Improving the Signal-to-Noise-Ratio of Free Induction Decay Signals Using a New Multi-linear Singular Value Decomposition-Based Filter

Author(s):  
Huan Liu ◽  
Zehua Wang ◽  
Changfeng Zhao ◽  
Jian Ge ◽  
Haobin Dong ◽  
...  
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.


2016 ◽  
Vol 33 (3) ◽  
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... 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...


2021 ◽  
pp. 356-362
Author(s):  
Rajesh Patil ◽  
Surendra Bhosale

Filtering noise to recreate a high-quality image in medical image processing is an important task. During acquisition, transmission, and retrieval from storage devices, generally images are getting corrupted. So, for further analysis images must get denoised. The noises can be categorised into different types based on their nature and origin. Researchers are still looking for the effective denoising technique. Wavelet Transform (WT) is an effective transform method for denoising. Similarly Singular Value Decomposition (SVD) is also an important tool for denoising. Combining WT with SVD results in further reduction of noise. This paper proposes use of WT along with SVD for medical image denoising. Performance of image denoising is evaluated on the basis of Signal to Noise Ratio (SNR) and Peak Signal-Noise Ratio (PSNR). In the proposed approach, experimental results of WT-SVD combination gives better SNR and PSNR values than WT and SVD, if used independently.


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 ◽  
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.


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.


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