scholarly journals Least Squares Reconstruction of Doppler Radar Spectra for Irregular PRT

2012 ◽  
Vol 29 (12) ◽  
pp. 1744-1756 ◽  
Author(s):  
John Kalogiros
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Signal To Noise Ratio ◽  
Simulated Data ◽  
Irregular Sampling ◽  
Filter Method ◽  
Reconstruction Method ◽  
Signal To Noise ◽  
Mean Velocity ◽  
Noise Ratio

Abstract A least squares method for the reconstruction of Doppler spectra of weather radars with irregular pulse repetition time used to increase the range of unambiguous velocity is presented and evaluated. This method is a robust spectral method that is based on the least squares minimum norm principle and reconstructs both the magnitude and the phase of the discrete Fourier transform of the signal. The phase spectrum is useful in the estimation of the differential phase in dual-polarization radars with staggered sampling schemes, which is a case of irregular sampling. A computationally efficient iterative algorithm for estimating the mean frequency of the signal, which is required for the reconstruction of the spectrum, is described for possible real-time applications. A clutter filter method based on spectral interpolation, which can be applied to echoes with generally nonzero mean velocity, is also described and combined with the spectrum reconstruction method. Using simulated data it is shown that the least squares reconstruction method with or without the presence of clutter gives results with small bias and standard error and can be applied to wide spectra. The application of the method to real X-band radar data with a low signal-to-noise ratio and a high stagger ratio value of ⅚ showed that the least squares method has low sensitivity to the stagger ratio and satisfactorily gives spectral reconstruction for signal-to-noise ratio values as low as 10 dB.

A Least-Squares Strain Estimator for Elastography

1997 ◽  
Vol 19 (3) ◽  
pp. 195-208 ◽  
Author(s):  
Faouzi Kallel ◽  
Jonathan Ophir
Keyword(s):  
Least Squares ◽  
Spatial Resolution ◽  
Dynamic Range ◽  
Signal To Noise Ratio ◽  
Simulated Data ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Gel Phantom

A least-squares strain estimator (LSQSE) for elastography is proposed. It is shown that with such an estimator, the signal-to-noise ratio in an elastogram ( SNRe) is significantly improved. This improvement is illustrated theoretically using a modified strain filter and experimentally using a homogeneous gel phantom. It is demonstrated that the LSQSE results in an increase of the elastographic sensitivity (smallest strain that could be detected), thereby increasing the strain dynamic range. Using simulated data, it is shown that a tradeoff exists between the improvement in SNRe and the reduction of strain contrast and spatial resolution.

scholarly journals The Effect of Signal-to-Noise Ratio on the Study of Sea Level Trends

2011 ◽  
Vol 24 (5) ◽  
pp. 1396-1408 ◽  
Author(s):  
B. D. Hamlington ◽  
R. R. Leben ◽  
R. S. Nerem ◽  
K.-Y. Kim
Keyword(s):  
Least Squares ◽  
Sea Level ◽  
Least Squares Method ◽  
Secular Trend ◽  
Signal To Noise Ratio ◽  
Empirical Orthogonal Functions ◽  
Signal To Noise ◽  
Orthogonal Functions ◽  
Geophysical Processes ◽  
Noise Ratio

Abstract Extracting secular sea level trends from the background ocean variability is limited by how well one can correct for the time-varying and oscillating signals in the record. Many geophysical processes contribute time-dependent signals to the data, making the sea level trend difficult to detect. In this paper, cyclostationary empirical orthogonal functions (CSEOFs) are used to quantify and improve the signal-to-noise ratio (SNR) between the secular trend and the background variability, obscuring this trend in the altimetric sea level record by identifying and removing signals that are physically interpretable. Over the 16-yr altimetric record the SNR arising from the traditional least squares method for estimating trends can be improved from 4.0% of the ocean having an SNR greater than one to 9.9% when using a more sophisticated statistical method based on CSEOFs. From a standpoint of signal detection, this implies that the secular trend in a greater portion of the ocean can be estimated with a higher degree of confidence. Furthermore, the CSEOF method improves the standard error on the least squares estimates of the secular trend in 97% of the ocean. The convergence of the SNR as the record length is increased is used to estimate the SNR of sea level trends in the near future as more measurements become available from near-global altimetric sampling.

Application of frequency-dependent multichannel Wiener filters to detect events in 2D three-component seismometer arrays

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. V133-V141 ◽  
Author(s):  
J. Wang ◽  
F. Tilmann ◽  
R. S. White ◽  
P. Bordoni
Keyword(s):  
Least Squares Method ◽  
Signal To Noise Ratio ◽  
Noise Levels ◽  
Signal To Noise ◽  
Coherent Noise ◽  
Gas Field ◽  
Frequency Dependent ◽  
Wiener Filters ◽  
Noise Ratio

Hydraulic fracture-induced microseismic events in producing oil and gas fields are usually small, and noise levels are high at the surface as a result of the heavy equipment in use. Similarly, in nonhydrocarbon settings, arrays for detecting local earthquakes will benefit from reduced noise levels and the ability to detect smaller events will be increased. We propose a frequency-dependent multichannel Wiener filtering technique with linear constraints that uses an adaptive least-squares method to remove coherent noise in seismic array data. The noise records on several reference channels are used to predict the noise on a primary channel and then can be subtracted from the observed data. On a test with an unconstrained version of this filter, maximal noise suppression leads to signal distortion. Two methods of im-posing constraints then achieve signal preservation. In one case study, synthetic signals are added to noise from a pilot deployment of a hexagonal array (nine three-component seismometers, approximately [Formula: see text]) above a gas field; noise levels are suppressed by up to [Formula: see text] (at [Formula: see text]). In a second case study, natural seismicity recorded at a dense array ([Formula: see text] spacing) in Italy is used, where the application of the filter improves the signal-to-noise ratio (S/N) more than [Formula: see text] (at [Formula: see text]) using 35 stations. In both cases, the performance of the multichannel Wiener filters is significantly better than stacking, espe-cially at lower frequencies where stacking does not help to suppress the coherent noise. The unconstrained version of the filter yields the best improvement in signal-to-noise ratio, but the constrained filter is useful when waveform distortion is unacceptable.

scholarly journals Applicability of deep learning-based reconstruction trained by brain and knee 3T MRI to lumbar 1.5T MRI

2021 ◽  
Vol 10 (6) ◽  
pp. 205846012110239
Author(s):  
Nobuo Kashiwagi ◽  
Hisashi Tanaka ◽  
Yuichi Yamashita ◽  
Hiroto Takahashi ◽  
Yoshimori Kassai ◽  
...  
Keyword(s):  
Deep Learning ◽  
Magnetic Resonance ◽  
Image Quality ◽  
Signal To Noise Ratio ◽  
Magnetic Resonance Images ◽  
Reconstruction Method ◽  
Signal To Noise ◽  
Scanning Time ◽  
Noise Ratio ◽  
Weighted Sequences

Background Several deep learning-based methods have been proposed for addressing the long scanning time of magnetic resonance imaging. Most are trained using brain 3T magnetic resonance images, but is unclear whether performance is affected when applying these methods to different anatomical sites and at different field strengths. Purpose To validate the denoising performance of deep learning-based reconstruction method trained by brain and knee 3T magnetic resonance images when applied to lumbar 1.5T magnetic resonance images. Material and Methods Using a 1.5T scanner, we obtained lumber T2-weighted sequences in 10 volunteers using three different scanning times: 228 s (standard), 119 s (double-fast), and 68 s (triple-fast). We compared the images obtained by the standard sequence with those obtained by the deep learning-based reconstruction-applied faster sequences. Results Signal-to-noise ratio values were significantly higher for deep learning-based reconstruction-double-fast than for standard and did not differ significantly between deep learning-based reconstruction-triple-fast and standard. Contrast-to-noise ratio values also did not differ significantly between deep learning-based reconstruction-triple-fast and standard. Qualitative scores for perceived signal-to-noise ratio and overall image quality were significantly higher for deep learning-based reconstruction-double fast and deep learning-based reconstruction-triple-fast than for standard. Average scores for sharpness, contrast, and structure visibility were equal to or higher for deep learning-based reconstruction-double-fast and deep learning-based reconstruction-triple-fast than for standard, but the differences were not statistically significant. The average scores for artifact were lower for deep learning-based reconstruction-double-fast and deep learning-based reconstruction-triple-fast than for standard, but the differences were not statistically significant. Conclusion The deep learning-based reconstruction method trained by 3T brain and knee images may reduce the scanning time of 1.5T lumbar magnetic resonance images by one-third without sacrificing image quality.

scholarly journals Estimations of uncertainties of frequencies

2015 ◽  
Vol 11 (A29A) ◽  
pp. 201-201
Author(s):  
Laurent Eyer ◽  
Jean-Marc Nicoletti ◽  
Stephan Morgenthaler
Keyword(s):  
Time Series ◽  
Light Curve ◽  
Frequency Estimation ◽  
Signal To Noise Ratio ◽  
Simulated Data ◽  
Signal To Noise ◽  
Periodic Signals ◽  
Noise Ratio ◽  
The Universe

AbstractDiverse variable phenomena in the Universe are periodic. Astonishingly many of the periodic signals present in stars have timescales coinciding with human ones (from minutes to years). The periods of signals often have to be deduced from time series which are irregularly sampled and sparse, furthermore correlations between the brightness measurements and their estimated uncertainties are common. The uncertainty on the frequency estimation is reviewed. We explore the astronomical and statistical literature, in both cases of regular and irregular samplings. The frequency uncertainty is depending on signal to noise ratio, the frequency, the observational timespan. The shape of the light curve should also intervene, since sharp features such as exoplanet transits, stellar eclipses, raising branches of pulsation stars give stringent constraints. We propose several procedures (parametric and nonparametric) to estimate the uncertainty on the frequency which are subsequently tested against simulated data to assess their performances.

Signal-to-Noise Ratio Enhancement by Least-Squares Polynomial Smoothing

1976 ◽  
Vol 48 (8) ◽  
pp. 705A-712A ◽  
Author(s):  
C. G. Enke ◽  
Timothy A. Nieman
Keyword(s):  
Least Squares ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Polynomial Smoothing

The value of constrained conjugate-gradient least-squares migration in seismic inversion: Application to a fractured-basement play, Texas Panhandle

2017 ◽  
Vol 5 (3) ◽  
pp. SN13-SN23 ◽  
Author(s):  
Thang Ha ◽  
Kurt Marfurt
Keyword(s):  
Least Squares ◽  
Signal To Noise Ratio ◽  
Seismic Inversion ◽  
High Signal ◽  
Radon Transforms ◽  
Signal To Noise ◽  
Data Set ◽  
Texas Panhandle ◽  
Noise Ratio ◽  
Least Squares Migration

Seismic inversion has become almost routine in quantitative 3D seismic interpretation. To ensure the quality of the seismic inversion, the input seismic data need to have a high signal-to-noise ratio. With the current low oil price environment, seismic reprocessing is often preferred over reacquisition to improve data quality. Common filter pairs include forward and inverse [Formula: see text]-[Formula: see text] and Radon transforms. Forward and inverse migrations (i.e., migration and demigration) are a more recently introduced transform pair that, when used together in an iterative workflow, results in a least-squares migration algorithm. Least-squares migration compensates for surface variation in data density and, when combined with a filter applied to prestack migrated images, suppresses the operator and data aliasing. We apply a least-squares migration workflow to a fractured-basement data set from the Texas Panhandle to demonstrate the enhancement in signal-to-noise ratio, the reduction in acquisition footprint and migration artifacts, and the improvement in the P-impedance inversion result.

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