast Fourier transform (NFFT) is introduced in the conventional fast discrete curvelet transform (FDCT). The non-equispaced fast discrete curvelet transform (NFDCT) can be achieved based on the regularized inversion of an operator that links the uniformly sampled curvelet coefficients to the non-uniformly sampled noisy data. The uniform curvelet coefficients can be calculated by using the inversion algorithm of the spectral projected-gradient for ℓ1-norm problems. Then local threshold factors are chosen for the uniform curvelet coefficients for each decomposition scale, and effective curvelet coefficients are obtained respectively for each scale. Finally, the conventional inverse FDCT is applied to the effective curvelet coefficients. This completes the proposed 3D denoising method using the non-equispaced curvelet transform in the source-receiver domain. The examples for synthetic data and real data reveal the effectiveness of the proposed approach in applications to noise attenuation for non-uniformly sampled data compared with the conventional FDCT method and wavelet transformation.

A method of combining coherence-constrained sparse coding and dictionary learning for denoising

We have addressed the seismic data denoising problem, in which the noise is random and has an unknown spatiotemporally varying variance. In seismic data processing, random noise is often attenuated using transform-based methods. The success of these methods in denoising depends on the ability of the transform to efficiently describe the signal features in the data. Fixed transforms (e.g., wavelets, curvelets) do not adapt to the data and might fail to efficiently describe complex morphologies in the seismic data. Alternatively, dictionary learning methods adapt to the local morphology of the data and provide state-of-the-art denoising results. However, conventional denoising by dictionary learning requires a priori information on the noise variance, and it encounters difficulties when applied for denoising seismic data in which the noise variance is varying in space or time. We have developed a coherence-constrained dictionary learning (CDL) method for denoising that does not require any a priori information related to the signal or noise. To denoise a given window of a seismic section using CDL, overlapping small 2D patches are extracted and a dictionary of patch-sized signals is trained to learn the elementary features embedded in the seismic signal. For each patch, using the learned dictionary, a sparse optimization problem is solved, and a sparse approximation of the patch is computed to attenuate the random noise. Unlike conventional dictionary learning, the sparsity of the approximation is constrained based on coherence such that it does not need a priori noise variance or signal sparsity information and is still optimal to filter out Gaussian random noise. The denoising performance of the CDL method is validated using synthetic and field data examples, and it is compared with the K-SVD and FX-Decon denoising. We found that CDL gives better denoising results than K-SVD and FX-Decon for removing noise when the variance varies in space or time.