Classical Denoising Methods Research Articles

Attenuation of non-stationary random noise in ground penetrating radar data based on time-varying filtering

The attenuation of random noise is significant in the enhancement of the signal-to-noise ratio in ground penetrating radar (GPR) data. However, the non-stationary nature of random noise poses significant challenges to most conventional denoising methods. We propose a time-varying bandpass filter (TVBF) based on the local maxima multiple synchrosqueezing transform (LMMSST), referred to as TVBFLMMSST, for the attenuation of non-stationary random noise in GPR data. The LMMSST method is introduced to achieve highly compressed time–frequency representation (TFR). By integrating an instantaneous frequency trajectory detection algorithm, we design the TVBF to successfully separate useful signals from random noise. The efficacy of the TVBFLMMSST is validated through synthetic and field experiments, demonstrating its capability to effectively isolate components of useful signals and noise signals. Compared to classical denoising methods, TVBFLMMSST exhibits robust performance in attenuating random noise while preserving the amplitude of useful signals.

Denoising OCT videos based on temporal redundancy

The identification of eye diseases and their progression often relies on a clear visualization of the anatomy and on different metrics extracted from Optical Coherence Tomography (OCT) B-scans. However, speckle noise hinders the quality of rapid OCT imaging, hampering the extraction and reliability of biomarkers that require time series. By synchronizing the acquisition of OCT images with the timing of the cardiac pulse, we transform a low-quality OCT video into a clear version by phase-wrapping each frame to the heart pulsation and averaging frames that correspond to the same instant in the cardiac cycle. Here, we compare the performance of our one-cycle denoising strategy with a deep-learning architecture, Noise2Noise, as well as classical denoising methods such as BM3D and Non-Local Means (NLM). We systematically analyze different image quality descriptors as well as region-specific metrics to assess the denoising performance based on the anatomy of the eye. The one-cycle method achieves the highest denoising performance, increases image quality and preserves the high-resolution structures within the eye tissues. The proposed workflow can be readily implemented in a clinical setting.

Image-Based Crack Detection Using Total Variation Strain DVC Regularization

Introduction: Accurately detecting cracks is crucial for assessing the health of materials. Manual detection methods are time-consuming, leading to the development of automatic detection techniques based on image processing and machine learning. These methods utilize morphological image processing and material deformation analysis through Digital Image or Volume Correlation techniques (DIC/DVC) to identify cracks. The strain field derived from DIC/DVC tends to be noisy. Traditional denoising methods sacrifice spatial resolution, limiting their effectiveness in capturing abrupt structural deformations such as fractures. Method: In this study, a novel DVC regularization method is proposed to obtain a sharper and less noisy strain field. The method minimizes the total variation of spatial strain field components based on the assumption of approximate strain constancy within material phases. Results: The proposed methodology is validated using simulated data and actual 4D μ-CT experimental data. Compared to classical denoising methods, the proposed DVC regularization method provides a more reliable crack detection with fewer false positives. Conclusions: These results highlight the possibility of estimating a low-noise strain field without relying on the spatial smoothness assumption, thereby improving accuracy and reliability in crack detection.

Deep learning-based denoising of acoustic images generated with point contact method

Abstract The versatile nature of ultrasound imaging finds applications in various fields. A point contact excitation and detection method is generally used for visualizing the acoustic waves in Lead Zirconate Titanate (PZT) ceramics. Such an excitation method with a delta pulse generates a broadband frequency spectrum and wide directional wave vector. The presence of noise in the ultrasonic signals severely degrades the resolution and image quality. Deep learning-based signal and image denoising has been demonstrated recently. This paper bench-marked and compared several state-of-the-art deep learning image denoising methods with the classical denoising methods. The best-performing deep learning models are observed to be performing at par or, in some cases, even better than the classical methods on ultrasonic images. We further demonstrate the effectiveness and versatility of the deep learning-based denoising model for the unexplored domain of ultrasound/ultrasonic data. We conclude with a discussion on selecting the best method for denoising ultrasonic images. The impact of this work may help ultrasound-based defects identification equipment manufacturers to adopt a deep learning-based denoising model for more wider and versatile use.

Synthetic aperture radar image despeckling neural network based on maximum a posteriori probability estimation

ABSTRACT Automatic despeckling from synthetic aperture radar (SAR) imagery plays a significant role in many urban applications. Recently, owing to the impressive performance of deep learning, various SAR despeckling methods based on the convolutional neural network (CNN) have been proposed for optical SAR images. However, existing CNN-based despeckling methods and spatial-domain-based methods exhibit certain limitations. The introduction of prior knowledge is not considered in the designing of classical denoising and certain CNN-based methods, thus leading to the loss of edge information and artefacts in the results. To address this issue, an a priori-based deep neural network SAR image despeckling method (SAR-PBDNN) was proposed. In this approach, the Bayesian formula is modelled to calculate the objective function suitable for the despeckling problem and is optimized using the alternating direction method of multipliers algorithm and deep learning method. The introduction of prior information effectively improved the denoising effect of SAR images. The SAR-PBDNN was evaluated using both simulated and real SAR images. The comparisons demonstrate the effectiveness of the proposed method. We conclude that the SAR-PBDNN has the potential to automatically despeckle SAR images with an accuracy that renders it a useful tool for practical application scenarios.

Outlier Denoising Using a Novel Statistics-Based Mask Strategy for Compressive Sensing

Denoising is always an important step in seismic processing, in order to produce high-quality data for subsequent imaging and inversion. Different types of noise can be suppressed using targeted denoising methods. For outlier noise with singular amplitudes, many classical denoising methods suffer from signal leakage. To mitigate this issue, we developed a statistics-based mask method and incorporated it into the compressive sensing (CS) framework, in order to remove outlier noise. A statistical analysis for seismic data amplitudes was first used to identify the locations of traces containing outlier noise. Then, the outlier trace locations were compared with a mask matrix generated by jitter sampling, and we replaced the sampled traces of the jitter mask that had the outlier noise with their nearby unsampled traces. The optimized sampling matrix enabled us to effectively identify and remove outliers. This optimized mask strategy converts an outlier denoising problem into a data reconstruction problem. Finally, a sparsely constrained inverse problem was solved using a soft-threshold iteration solver to recover signals at the null locations. The feasibility and adaptability of the proposed method were demonstrated through numerical experiments for synthetic and field data. The results showed that the proposed method outperformed the conventional f-x deconvolution and median filter method, and could accurately suppress outlier noise and recover missed expected signals.

Rapid Response DAS Denoising Method Based on Deep Learning

In most optical fiber distributed acoustic sensing (DAS) systems, to obtain the desired outcome, the sensing signal acquired by DAS systems normally needs to be denoised. In some applications, such as the identifiation of the position of fast-moving targets, we need DAS systems to respond with sufficient speed. However, most classical denoising algorithms do not work if the signals are insufficiently collected within a short period (called a short-time signal). To obtain ideal results within a short time window, we propose an attention-based convolutional neural network (CNN) structure with extremely short signal windows to learn and approximate the results of classical denoising methods. To evaluate the effectiveness of the proposed method, the experiment is conducted under a real field highway scenario where the desired signals are overwhelmed with noise. The results show that by using signals collected within extremely short time windows of 100 ms, an insufficient time for the processing of existing denoising algorithms, our structure yields a satisfactory denoising performance.

A Modified Higher-Order Singular Value Decomposition Framework With Adaptive Multilinear Tensor Rank Approximation for Three-Dimensional Magnetic Resonance Rician Noise Removal.

The magnetic resonance (MR) images are acknowledged to be inevitably corrupted by Rician distributed noise, which adversely affected the image quality for diagnosis purpose. However, the traditional denoising methods may recover the images from corruptions with severe loss of detailed structure and edge information, which would affect the lesion detections and diagnostic decision making. In this study, we challenged improving the Rician noise removal from three-dimensional (3D) MR volumetric data through a modified higher-order singular value decomposition (MHOSVD) method. The proposed framework of MHOSVD involved a parameterized logarithmic nonconvex penalty function for low-rank tensor approximation (LRTA) algorithm optimization to suppress the image noise in MR dataset. Reference cubes were extracted from the noisy image volume, and block matching was performed according to nonlocal similarity for a fourth-order tensor construction. Then the LRTA problem was implemented by tensor factorization approaches, and the ranks of unfolding matrices along different modes of the tensor were estimated utilizing an adaptive nonconvex low-rank method. The denoised MR images were finally restored through aggregating all recovered cubes. We investigated the proposed algorithm MHOSVD on both the synthetic and real clinic 3D MR images for Rician noise removal, and relative results demonstrated that the MHOSVD can recover images with fine structures and detailed edge preservation with heavy noise even as high as 15% of the maximum intensity. The experimental results were also compared along with several classical denoising methods; the MHOSVD exhibited a sufficient improvement in noise-removal performance at various noise conditions in terms of different measurement indices such as peak signal-to-noise ratio and structural similarity index metrics. Based upon the comparison, the proposed MHOSVD has proved a relative state-of-the-art performance with excellent detailed structure reservation.

Semi-parametric joint detection and estimation for speech enhancement based on minimum mean square error

We propose a novel estimator for estimating the amplitude of speech coefficients in the time-frequency domain. In order to avoid a phase spectrum estimator of complex coefficients when using the Fourier transform, we consider the discrete cosine transform (DCT). This estimator aims at minimizing the mean square error of the absolute values of the speech DCT coefficients. In order to take advantage of both parametric and non-parametric approaches, the proposed method combines block shrinkage and Bayesian statistical estimation. First, the absolute value of the clean coefficient is estimated by block smoothed sigmoid-based shrinkage (Block-SSBS). The block size required by the Block-SSBS is obtained by statistical optimization. This step enables us to reduce the negative impact on speech intelligibility of classical denoising methods similarly to smoothed binary masking. Second, for refining the estimation, an optimal statistical estimator is added to handle musical noise. For evaluating the performance of the proposed method, objective criteria are used. The experiments enhance the relevance of the approach, in terms of speech quality and intelligibility.

An Effective Weighted Hybrid Regularizing Approach for Image Noise Reduction

Digital images are mostly noised due to transmission and capturing disturbances. Hence, denoising becomes a notable issue because of the necessity of removing noise before its use in any application. In denoising, the important challenge is to remove the noise while protecting true information and avoiding undesirable modification in the images. The performance of classical denoising methods including convex total variation or some nonconvex regularizers is not effective enough. Thus, it is still an ongoing research toward better denoising result. Since edge preservation is a tricky issue during denoising process, designing an appropriate regularizer for a given fidelity is a mostly crucial matter in real-world problems. Therefore, we attempt to design a robust smoothing term in energy functional so that it can reduce the possibility of discontinuity and distortion of image edge details. In this work, we introduce a new denoising technique that inherits the benefits of both convex and nonconvex regularizers. The proposed method encompasses with a novel weighted hybrid regularizer in variational framework to ensure a better trade-off between the noise removal and image edge preservation. A new algorithm based on Chambolle’s method and iteratively reweighting method is proposed to solve the model efficiently. The numerical results ensure that the proposed hybrid denoising approach can perform better than the classical convex, nonconvex regularizer-based denoising and some other methods.

Signal separation from X-ray image sequence using singular value decomposition

Abstract This work proposes singular value decomposition (SVD) to separate the signal from a noisy X-ray image sequence without any prior knowledge of the noise. SVD is based on the theory that the noise is always uncorrelated to the signal in a noisy image, and SVD, which belongs to Blind Source Separation (BSS), can decorrelate the signal from the noise components. To apply this proposed denoising method, two groups of X-ray images produced at 25 kV & 20 mAs and 34 kV & 20 mAs are sampled. To measure the proposed denoising method, ROIs with differing glandularity are selected. This work supports the use of SVD in X-ray image denoising. Normally, the separated signal will be less noisy when more noisy images are included for separating signals. Compared with other classical denoising methods, SVD is superior in reducing noise and improving CNR or SNR.

Supervised Dictionary Learning with Smooth Shrinkage for Image Denoising

The dictionary-based method is an important approach to image denoising. In the existing methods, the dictionary is either pre-defined or learned adaptively from the data under certain constraints such as sparsity or orthogonality, which often leads to an approximation solution. In this paper, we propose a novel supervised dictionary learning model with smooth shrinkage for image denoising. By incorporating the dictionary learning into the denoising target, our model is trained in a task-driven fashion without the need of explicit constraints. We analyze the proposed model theoretically and show that it tends to learn sparse and orthogonal dictionaries, which is further verified empirically. Experimental results on four different noise levels demonstrate the effectiveness of our model both quantitatively and visually in comparison with the classical dictionary-based denoising methods.

Denoising effect of multiscale multiway analysis on high-rate GPS observations

In general, high-rate GPS data sets are subject to common mode error (CME), multipath error, and high-frequency random noise, which adversely affect the GPS positioning accuracy. In order to improve the precision and reliability of GPS positioning, a multiscale multiway principal component analysis (MSMPCA) denoising method is introduced here. The 1-Hz GPS coordinate time series at ten stations from the California Real Time GPS Network are employed to assess the performance of MSMPCA. Its results are compared with those of the classical denoising methods, including wavelet denoising, PCA, multiway PCA, and multiscale PCA. The results indicate that MSMPCA is able to eliminate not only high-frequency random noise but also low-frequency errors and CME. Furthermore, quantitative analysis shows that MSMPCA is more accurate than the classical denoising methods. Spectral analysis shows that a combination of white plus flicker noise is considered to be the adequate model for the noise characteristics of all three components. Both white and power-law noise amplitudes are smallest in the north component and largest in the vertical component. MSMPCA decreases the mean amplitudes of white noise from 1.3 to 0.0, 0.9 to 0.0, and 2.8 to 0.1 mm in north, east, and vertical components, and those of power-law noise from 4.6 to 1.2, 3.9 to 1.1, and 19.9 to 8.4 mm, respectively. MSMPCA is a promising alternative for removing noise of various frequencies (0.00025---0.5 Hz) from high-rate GPS signals.

Hysteresis Thresholding: A Graph-Based Wavelet Block Denoising Algorithm

This communication aims to combine several previously proposed wavelet denoising algorithms into a novel heuristic block method. The proposed ``hysteresis'' thresholding uses two thresholds simultaneously in order to combine detection and minimal alteration of informative features of the processed signal. This approach exploits the graph structure of the wavelet decomposition to detect clusters of significant wavelet coefficients. The new algorithm is compared with classical denoising methods on simulated benchmark signals.

An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images

A critical issue in image restoration is the problem of noise removal while keeping the integrity of relevant image information. Denoising is a crucial step to increase image quality and to improve the performance of all the tasks needed for quantitative imaging analysis. The method proposed in this paper is based on a 3-D optimized blockwise version of the nonlocal (NL)-means filter (Buades, et al., 2005). The NL-means filter uses the redundancy of information in the image under study to remove the noise. The performance of the NL-means filter has been already demonstrated for 2-D images, but reducing the computational burden is a critical aspect to extend the method to 3-D images. To overcome this problem, we propose improvements to reduce the computational complexity. These different improvements allow to drastically divide the computational time while preserving the performances of the NL-means filter. A fully automated and optimized version of the NL-means filter is then presented. Our contributions to the NL-means filter are: 1) an automatic tuning of the smoothing parameter; 2) a selection of the most relevant voxels; 3) a blockwise implementation; and 4) a parallelized computation. Quantitative validation was carried out on synthetic datasets generated with BrainWeb (Collins, et al., 1998). The results show that our optimized NL-means filter outperforms the classical implementation of the NL-means filter, as well as two other classical denoising methods [anisotropic diffusion (Perona and Malik, 1990)] and total variation minimization process (Rudin, et al., 1992) in terms of accuracy (measured by the peak signal-to-noise ratio) with low computation time. Finally, qualitative results on real data are presented .