Severe Aliasing Research Articles

Cone-beam computed laminography with anisotropic adaptive weighted total variation minimization based on the framework of the Chambolle-Pock algorithm

Cone-beam computed laminography (CL) is still a very challenging problem for the inspection of thin-plate objects. Since CL projections are incomplete, the reconstructed images always suffer from severe aliasing and blurring in the z direction. To mitigate this problem, we propose an anisotropic adaptive weighted total variation (AAwTV) reconstruction model, which takes the edge properties between adjacent voxels into account and introduces different weights in different directions. In addition, we solved the proposed AAwTV using the Chambolle-Pock (CP) framework, since it has good computational efficiency and stable convergence, and is often easy to get a satisfactory reconstruction result. Experiments on simulated PCB phantom and simulated workpiece phantom show that the proposed algorithm can preserve the detailed features of the object well, and can effectively suppress inter-slice aliasing and blurring.

Cause-and-effect diagram-based supersaturated designs

Supersaturated designs (SSDs) are often used for screening experiments, and cause-and-effect diagrams (CEDs) are useful quality tools that help engineers decide which factors to use in experiments. Based on engineers’ prior knowledge, certain factors (referred to as the primary factors) in the cause-and-effect diagram are considered more likely to be active than the others (referred to as the potential factors). Due to the unequal importance of the factors, the traditional E ( s 2 ) criterion is not suitable for selecting supersaturated designs. In this article, we propose a CED-based approach to select supersaturated designs that have smaller variance in the estimates of the primary factor effects and less severe aliasing between the effects of the primary and potential factors. Simulation studies show that the proposed method selects supersaturated designs that outperform other supersaturated designs in terms of power and type I error when engineers have accurate prior knowledge.

Efficient magnetotelluric data acquisition using irregular stations and compressive sensing reconstruction

A major challenge in magnetotelluric (MT) surveys is the limited number of stations that can be collected due to the cost of receiver instrumentation and the time required to deploy them in large numbers. Many equal-distance acquisition grid used in MT surveys are either over sampling or faced with severe aliasing. We have applied the compressive sensing theory to MT acquisition and developed an efficient acquisition approach that uses optimized station layout with sparse irregular patterns. This acquisition strategy uses the optimized survey designs to acquire a sparse data set first, and then applies a compressive sensing reconstruction to obtain the equivalent dense data set on a regularly spaced grid. Once reconstructed, the dense data can be used in the traditional manner in the subsequent steps of processing, inversion, and interpretation. Our simulations show that comparable information can be obtained as that from a full regular grid in exploration settings by using as fewer as 25% stations. Furthermore, redeploying the same number of stations in a coarse grid used crustal studies can collect much more information. This new acquisition approach can lead to significant savings in both the acquisition cost and operational time and to maximized information from a given number of stations. The substantial savings in the cost, or the increase in the information content, could make many geoscientific investigations viable that might otherwise be impossible due to limited budget.

Distortion Reduction via CAE and DenseNet Mixture Network for Low Bitrate Spatial Audio Object Coding

Object-based audio content is becoming popular to represent immersive spatial sound because audio object positions can be totally independent of the locations of available loudspeakers. The encoder of the spatial audio object coding (SAOC) method transmits a mono downmix signal with spatial parameters of all audio objects, and the decoder reconstructs the original audio objects. However, the decoded audio object by SAOC has severe aliasing distortion, especially at low bitrates. This study focuses on distortion reduction of decoded audio objects at low bitrates. We present a new audio coding method via nonuniform fine sub-bands division strategy with convolutional autoencoder and a dense convolutional network mixture model, aiming to effectively compress spatial parameters of all audio objects. Evaluations indicate that the proposed approach reduces the aliasing distortion by 2.02%. It has achieved the best performances in both objective and subjective results with a low bitrate 1 kb/s per object.

Chebyshev Ambient Occlusion

Ambient Occlusion (AO) is a widely used shadowing technique in 3D rendering. One of the main disadvantages of using it is that it requires not only the surface depth but also the normal vector, which usually causes severe aliasing. This work introduces a novel AO algorithm by applying Chebyshev’s inequality. Instead of requiring the normal vector, we process the mean ( $\mu $ ) of the distribution of depth values from the screen space. We can efficiently calculate the variance ( $\sigma ^{2}$ ) over any kernel region. Using the Chebyshev AO, we can get the upper bound on the percentage of the shaded surface that is occluded. Our proposed method can usually provide a good approximation of true occlusion and can be used as an approximate value for AO rendering. As a post-processing rending, the time complexity of Chebyshev AO is $O\left ({2k}\right)$ which is simple to implement on current graphics devices and can be applied to the next generation of ray tracing technology.

Max-MUSIC: A Low-Complexity High-Resolution Direction Finding Method for Sparse MIMO Radars

In this paper, we propose a low-complexity high-resolution direction-of-arrival (DoA) method (max-MUSIC) by exploiting multiple subarrays of a sparse multiple-input multiple-output (MIMO) radar. In this method, specific subarrays for different MIMO configurations are selected according to a proposed selection criterion for generating diverse MUSIC spatial spectrums. Subsequently, we design a new spatial spectrum function that can perform high DoA estimation accuracy and resolution without spatial aliasing, by leveraging the advantages of the diverse spatial spectrums. With a given number of antenna elements, enhancements in array aperture size can improve estimation accuracy while causing severe aliasing, which cannot be mitigated. To define a legitimate MIMO configuration for aliasing suppression, a criterion that offers an optimal compromise between DoA estimation performance and anti-aliasing ability is provided. Simulations are provided to verify the effectiveness of the proposed method.

Overcoming the challenges of a shallow-water sparse wide-azimuth survey to improve deep reservoir imaging in the East China Sea

A new broadband wide-azimuth towed-streamer (WATS) survey was acquired to better resolve reservoir compartments in a shallow-water region of the East China Sea. To offset the shortcomings of narrow-azimuth acquisition along the strike direction, two vessels were added side-by-side as additional source vessels to form the WATS acquisition geometry for this survey. This WATS acquisition was much sparser than typical WATS surveys used in deepwater environments due to its one-sided configuration. The combination of sparse acquisition, shallow water, and deep targets set the challenge of how to optimally reveal the potential of side-gun data to improve the final image. Three-dimensional effects and severe aliasing in the crossline direction pose significant challenges for side-gun data processing. We present a comprehensive workflow to resolve these challenges consisting of 3D deghosting, 3D model-based water-layer demultiple, 3D surface-related multiple elimination, and 4D regularization for sparse and shallow-water wide-azimuth data. A tilted orthorhombic velocity model is built with better constraints from the wide-azimuth data, leading to improved fault positioning and imaging. Side-gun data clearly enhance the final target reservoir image and tie better with well data due to improved illumination. A new channel is discovered based on interpretation from the inverted VP/VS, explaining the previous incorrect prediction for one failed well that was drilled into a thinner and shallower channel unconnected to the main reservoir. An analysis of the impact of side-gun data from different offsets and azimuths shows that better azimuthal distribution within middle offset ranges had a more significant impact than far offsets in the final image of this survey. This information provides valuable reference in similar geologic conditions for future acquisition designs.

Multichannel antileakage least-squares spectral analysis for seismic data regularization beyond aliasing

The antileakage least-squares spectral analysis is a new method of regularizing irregularly spaced data series. This method mitigates the spectral leakages in the least-squares spectrum caused by non-orthogonality of the sinusoidal basis functions on irregularly spaced series, and it is robust when data series are wide-sense stationary. An appropriate windowing technique can be applied to adapt this method to non-stationary data series. When data series present mild aliasing, this method can effectively regularize the data series; however, additional information or assumption is needed when the data series is coarsely sampled. In this paper, we show how to incorporate the spatial gradients of the data series into the method to regularize data series presenting severe aliasing and show its robust performance on synthetic and marine seismic data examples.

Acquisition of a full-resolution image and aliasing reduction for a spatially modulated imaging polarimeter with two snapshots.

A snapshot imaging polarimeter using spatial modulation can encode four Stokes parameters allowing instantaneous polarization measurement from a single interferogram. However, the reconstructed polarization images could suffer a severe aliasing signal if the high-frequency component of the intensity image is prominent and occurs in the polarization channels, and the reconstructed intensity image also suffers reduction of spatial resolution due to low-pass filtering. In this work, a method using two anti-phase snapshots is proposed to address the two problems simultaneously. The full-resolution target image and the pure interference fringes can be obtained from the sum and the difference of the two anti-phase interferograms, respectively. The polarization information reconstructed from the pure interference fringes does not contain the aliasing signal from the high-frequency component of the object intensity image. The principles of the method are derived and its feasibility is tested by both computer simulation and a verification experiment. This work provides a novel method for spatially modulated imaging polarization technology with two snapshots to simultaneously reconstruct a full-resolution object intensity image and high-quality polarization components.

Reference guided CS-MRI with gradient orientation priors.

The theory of Compressed sensing (CS) provides a systematic framework for MR image reconstruction from under-sampled k-space data. However, severe aliasing artifacts still occurs in the case of high acceleration. Thereupon, an extensive body of works investigates exploiting additional prior information extracted from a reference image which can be acquired with relative ease in many MR applications. In this work, we propose a novel reference guided CS-MRI reconstruction method using gradient orientation priors (GOP). Specifically, we regularize the tangent vector in the target image to be perpendicular to the corresponding normal vector in the reference image over all spatial locations. The proposed method was validated using multi-scan experiment data and is shown to provide high speed and high quality imaging.

Visualizing Nonmanifold and Singular Implicit Surfaces with Point Clouds

We use octree spatial subdivision to generate point clouds on complex nonmanifold implicit surfaces in order to visualize them. The new spatial subdivision scheme only uses point sampling and an interval exclusion test. The algorithm includes a test for pruning the resulting plotting nodes so that only points in the closest nodes to the surface are used in rendering. This algorithm results in improved image quality compared to the naive use of intervals or affine arithmetic when rendering implicit surfaces, particularly in regions of high curvature. We discuss and compare CPU and GPU versions of the algorithm. We can now render nonmanifold features such as rays, ray-like tubes, cusps, ridges, thin sections that are at arbitrary angles to the octree node edges, and singular points located within plot nodes, all without artifacts. Our previous algorithm could not render these without severe aliasing. The algorithm can render the self-intersection curves of implicit surfaces by exploiting the fact that surfaces are singular where they self-intersect. It can also render the intersection curves of two implicit surfaces. We present new image space and object space algorithms for rendering these intersection curves as contours on one of the surfaces. These algorithms are better at rendering high curvature contours than our previous algorithms. To demonstrate the robustness of the node pruning algorithm we render a number of complex implicit surfaces such as high order polynomial surfaces and Gaussian curvature surfaces. We also compare the algorithm with ray casting interms of speed and image quality. For the surfaces presented here, the point clouds can be computed in seconds to minutes on atypical Intel based PC. Once this is done, the surfaces can be rendered at much higher frame rates to allow some degree of interactive visualization.

Shallow-structure characterization by 2D elastic full-waveform inversion

Assessing the effectiveness of elastic full-waveform-inversion (FWI) algorithms when applied to shallow 2D structures in the presence of a complex topography is critically important. By using FWI, we overcome inherent limitations of conventional seismic methods used for near-surface prospecting (acoustic tomography and multichannel spectral analysis of surface waves). The elastic forward problem, formulated in the frequency domain, is based on a mixed finite-element P0-P1 discontinuous Galerkin method to ensure accurate modeling of complex topography effects at a reasonable computing cost. The inversion problem uses an FWI algorithm to minimize the misfit between observed and calculated data. Based on results from a numerical experiment performed on a realistic landslide model inspired from the morphostructure of the Super-Sauze earthflow, we analyzed the effect of using a hierarchical preconditioning strategy, based on a simultaneous multifrequency inversion of damped data, to mitigate the strong nonlinearities coming from the surface waves. This strategy is a key point in alleviating the strong near-surface effects and avoiding convergence toward a local minimum. Using a limited-memory quasi-Newton method improved the convergence level. These findings are analogous to recent applications on large-scale domains, although limited source-receiver offset ranges, low-frequency content of the source, and domination of surface waves on the signal led to some difficulties. Regarding the impact of data decimation on the inversion results, we have learned that an inversion restricted to the vertical data component can be successful without significant loss in terms of parameter imagery resolution. In our investigations of the effect of increased source spacing, we found that a sampling of 4 m (less than three times the theoretical maximum of one half-wavelength) led to severe aliasing.

Residue Number System Arithmetic-Inspired Hopping-Pilot Pattern Design

In this paper, we propose a novel application of residue number system (RNS) arithmetic in designing hopping-pilot patterns for cellular downlink orthogonal frequency-division multiple access (OFDMA). By hopping the scan lines in either the time or the frequency domain, RNS-based pilot patterns fulfill the Nyquist sampling theorem. That is, by using RNS-based pilot patterns, the channel's delay-Doppler response can fully be reconstructed without severe aliasing. In addition to channel estimation, our proposed scheme can achieve other objectives, such as device/cell identification and time-frequency synchronization. We show that the RNS-based approach has more pairs of hopping-pilot patterns that are collision free than the Costas-array-based method. This is helpful in not only mitigating intra-/intercell interference but also identifying multiple devices in a multicell multiantenna environment. Moreover, hopping in time increases the pilot's time support, which, in turn, enables quick initial acquisition of time-frequency offsets.

Stable stylized wireframe rendering

AbstractStylized wireframe rendering of 3D model is widely used in animation software in order to depict the configuration of deformable model in comprehensible ways. However, since some inherent flaws in traditional depth test based rendering technology, shape of lines can not been preserved as continuous movement or deformation of models. There often exists severe aliasing like flickering artifact when objects rendered in line form animate, especially rendered with thick or dashed line. To cover this artifact, unlike traditional approach, we propose a novel fast line drawing method with high visual fidelity for wireframe depiction which only depends on intrinsic topology of primitives without any preprocessing step or extra adjacent information pre‐stored. In contrast to previous widely‐used solutions, our method is advantageous in highly accurate visibility, clear and stable line appearance without flickering even for thick and dashed lines with uniform width and steady configuration as model moves or animates, so that it is strongly suitable for animation system. In addition, our approach can be easily implemented and controlled without any additional preestimate parameters supplied by users. Copyright © 2010 John Wiley & Sons, Ltd.

Robust super-resolution by minimizing a Gaussian-weighted L2 error norm

Super-resolution restoration is the problem of restoring a high-resolution scene from multiple degraded low-resolution images under motion. Due to imaging blur and noise, this problem is ill-posed. Additional constraints such as smoothness of the solution via regularization is often required to obtain a stable solution. While adding a regularization term to the cost function is a standard practice in image restoration, we propose a restoration algorithm that does not require this extra regularization term. The robustness of the algorithm is achieved by a Gaussian-weighted L2-norm in the data misfit term that does not response to intensity outliers. With the outliers suppressed, our solution behaves similarly to a maximum-likelihood solution in the presence of Gaussian noise. The effectiveness of our algorithm is demonstrated with super-resolution restoration of real infrared image sequences under severe aliasing and intensity outliers.

Discrete-cosine-transform–domain downsizing with windowing operation

A simple and effective method is presented for discrete- cosine-transform (DCT)-domain downsizing. Various methods em- ployed in DCT-domain downsizing simply reuse the frequency com- ponent of DCT, which shows a severe aliasing effect. The proposed approach extends the downsizing method for alleviating or reducing the aliasing effect with a windowing operation, which adjusts the magnitude of the DCT coefficient. Visual inspection showed satis- factory results, with no complexity overhead and performance deg- radation regarding the peak-signal-to noise ratio (PSNR) after upsampling. © 2007 SPIE and IS&T. DOI: 10.1117/1.2818176

Bayesian Inference from Observations of Solar‐like Oscillations

Stellar oscillations, which can be extracted from observed time series of the star's brightness or radial velocity, can provide a wealth of information about a star. In this paper we address the question of how to extract as much information as possible from such a data set. We have developed a Markov chain Monte Carlo (MCMC) code that is able to infer the number of oscillation frequencies present in the signal and their values (with corresponding uncertainties), without having to fit the amplitudes and phases. Gaps in the data do not have any serious consequences for this method; in cases where severe aliasing exists, any ambiguity in the frequency determinations will be reflected in the results. It also allows us to infer parameters of the frequency pattern, such as the large separation Δν. We have previously applied this method to the star ν Indi, and here we describe the method fully and apply it to simulated data sets, showing that the code is able to give correct results even when some of the model assumptions are violated. In particular, the nonsinusoidal nature of the individual oscillation modes due to stochastic excitation and damping has no major impact on the usefulness of our approach.

Time‐Series Analysis of Super‐Kamiokande Measurements of the Solar Neutrino Flux

The Super-Kamiokande Consortium has recently released data suitable for time-series analysis. The binning is highly regular: the power spectrum of the acquisition times has a huge peak (power S > 120) at the frequency (in cycles per year) 35.98 (period 10.15 days), where power measurements are such that the probability of obtaining a peak of strength S or more by chance at a specified frequency is exp(-S). This inevitably leads to severe aliasing of the power spectrum. The strongest peak in the range 0 - 100 in a power spectrum formed by a likelihood procedure is at 26.57 (period 13.75 days) with S = 11.26. For the range 0 - 40, the second-strongest peak is at 9.42 (period 38.82 days) with S = 7.3. Since 26.57 + 9.42 = 35.99, we conclude that the weaker peak at 9.42 is an alias of the stronger peak at 26.57. We note that 26.57 falls in the band 26.36 - 27.66, formed from twice the range of synodic rotation frequencies of an equatorial section of the Sun for normalized radius larger than 0.1. Oscillations at twice the rotation frequency, attributable to "m = 2" structures, are not uncommon in solar data. We find from the shuffle test that the probability of obtaining a peak of S = 11.26 or more by chance in this band is 0.1 %. This new result therefore supports at the 99.9% confidence level previous evidence, found in Homestake and GALLEX-GNO data, for rotational modulation of the solar neutrino flux. The frequency 25.57 points to a source of modulation at or near the tachocline.

The Boundary Layer of Mars: Fluxes, Stability, Turbulent Spectra, and Growth of the Mixed Layer

Spectra of wind from high-frequency measurements in the Martian atmospheric surface layer, along with the diurnal variation of the height of the mixed surface layer, are calculated for the first time for Mars. Heat and momentum fluxes, stability, and z(sub 0) are estimated for early spring from a surface temperature model and from Viking Lander 2 temperatures and winds at 44 deg N, using Monin-Obukhov similarity theory. Flow distortion by the lander is also taken into account. Model spectra for two measuring heights and three surface roughnesses are calculated using the depth of the mixed layer and the surface-layer parameters. These experiments indicate that z(sub 0) probably lies between 1.0 and 3.0 cm, and most likely is closer to 1.0 cm. The spectra are adjusted to simulate aliasing and high-frequency rolloff, the latter caused by both the sensor response and the large Kolmogorov length on Mars. Since the spectral models depend on the surface parameters, including the estimated surface temperature, their agreement with the calculated spectra indicates that the surface-layer estimates are self-consistent. This agreement is especially noteworthy in that the inertial subrange is virtually absent in the Martian atmosphere at this height, due to the large Kolmogorov length scale. These analyses extend the range of applicability of terrestrial results and demonstrate that it is possible to estimate the effects of severe aliasing of wind measurements, to produce models that agree well with the measured spectra. The results show that similarity theory developed for Earth applies to Mars, and that the spectral models are universal.