Local singular value decomposition for signal enhancement of seismic data

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. V59-V65 ◽  
Author(s):  
Maïza Bekara ◽  
Mirko Van der Baan

Singular value decomposition (SVD) is a coherency-based technique that provides both signal enhancement and noise suppression. It has been implemented in a variety of seismic applications — mostly on a global scale. In this paper, we use SVD to improve the signal-to-noise ratio of unstacked and stacked seismic sections, but apply it locally to cope with coherent events that vary with both time and offset. The local SVD technique is compared with [Formula: see text] deconvolution and median filtering on a set of synthetic and real-data sections. Local SVD is better than [Formula: see text] deconvolution and median filtering in removing background noise, but it performs less well in enhancing weak events or events with conflicting dips. Combining [Formula: see text] deconvolution or median filtering with local SVD overcomes the main weaknesses associated with each individual method and leads to the best results.

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Muhammad Mohsin Riaz ◽  
Abdul Ghafoor

Singular value decomposition and information theoretic criterion-based image enhancement is proposed for through-wall imaging. The scheme is capable of discriminating target, clutter, and noise subspaces. Information theoretic criterion is used with conventional singular value decomposition to find number of target singular values. Furthermore, wavelet transform-based denoising is performed (to further suppress noise signals) by estimating noise variance. Proposed scheme works also for extracting multiple targets in heavy cluttered through-wall images. Simulation results are compared on the basis of mean square error, peak signal to noise ratio, and visual inspection.


Geophysics ◽  
1991 ◽  
Vol 56 (4) ◽  
pp. 528-533 ◽  
Author(s):  
G. M. Jackson ◽  
I. M. Mason ◽  
S. A. Greenhalgh

Polarization analysis can be achieved efficiently by treating a time window of a single‐station triaxial recording as a matrix and doing a singular value decomposition (SVD) of this seismic data matrix. SVD of the triaxial data matrix produces an eigenanalysis of the data covariance (cross‐energy) matrix and a rotation of the data onto the directions given by the eigenanalysis (Karhunen‐Loève transform), all in one step. SVD provides a complete principal components analysis of the data in the analysis time window. Selection of this time window is crucial to the success of the analysis and is governed by three considerations: the window should contain only one arrival; the window should be such that the signal‐to‐noise ratio is maximized; and the window should be long enough to be able to discriminate random noise from signal. The SVD analysis provides estimates of signal, signal polarization directions, and noise. An F‐test is proposed which gives the confidence level for the hypothesis of rectilinear polarization. This paper illustrates the analysis and interpretation of synthetic rectilinearly and elliptically polarized arrivals at a single triaxial station by SVD.


PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0256700
Author(s):  
Olivia W. Stanley ◽  
Ravi S. Menon ◽  
L. Martyn Klassen

Magnetic resonance imaging radio frequency arrays are composed of multiple receive coils that have their signals combined to form an image. Combination requires an estimate of the radio frequency coil sensitivities to align signal phases and prevent destructive interference. At lower fields this can be accomplished using a uniform physical reference coil. However, at higher fields, uniform volume coils are lacking and, when available, suffer from regions of low receive sensitivity that result in poor sensitivity estimation and combination. Several approaches exist that do not require a physical reference coil but require manual intervention, specific prescans, or must be completed post-acquisition. This makes these methods impractical for large multi-volume datasets such as those collected for novel types of functional MRI or quantitative susceptibility mapping, where magnitude and phase are important. This pilot study proposes a fitted SVD method which utilizes existing combination methods to create a phase sensitive combination method targeted at large multi-volume datasets. This method uses any multi-image prescan to calculate the relative receive sensitivities using voxel-wise singular value decomposition. These relative sensitivities are fitted to the solid harmonics using an iterative least squares fitting algorithm. Fits of the relative sensitivities are used to align the phases of the receive coils and improve combination in subsequent acquisitions during the imaging session. This method is compared against existing approaches in the human brain at 7 Tesla by examining the combined data for the presence of singularities and changes in phase signal-to-noise ratio. Two additional applications of the method are also explored, using the fitted SVD method in an asymmetrical coil and in a case with subject motion. The fitted SVD method produces singularity-free images and recovers between 95–100% of the phase signal-to-noise ratio depending on the prescan data resolution. Using solid harmonic fitting to interpolate singular value decomposition derived receive sensitivities from existing prescans allows the fitted SVD method to be used on all acquisitions within a session without increasing exam duration. Our fitted SVD method is able to combine imaging datasets accurately without supervision during online reconstruction.


he proposed paper work is implemented using Stationary Wavelet Transformation (SWT) with Singular Value Decomposition (SVD).Even though, there are many other transformations, the Stationary Wavelet Transformation method is chosen for its shift invariance property. The designed method has three steps; the first step is the decomposing of the Medical image into sub-bands using SWT to find the value of sub band and as a second step is to apply SVD, third step will combine both the images with scaling factor. The experiments were conducted over gray scale of MRI and CT Medical images. The statistics of proposed method indicates that imperceptibility of Watermarked Medical images have a Peak Signal to Noise Ratio (PSNR) value of 50 DB for medical images. The robustness is ensured by having Correlation Coefficient (CC) of 1 for the retrieved watermark images. Security for the watermark is extended by encrypting the watermark with chaotic sequence.


2015 ◽  
Vol 33 (3) ◽  
pp. 421
Author(s):  
Danilo S. Cruz ◽  
Milton J. Porsani

ABSTRACT. The land seismic data often have low signal-to-noise ratio due, among other factors, the presence of ground roll. It is a coherent noise present in seismograms that appears as linear events, with low frequencies and high amplitudes, low velocities and, in most cases, overlapping the reflections and harm both the processing and the interpretation of the data. In this work we present a filtering approach to attenuate the ground roll, which is based on the Singular Value Decomposition (SVD) method applied in the frequency (f-k) domain. Before filtering the data we applied the standard pre-processing procedure to the original seismograms: the static corrections, the spherical divergence and a gain to improving the quality of the seismic records. After application of the 2D Fourier transform, the SVD is applied to a small frequency range using a sliding window approach. The f-k filtered spectrum is obtained with the difference between the original spectrum and the predicted ones and the family of filtered traces is obtained by performing a 2D inverse Fourier transform. The method was applied on a land seismic line of Tacutu Basin locatedin northeastern part of Brazil. The results show that the method is effective for mitigating the ground roll and provides better results when compared to conventionalfiltering method f-k.Keywords: ground roll attenuation, seismic processing, SVD filtering, f-k filtering.RESUMO. Os dados sísmicos terrestres geralmente apresentam baixa razão sinal-ruído devido, entre outros fatores, à presença do ground roll . Trata-se de um ruído dominado por altas amplitudes, baixas frequências, baixas velocidades e de caráter dispersivo, representado no domínio x-t como eventos lineares. Este ruído se sobrepõe às reflexões e prejudica tanto o processamento quanto a interpretação dos dados. Para atenuação do ground roll , utilizamos uma técnica de filtragem adaptativa baseada no método Singular Value Decomposition (SVD) e aplicada no domínio f-k. Como parte do pré-processamento dos dados foram aplicadas a correção estática, a correção de divergência esférica além da aplicação de um ganho com intuito de melhorar a qualidade do registro sísmico. Em seguida, as famílias de ponto de tiro comum foram levadas para o domínio da frequência (f-k), através da transformada dupla de Fourier, e a filtragem SVD foi aplicada na forma de janelas deslizantes confinadas à faixa de frequências dominada pelo ground roll. O espectro f-k filtrado foi obtido tomando a diferença entre o espectro original e o espectro SVD predito com a primeira autoimagem. A família de traços filtrada no domínio x-t é obtida através da transformada inversa dupla de Fourier. O método foi aplicado sobre uma linha sísmica terrestre da Bacia do Tacutu, localizada na parte norte do Brasil. Os resultados mostram que o método proposto é eficaz para atenuar o ground roll e fornece resultados melhores quando comparados ao método convencional de filtragem f-k.Palavras-chave: atenuação do ground roll , processamento sísmico, filtragem SVD, filtragem f-k.


2020 ◽  
Vol 10 (4) ◽  
pp. 1409
Author(s):  
Gang Zhang ◽  
Benben Xu ◽  
Kaoshe Zhang ◽  
Jinwang Hou ◽  
Tuo Xie ◽  
...  

Reducing noise pollution in signals is of great significance in the field of signal detection. In order to reduce the noise in the signal and improve the signal-to-noise ratio (SNR), this paper takes the singular value decomposition theory as the starting point, and constructs various singular value decomposition denoising models with multiple multi-division structures based on the two-division recursion singular value decomposition, and conducts a noise reduction analysis on two experimental signals containing noise of different power. Finally, the SNR and mean square error (MSE) are used as indicators to evaluate the noise reduction effect, it is verified that the two-division recursion singular value decomposition is the optimal noise reduction model. This noise reduction model is then applied to the diagnosis of faulty bearings. By this method, the fault signal is decomposed to reduce noise and the detail signal with maximum kurtosis is extracted for envelope spectrum analysis. Comparison of several traditional signal processing methods such as empirical modal decomposition (EMD), ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), wavelet decomposition, etc. The results show that multi-resolution singular value decomposition (MRSVD) has better noise reduction effect and can effectively diagnose faulty bearings. This method is promising and has a good application prospect.


Sign in / Sign up

Export Citation Format

Share Document