Curvelet Denoising Research Articles

Complicated thermo-chemical heterogeneity of the mantle transition zone beneath the Philippine Sea Plate revealed by SS precursors investigation

The Philippine Sea Plate (PSP), a region renowned for its intricate history of multi-stage subduction and back-arc extension, encounters difficulties in elucidating its deep seismic structure, primarily due to the sparse distribution of seismic stations. This study uses over 44,086 traces of SS precursors collected from >1,000 seismic stations over 10–20 years period, to image the mantle transition zone (MTZ) beneath the PSP. With the curvelet denoising technique, we provide high-resolution maps of the depths of the 410 km (D410) and 660 km (D660) discontinuities and the thickness of the MTZ. Notably, we demonstrate a 10–35 km MTZ thickening extending from the West Philippine Basin to the Shikoku Basin, which may be associated with the thermal effect and dehydration of stagnated slabs in the MTZ. Furthermore, the reflection gap and multiple reflectors were both observed in D410 and D660 beneath the Mariana Trench, which suggests that the vertically subducted Pacific plate transports substantial water and non-olivine components into the MTZ in this area. Additionally, a ∼10–25 km MTZ thinning with an abnormally shallow D660 has been observed beneath the Parece Vela Basin and Caroline Plate in the southern PSP, suggesting the potential existence of thermal upwelling from a secondary plume, which may be possibly the tree branch of the Caroline mantle plume in MTZ. Our results provide new seismological constraints on present and past mantle dynamics in and around the PSP.

Seismic data denoising using the 3D curvelet transform method

One of the major difficulties in processing and interpreting seismic data is the contamination of seismic signals by noise from numerous sources. Conventional denoising methods are mostly used for processing 2D seismic data, but noise also exists in the 3D data space, resulting in poor results using conventional denoising methods. Consequently, here, for seismic data denoising, a multiscale and multidirectional 3D curvelet transform was adopted. Our study combined the core principle of the 3D curvelet approach with the threshold iteration method to denoise simulated and actual seismic data with varying signal-to-noise ratios, and the results were quantitatively compared with the processing outcomes of existing denoising methods. The effectiveness of our method is illustrated using both genuine 2D and 3D post-stack seismic data, and synthetic 2D sections with added white and colored noise. Finally, we demonstrate how to prepare the data for frequency-domain full-waveform inversion using curvelet denoising. Despite the complexity of the procedure used to create the training samples, testing results using synthetic and real seismic data demonstrate that this method has mastered the capacity to suppress Gaussian and super-Gaussian noise from various training samples.

Curvelet Denoising for Preconditioning of 2D Poststack Seismic Data Inversion: Application to Data from the Marimbá Oil Field, Offshore Brazil

Curvelet Denoising for Preconditioning of 2D Poststack Seismic Data Inversion: Application to Data from the Marimbá Oil Field, Offshore Brazil

Deep learning approaches for thermographic imaging

In this paper, we investigate two deep learning approaches to recovering initial temperature profiles from thermographic images in non-destructive material testing. First, we trained a deep neural network (DNN) in an end-to-end fashion by directly feeding the surface temperature measurements to the DNN. Second, we turned the surface temperature measurements into virtual waves (a recently developed concept in thermography), which we then fed to the DNN. To demonstrate the effectiveness of these methods, we implemented a data generator and created a dataset comprising a total of 100 000 simulated temperature measurement images. With the objective of determining a suitable baseline, we investigated several state-of-the-art model-based reconstruction methods, including Abel transformation, curvelet denoising, and time- and frequency-domain synthetic aperture focusing techniques. Additionally, a physical phantom was created to support evaluation on completely unseen real-world data. The results of several experiments suggest that both the end-to-end and the hybrid approach outperformed the baseline in terms of reconstruction accuracy. The end-to-end approach required the least amount of domain knowledge and was the most computationally efficient one. The hybrid approach required extensive domain knowledge and was more computationally expensive than the end-to-end approach. However, the virtual waves served as meaningful features that convert the complex task of the end-to-end reconstruction into a less demanding undertaking. This in turn yielded better reconstructions with the same number of training samples compared to the end-to-end approach. Additionally, it allowed more compact network architectures and use of prior knowledge, such as sparsity and non-negativity. The proposed method is suitable for non-destructive testing (NDT) in 2D where the amplitudes along the objects are considered to be constant (e.g., for metallic wires). To encourage the development of other deep-learning-based reconstruction techniques, we release both the synthetic and the real-world datasets along with the implementation of the deep learning methods to the research community.

3D Shape Modeling and Analysis of Retinal Microvasculature in OCT-Angiography Images.

3D optical coherence tomography angiography (OCT-A) is a novel and non-invasive imaging modality for analyzing retinal diseases. The studies of microvasculature in 2D en face projection images have been widely implemented, but comprehensive 3D analysis of OCT-A images with rich depth-resolved microvascular information is rarely considered. In this paper, we propose a robust, effective, and automatic 3D shape modeling framework to provide a high-quality 3D vessel representation and to preserve valuable 3D geometric and topological information for vessel analysis. Effective vessel enhancement and extraction steps by means of curvelet denoising and optimally oriented flux (OOF) filtering are first designed to produce 3D microvascular networks. Afterwards, a novel 3D data representation of OCT-A microvasculature is reconstructed via advanced mesh reconstruction techniques. Based on the 3D surfaces, shape analysis is established to extract novel shape-based microvascular area distortion via the Laplace-Beltrami eigen-projection. The extracted feature is integrated into a graph-cut segmentation system to categorize large vessels and small capillaries for more precise shape analysis. The proposed framework is validated on a dedicated repeated scan dataset including 260 volume images and shows high repeatability. Statistical analysis using the surface area biomarker is performed on small capillaries to avoid the effect of tailing artifact from large vessels. It shows significant differences ( ) between DR stages on 100 subjects in a OCTA-DR dataset. The proposed shape modeling and analysis framework opens the possibility for further investigating OCT-A microvasculature in a new perspective.

Scale and rotation statistic-based self-adaptive function for ground penetrating radar denoising in curvelet domain

Nonlinear and non-stationary ground penetrating radar (GPR) data for geophysics exploration are often mixed with various complex noise sources, such as random and coherent noise. Those complex noise sources are introduced by the acquisition system and other sources of measurement uncertainty. The data sets which are contaminated by the above noises have a serious influence on the accurate extraction of weak reflected signals and the effective identification of diffracted wave hyperbolic coaxial characteristics. The ignorance of the influence of noise will cause great errors in the interpretation of GPR data and the subsequent migration imaging with full waveform. The curvelet transform not only is related to position and frequency as compared with the wavelet transform, but also is controlled by the translation angle. With such a unique advantage, curvelets are used for ground roll whitening, coherent noise denoising and separation of overlapping events. The traditional curvelet transform denoising with a hard threshold function needs to give a reasonable threshold function control coefficient according to the noise level of GPR data. As a result, an appropriate choice of a hard threshold is a basic requirement, and this presents a challenging task in curvelet denoising. To overcome these shortcomings, an self-adaptive threshold function for GPR data denoising with curve transform is proposed in this paper. For detailing the reasonable control coefficient of the threshold function, the complex block threshold function algorithm is used to analyze the distribution of peak-signal-to-noise ratio value of the noisy synthetic GPR data contaminated with random and coherent noise by using the traditional threshold function curvelet transform. Based on the high order statistical theory, the accuracy distribution of the curvelet coefficient for useful signals in scale and rotation direction are correlatively stacked and determined by using the statistical self-adaptive function. And then the threshold range of noise removal components is given by the statistical self-adaptive function. The effectiveness of the proposed denoising algorithm for the noisy synthetic contaminated with different types of noise (i.e., Gaussian random and coherent), and field GPR data is demonstrated by comparing the denoising results via curvelet transform with those from traditional thresholding function. The presented denoising results by the statistical self-adaptive function is helpful and instructive for the accurate inference and interpretation of complex GPR data.

Improvement of image quality in PET using post-reconstruction hybrid spatial-frequency domain filtering

PET images commonly suffer from the high noise level and poor signal-to-noise ratio (SNR), thus adversely impacting lesion detectability and quantitative accuracy. In this work, a novel hybrid dual-domain PET denoising approach is proposed, which combines the advantages of both spatial and transform domain filtering to preserve image textures while minimizing quantification uncertainty. Spatial domain denoising techniques excel at preserving high-contrast patterns compared to transform domain filters, which perform well in recovering low-contrast details normally smoothed out by spatial domain filters. For spatial domain filtering, the non-local mean algorithm was chosen owing to its performance in denoising high-contrast features whereas multi-scale curvelet denoising was exploited for the transform domain owing to its capability to recover small details. The proposed hybrid method was compared to conventional post-reconstruction Gaussian and edge preserving bilateral filters. Computer simulations of a thorax phantom containing three small lesions, experimental measurements using the Jaszczak phantom and clinical whole-body PET/CT studies were used to evaluate the performance of the proposed PET denoising technique. The proposed hybrid filter increased the SNR from 8.0 (non-filtered PET image) to 39.3 for small lesions in the computerized thorax phantom, while Gaussian and bilateral filtering led to SNRs of 23.3 and 24.4, respectively. For the experimental Jaszczak phantom, the contrast-to-noise ratio (CNR) improved from 10.84 when using Gaussian smoothing to 14.02 and 19.39 using the bilateral and the proposed hybrid filters, respectively. The clinical studies further demonstrated the superior performance of the hybrid method, yielding a quantification change (the original noisy OSEM image was used as reference in the absence of ground truth) in malignant lesions of −2.4% compared to −11.9% and −6.6% achieved using Gaussian and bilateral filters, respectively. In some cases, the visual difference between the bilateral and hybrid filtered images is not substantial; however the improved CNR score from 11.3 by OSEM to 17.1 and 21.8 by bilateral to the hybrid filtering, respectively, demonstrates the overall gain achieved by the hybrid approach. The proposed hybrid algorithm improved the contrast, SNR and quantitative accuracy compared to Gaussian and bilateral approaches, and can be utilized as an alternative post-reconstruction filter in clinical PET/CT imaging.

Detection Performance Improvement of Distributed Vibration Sensor Based on Curvelet Denoising Method.

A curvelet denoising method has been proposed to reduce the time domain noise to improve the detection performance in the distributed fiber vibration sensing system based on phase-sensitive optical time domain reflectometry. The raw Rayleigh backscattering traces are regarded as a gray image and the random noise can be eliminated by the curvelet transform; hence, the amplitude difference induced by the external vibration can be extracted. The detection of a vibration event with 10 m spatial resolution along a 4 km single mode fiber is demonstrated. The signal-to-noise ratio (SNR) of location information for 50 Hz and 1 kHz vibration based on this new method increases to as high as 7.8 dB and 8.0 dB, respectively, compared to the conventional method, showing the remarkable denoising capability of this new approach.

A restoration–segmentation algorithm based on flexible Arnoldi–Tikhonov method and Curvelet denoising

In this paper, we illustrate a two-stage algorithm consisting of restoration and segmentation to reach binary segmentation from the noisy and blurry image. The results of our method can be applied in main fields of the image processing such as object extraction. In the first stage, we have a linear discrete ill-posed problem with a noise-contaminated right-hand side, arising from the image restoration. We consider problems in which the coefficient matrix is the sum of Kronecker products of matrices and present a global flexible Arnoldi–Tikhonov method coupled with the generalized cross-validation for the computation of the regularization parameter at each iteration. The proposed algorithm is based on the global Arnoldi method that allows using a more flexible solution subspace. In the second stage, we segment the restored image in order to reach a binary image in which the target object is emphasized. In our segmentation method, we use Gaussian scale-space technique to compute discrete gradients of the restored image for pre-segmenting. Also, in order to denoise, we use a tight frame of Curvelet transforms and thresholding which is based on the principle obtained by minimizing Stein’s unbiased risk estimate. This algorithm has an iterative part based on the iterative part of TFA (Cai et al. in SIAM J Imaging 6(1):464–486, 2013), but we use eigenvectors of Hessian matrix of image for improving this part. Theoretical properties of the method of both stages and numerical experiments are presented.

A novel thresholding technique in the curvelet domain for improved speckle removal in SAR images

Speckle noise is the grainy salt-and-pepper pattern present in radar imagery caused by the interaction of out-of-phase waves with a target. Speckle degrade the spatial resolution, contrast of the image, decreases object detectability and causes inconvenience to the SAR (Synthetic Aperture Radar) image interpreter. Reduction of speckle can be carried out for proper interpretation and object detection. In this work, an improved thresholding technique in the curvelet domain is proposed to reduce the speckle in SAR images and preserve the details of the image. The results of denoised images are compared visually and statistically. The performance of the proposed technique is better compared with improved thresholding technique in the wavelet domain, curvelet denoising and curvelet cycle spin technique.

Enhancing 3D post‐stack seismic data acquired in hardrock environment using 2D curvelet transform

ABSTRACTSeismic data acquired in hardrock environment pose a special challenge for processing. Frequent lack of clear coherent events hinders imaging and interpretation. Additional difficulty arises from the presence of significant amount of cultural noise associated with production and processing of ore, which often remains in the processed, stacked data. Motivated by those challenges, we developed an efficient workflow of denoising 3D post‐stack seismic data by using 2D discrete curvelet transform aimed at improving signal‐to‐noise ratio of the data. Our approach is based on the adjustment of the thresholds according to scales and angles in the curvelet domain, making parameterization flexible. We demonstrate effectiveness of our method using 3D post‐stack volumes from the three different mining camps in Canada, which were characterized by variable data quality. Remarkable signal enhancement, confirmed by the improvements in the mean signal‐to‐noise ratio of the dataset, is obtained not only due to random energy attenuation but also by removal of certain features corrupting the data (e.g., acquisition footprint). Comparison with the F‐X/F‐XY deconvolution results shows the superiority of our algorithm in respect to signal enhancement, signal preservation, and amount of the removed noise. Imaged structures, even if initially dominated by random energy, are easier to follow after curvelet denoising and enhanced for interpretation. Therefore, our approach can significantly reduce interpretation uncertainties when dealing with the seismic data acquired in the hardrock environment.

FETAL ULTRASOUND IMAGE DENOISING USING CURVELET TRANSFORM

The random speckle noise in the acquired fetal ultrasound images is caused by the interference of reflected ultrasound wave fronts. The presence of speckle noise will degrade the quality of the image and even hide image details, which in turn affect the process of image segmentation, feature extraction and recognition and most importantly disease diagnosis. The standardization of measurements from the fetal ultrasound images will help the physicians to make correct diagnosis. The accuracy of diagnosis is possible only when the image is noise free. Hence it is very much important to perform filtering of the speckle noise. It is proposed that curvelet transform serves as a better edge preserving filter compared to other speckle reducing anisotropic diffusion filters. Curvelet transform is designed to handle images which involve curves using only a less number of coefficients. Hence a multiscale representation called curvelet transform is applied to enhance the visual quality of the ultrasound images. The experimented results indicate that the proposed curvelet denoising suppresses the noise effectively both in quantitative and visual means by producing high PSNR.

A Wavelet-Based Approach for Ultrasound Image Restoration

Ultrasound's images are generally affected by speckle noise which is mainly due to the scattering phenomenon’s coherent nature. Speckle filtration is accompanied with loss of diagnostic features. In this paper a modest new trial introduced to remove speckles while keeping the fine features of the tissue under diagnosis by enhancing image’s edges; via Curvelet denoising and Wavelet based image fusion. Performance evaluation of our work is done by four quantitative measures: the peak signal to noise ratio (PSNR), the square root of the mean square of error (RMSE), a universal image quality index (Q), and the Pratt’s figure of merit (FOM) as a quantitative measure for edge preservation. Plus Canny edge map which is extracted as a qualitative measure of edge preservation. The measurements of the proposed approach assured its qualitative and quantitative success into image denoising while maintaining edges as possible. A Gray phantom is designed to test our proposed enhancement method. The phantom results assure the success and applicability of this paper approach not only to this research works but also for gray scale diagnostic scans’ images including ultrasound’s B-scans.

Visual Improvement for Hepatic Abscess Sonogram by Segmentation after Curvelet Denoising

A wise automated method for wisely improving the visualization of hepatic abscess sonogram, a modest trial is being done to denoise and reduce the ultrasound scan speckles wisely and effectively. As an effective way for improving the diagnostic decision; improved sonogram for hepatic abscess is reconstructed by ultrasound scan image segmentation after denoising in Curvelet transform domain. Better sonogram visualization is required for better human interpretation. Speckle noise filtering of medical ultrasound images is needed for enhanced diagnosis. Double thresholding segmentation was applied on, an ultrasound scan image for a Liver with amebic abscess, after it had been denoised in Curvelet transform domain. The result is enhanced wise effect on the hepatic abscess sonogram image's visualization which improves physicians' decisions. Moreover, this method effectively reduces the memory storage size for the image which consequently decreases computation processing time.

Image denoising by supervised adaptive fusion of decomposed images restored using wave atom, curvelet and wavelet transform

This paper presents an efficient image denoising method that adaptively combines the features of wavelets, wave atoms and curvelets. Wavelet shrinkage is used to denoise the smooth regions in the image while wave atoms are employed to denoise the textures, and the edges will take advantage of curvelet denoising. The received noisy image is firstly decomposed into a homogenous (smooth/cartoon) part and a textural part. The cartoon part of the noisy image is denoised using wavelet transform, and the texture part of the noisy image is denoised using wave atoms. The two denoised images are then fused adaptively. For adaptive fusion, different weights are chosen from the variance map of the denoised texture image. Further improvement in denoising results is achieved by denoising the edges through curvelet transform. The information about edge location is gathered from the variance map of denoised cartoon image. The denoised image results in perfect presentation of the smooth regions and efficient preservation of textures and edges in the image.

Fractional Diffusion, Low Exponent Lévy Stable Laws, and 'Slow Motion' Denoising of Helium Ion Microscope Nanoscale Imagery.

Helium ion microscopes (HIM) are capable of acquiring images with better than 1 nm resolution, and HIM images are particularly rich in morphological surface details. However, such images are generally quite noisy. A major challenge is to denoise these images while preserving delicate surface information. This paper presents a powerful slow motion denoising technique, based on solving linear fractional diffusion equations forward in time. The method is easily implemented computationally, using fast Fourier transform (FFT) algorithms. When applied to actual HIM images, the method is found to reproduce the essential surface morphology of the sample with high fidelity. In contrast, such highly sophisticated methodologies as Curvelet Transform denoising, and Total Variation denoising using split Bregman iterations, are found to eliminate vital fine scale information, along with the noise. Image Lipschitz exponents are a useful image metrology tool for quantifying the fine structure content in an image. In this paper, this tool is applied to rank order the above three distinct denoising approaches, in terms of their texture preserving properties. In several denoising experiments on actual HIM images, it was found that fractional diffusion smoothing performed noticeably better than split Bregman TV, which in turn, performed slightly better than Curvelet denoising.

Seismic denoising using curvelet analysis

A curvelet is a new and effective spectral transform, that allows sparse representations of complex data. It has many applications in several fields, including denoising, wave propagation in disordered media and pattern recognition. This spectral technique is based on directional basis functions that represent objects having discontinuities along smooth curves. In this work we apply this technique to the removal of Ground Roll, which is an undesired feature signal present in seismic data obtained by sounding the geological structures of the Earth. In this methodology the original seismic data is decomposed by curvelet transform in scales and angular domains. For each scale the curvelet denoising technique allows a very efficient separation of the Ground Roll in angle sections. The precise identification of the Ground Roll pattern allows an effective erasing of its coefficients. In contrast to conventional denoising techniques we do not use any artificial attenuation factor to decrease the amplitude of the Ground Roll coefficients. We have estimated that, depending on the scale, around 75% of the energy of the strong undesired signal is removed.

Single pixel optical imaging using a scanning MEMS mirror

The paper describes a low-complexity optical imaging system using demagnifying optics, a single scanning MEMS mirror and a single photodetector. Light at visible wavelengths from the object passes through a lens assembly and is incident on a scanning MEMS micromirror. After reflection from the micromirror, a complete image of the object is projected at the image plane of the optical system where a single-element photodetector with a pinhole at its entrance is located. By tilting the micromirror in the x and y directions, the projected image is translated across the image plane in the x and y directions. The photodetector sequentially detects the intensity of different areas of the projected optical image, thereby enabling a digital image to be generated pixel-by-pixel. However, due to the noisy raw image obtained experimentally, an image enhancement algorithm based on iterative-combined wavelet and curvelet denoising has been developed. Using blind image quality indices (BIQI) as an objective performance measure, it is shown that the proposed image enhancement method enhances the raw image by up to 40% and outperforms state-of-the-art denoising methods for up to 10 units of BIQI.

Enhancing crustal reflection data through curvelet denoising

Suppression of incoherent noise, which is present in the seismic signal and may often lead to ambiguous interpretation, is a key step in processing associated with crustal reflection data. In this paper, we make use of the parsimonious representation of seismic data in the curvelet domain to perform the noise attenuation while preserving the coherent energy and its amplitude information. Curvelets are a recently developed mathematical transform that has as one of its properties minimal overlap between seismic signal and noise in the transform domain, thereby facilitating signal-noise separation. The problem is cast as an inverse problem and the results are obtained by updating the solution at each iteration. We demonstrate the effectiveness of this procedure at removing noise on both synthetic shot gathers and a synthetic stacked seismic section. We then apply curvelet denoising to deep crustal seismic reflection data where the signal-to-noise ratio is low. The reflection data were recorded along Lithoprobe's SNORCLE Line 1 across Paleoproterozoic-Archean domains in Canada's Northwest Territories. After initial processing, we apply the iterative curvelet denoising to both pre-stack shot gathers and post-stack data. Ground roll, random noise and much of the anomalous vertical energy is removed from the pre-stack shot gathers, to the extent that crustal reflections, including those from the Moho, are clearly seen on individual gathers. Denoised stacked data show a series of dipping reflections in the lower crust that extend into the Moho. The Moho itself is relatively flat and characterized by a sharp, narrow band of reflections. Comparing the results for the stacked data with those from F-X deconvolution, curvelet denoising outperforms the latter by attenuating incoherent noise with minimal harm to the signal. Because curvelet denoising retains amplitude information, it provides opportunities for further studies of seismic sections through attribute analyses. Curvelet denoising provides an important new tool in the processing toolbox for crustal seismic reflection data.

Velocity distributions of single F-actin trajectories from a fluorescence image series using trajectory reconstruction and optical flow mapping

We present an approach for the computation of single-object velocity statistics in a noisy fluorescence image series. The algorithm is applied to molecular imaging data from an in vitro actin-myosin motility assay. We compare the relative efficiency of wavelet and curvelet transform denoising in terms of noise reduction and object restoration. It is shown that while both algorithms reduce background noise efficiently, curvelet denoising restores the curved edges of actin filaments more reliably. Noncrossing spatiotemporal actin trajectories are unambiguously identified using a novel segmentation scheme that locally combines the information of 2-D and 3-D segmentation. Finally, the optical flow vector field for the image sequence is computed via the 3-D structure tensor and mapped to the segmented trajectories. Using single-trajectory statistics, the global velocity distribution extracted from an image sequence is decomposed into the contributions of individual trajectories. The technique is further used to analyze the distribution of the x and y components of the velocity vectors separately, and it is shown that directed actin motion is found in myosin extracts from single skeletal muscle fibers. The presented approach may prove helpful to identify actin filament subpopulations and to analyze actin-myosin interaction kinetics under biochemical regulation.