Aliased Data Research Articles

New algorithms for spherical harmonic analysis of area mean values over blocks delineated by equiangular and Gaussian grids

Spherical harmonic analysis is widely used in all aspects of geoscience. Exact quadrature methods are available for the spherical harmonic analysis of band-limited point values at the grid points of equiangular and Gaussian grids. However, no similarly exact quadrature methods are available for the spherical harmonic analysis of area mean values over the blocks delineated by these grids. In this study, new algorithms appropriate for the exact spherical harmonic analysis of the band-limited area mean values over the blocks delineated by equiangular and Gaussian grids are proposed. For band-limited data, precision that is between that of the least-squares estimation method and of the approximate quadrature methods can be achieved by using the new algorithms. Regarding the computational complexity, fewer operations are needed by the new methods as compared to those needed by the least-squares estimation method and the approximate quadrature methods in the preparation stage when the maximum degree of the spherical harmonic analysis is very large. Simulation experiments are performed to compare the ability to recover the spherical harmonic coefficients by using the least-squares estimation method, the approximate quadrature methods and these new algorithms from aliased data with aliasing components of realistic magnitudes. The results suggest that these new algorithms, with time complexity one order less than that of the least-squares estimation method in the solving stage, perform roughly the same as the least-squares estimation method in recovering spherical harmonic coefficients from the aliased data.

Joint camera blur and pose estimation from aliased data.

A joint-estimation algorithm is presented that enables simultaneous camera blur and pose estimation from a known calibration target in the presence of aliasing. Specifically, a parametric maximum-likelihood (ML) point-spread function estimate is derived for characterizing a camera's optical imperfections through the use of a calibration target in an otherwise loosely controlled environment. The imaging perspective, ambient-light levels, target reflectance, detector gain and offset, quantum efficiency, and read-noise levels are all treated as nuisance parameters. The Cramér-Rao bound is derived, and simulations demonstrate that the proposed estimator achieves near optimal mean squared error performance. The proposed method is applied to experimental data to validate the fidelity of the forward models as well as to establish the utility of the resulting ML estimates for both system identification and subsequent image restoration.

Exploiting surface consistency for surface-wave characterization and mitigation — Part 1: Theory and 2D examples

We have developed a new tomographic inversion method that is able to determine the properties of complex surface waves, which are multimodal and heterogeneous. These properties can be used to generate a detailed near-surface earth model or to predict and remove the surface waves, while protecting reflection signals even with aliased data. The inversion assumes plane-wave physics and generates surface-consistent model parameters as a function of frequency. In this paper, we validate our method with 2D models and data. In a companion paper, we demonstrate its application to 3D data. Inversion for a single mode is linear, but the linearity does not hold at higher frequencies, where multiple modes interfere. However, single-mode inversion results can be used to create a starting model for the subsequent nonlinear multimode tomography. The resulting velocity-frequency grid has greater resolution compared with a beam-forming method. The dispersion curves can be used as input to a subsequent standard 1D surface-wave inversion to generate a velocity-depth model. The tomographic method also determines a grid of attenuation quality factors and variations in the source amplitude and bandwidth, which correlate with the near-surface elevation changes. The amplitude and phase properties can be used together to predict the surface-wave waveforms, which can then be adaptively subtracted from the data on a trace-to-trace basis.

Exploiting the control of phase in marine vibrators

Marine seismic vibrators are considered to be more environmentally friendly than air guns and this has prompted a resurgence of interest in their use. However, these devices have novel features that are potentially of great benefit to seismic imaging and that have not yet been exploited - in particular, we can control the phase. With marine vibrators, the emitted waveform can be chosen freely, provided that it lies within the envelope of what the device can emit. Typically, the waveform is a swept-frequency sinusoid. In this paper, we show how the sweep phase can be used to suppress the residual shot noise (RSN) and to separate simultaneous sources of high multiplicity. This work is also described by Laws and Halliday (2013) and is closely related to that of Laws (2012). The control of phase is a benefit of marine vibrators that can be exploited to great effect. First, we look at the RSN situation. The conventional wisdom is that roughly a 10s shot-time interval is required in marine seismic data acquisition so that the RSN is acceptably small relative to the signal. Because both signal and RSN originate from the seismic source, the ratio of signal/RSN is not improved by using a larger source (pace Landro, 2008). We show a simple case of RSN attenuation using alternating sine and cosine sweeps. That is to say, the sequence of source phases goes, for successive shots, [0° 90° 0° 90° 0° 90° 0° 90°... and so on]. We show schematically how this ‘phase sequencing’ leads to a dramatic attenuation of the RSN. It does so by moving the RSN into parts of the frequency-wavenumber spectrum where there is no signal. We then use frequency-wavenumber filtering to remove the RSN. This can be done with simple filtering up to the limit imposed by spatial aliasing and beyond that limit by using wavefield reconstruction methods, such as generalized matching pursuit (Ozbek et al., 2010; Vassallo et al., 2010). Reconstruction methods decompose the seismic wavefield into a set of basis functions that allow the signal and RSN to be identified and separated. Then, we look at the simultaneous source situation. The RSN removal problem can be considered as a special case of the more general simultaneous source separation problem. As an example, in the case of two simultaneous sources, one source can be swept with consistent phase, while the other source is swept with alternating phase, i.e., the sequence of relative phases is [0° 180° 0° 180° 0° 180° 0° 180°... and so on]. The simultaneous source separation is demonstrated using the same type of reconstruction method as described above for the RSN. See also Moore et al. (2008) and Ji et al. (2012). The use of phase sequencing opens up possibilities for simultaneous source separation using large numbers of sources. By having complete control over the phases of all the sources it is possible, in certain domains, to make simultaneous source data look similar to aliased data from a single source. This opens the door to using many established wavefield interpolation and dealiasing-techniques to perform high-multiplicity simultaneous source separation.

Adaptive Dealiasing for Doppler Velocities Scanned from Hurricanes and Typhoons

AbstractBy fitting a parametric vortex model directly to aliased radar radial velocities scanned from a hurricane, the maximum tangential velocity and its radial distance from the hurricane vortex center can be estimated by the recently developed alias-robust vortex analysis. This vortex analysis can be refined to produce a suitable reference radial velocity field on each tilt of a radar scan for the reference check in the first main step of dealiasing. This paper presents the techniques developed for the refinements and shows how and to what extent the refined vortex analysis can improve the reference check and thus enhance the dealiased data coverage, especially over severely aliased data areas around the vortex core of a hurricane or typhoon. In addition, stringent threshold conditions are used in the reference check and the subsequent continuity check to ensure the accepted data are free of alias or almost so. The robustness and improved performance of the method are exemplified by the results tested with severely aliased radial velocities scanned by operational WSR-88D radars from hurricanes in the United States and by operational China New Generation Weather Radar (CINRAD) base data format SA radars from typhoons in China.

Ultrasonic Assessment of Myocardial Microstructure

Echocardiography is a widely accessible imaging modality that is commonly used to noninvasively characterize and quantify changes in cardiac structure and function. Ultrasonic assessments of cardiac tissue can include analyses of backscatter signal intensity within a given region of interest. Previously established techniques have relied predominantly on the integrated or mean value of backscatter signal intensities, which may be susceptible to variability from aliased data from low frame rates and time delays for algorithms based on cyclic variation. Herein, we describe an ultrasound-based imaging algorithm that extends from previous methods, can be applied to a single image frame and accounts for the full distribution of signal intensity values derived from a given myocardial sample. When applied to representative mouse and human imaging data, the algorithm distinguishes between subjects with and without exposure to chronic afterload resistance. The algorithm offers an enhanced surrogate measure of myocardial microstructure and can be performed using open-access image analysis software.

Ultrasonic Assessment of Myocardial Microstructure

Echocardiography is a widely accessible imaging modality that is commonly used to noninvasively characterize and quantify changes in cardiac structure and function. Ultrasonic assessments of cardiac tissue can include analyses of backscatter signal intensity within a given region of interest. Previously established techniques have relied predominantly on the integrated or mean value of backscatter signal intensities, which may be susceptible to variability from aliased data from low frame rates and time delays for algorithms based on cyclic variation. Herein, we describe an ultrasound-based imaging algorithm that extends from previous methods, can be applied to a single image frame and accounts for the full distribution of signal intensity values derived from a given myocardial sample. When applied to representative mouse and human imaging data, the algorithm distinguishes between subjects with and without exposure to chronic afterload resistance. The algorithm offers an enhanced surrogate measure of myocardial microstructure and can be performed using open-access image analysis software.

A VAD-Based Dealiasing Method for Radar Velocity Data Quality Control

AbstractThis paper describes a new velocity–azimuth display (VAD)-based dealiasing method developed for automated radar radial velocity data quality control to satisfy the high-quality standard and efficiency required by operational radar data assimilation. The method is built on an alias-robust velocity–azimuth display (AR-VAD) analysis. It upgrades and simplifies the previous three-step dealiasing method in three major aspects. First, the AR-VAD is used with sufficiently stringent threshold conditions in place of the original modified VAD for the preliminary reference check to produce alias-free seed data in the first step. Second, the AR-VAD is more accurate than the traditional VAD for the refined reference check in the original second step, so the original second step becomes unnecessary and is removed. Third, a block-to-point continuity check procedure is developed, in place of the point-to-point continuity check in the original third step, which serves to enhance the use of the available seed data in a properly enlarged block area around each flagged data point that is being checked with multiple threshold conditions to avoid false dealiasing. The new method has been tested extensively with aliased radial velocity data collected under various weather conditions, including hurricane high-wind conditions. The robustness of the new method is exemplified by the results tested with three cases. The limitations of the new method and possible improvements are discussed.

Data reconstruction with shot-profile least-squares migration

We introduce shot-profile migration data reconstruction (SPDR). SPDR constructs a least-squares migrated shot gather using shot-profile migration and demigration operators. Both operators are constructed with a constant migration velocity model for efficiency and so that SPDR requires minimal information about the underlying geology. Applying the demigration operator to the least-squares migrated shot gather gives the reconstructed data gather. SPDR can reconstruct a shot gather from observed data that are spatially aliased. Given a constraint on the geological dips in an approximate model of the earth’s reflector, signal and aliased energy that interfere in the common shot data gather are disjoint in the migrated shot gather. In the least-squares migration algorithm, we construct weights to take advantage of this separation, suppressing the aliased energy while retaining the signal, and allowing SPDR to reconstruct a shot gather from aliased data. SPDR is illustrated with synthetic data examples and one real data example.

Alias-free image subsampling using Fourier-based windowing methods

An antialiasing image subsampling method using Fourier-based windowing is presented. To reduce resolution, directly subsampling an image results in aliased data. To avoid aliasing, the original image has to be low-pass filtered within the bandwidth of the subsampled image prior to subsampling. However, applying a simple rectangular filter causes ringing effect (ripples), which is also called the Gibbs phenomenon. Conventional finite impulse response (FIR) or infinite impulse response (IIR) filters use spectral windows (e.g., Gaussian, Hamming, Hanning, or Butterworth windows, etc.) to yield a smooth transition band at the cutoff frequency. Yet this approach attenuates the higher frequency contents of the subsampled image and results in the widening of the transition band of the impulse response. An alias-free image subsampling method is developed using a power window to reduce the spatial domain ringing effect and to preserve most of the spatial frequency contents of the subsampled image.

Spatial undersampling for synthetic aperture ultrasonic imaging via digital spotlighting technique

High resolution ultrasonic imaging may be achieved via the synthetic aperture focusing technique, provided that the synthetic antenna is correctly spatially sampled. We show that spatial undersampling is possible, using a digital spotlighting technique that permits to recover the correct reconstructed images from aliased data. The proposed method is applied to experimental ultrasonic data.

Stability of an algorithm to restore continuously sampled band-limited images from aliased data

A continuously sampled object is one periodically set to zero. A continuously sampled band-limited object can be restored by multiplying by an appropriately parameterized periodic function and filtering the product. The sensitivity of this restoration procedure to additive noise is considered. In general, the restoration noise level increases dramatically as the degree of aliasing of the data increases or the duty cycle of the degradation decreases. Numerical results are given for white noise and noise with Laplace autocorrelation. The results are compared with the noise sensitivity of conventional (discrete) Shannon-sampling-theorem interpolation, in which fewer data are used.

Restoration of continuously sampled band-limited signals from aliased data

A continuously sampled signal is obtained by periodically placing a signal to zero. A straightforward closed form method is presented for restoration of continuously sampled bandlimited signals-even when the data is aliased. The sampled signal is simply multiplied by a periodic function specified by the duty cycle of the degradation and the severity of aliasing. This product is then placed through a filter with bandwidth equal to that of the signal. The filter acts as an interpolator and the original signal is restored.