Presence Of Aliasing Research Articles

Reconstructing Aliased Frequency Spectra by Using Multiple Sample Rates

A novel algorithm is presented that can resolve frequency ambiguity that arises from sampling a set of signals spanning more than a single Nyquist zone. The method uses two samplers, each sampling the same input signal with different (non-integer multiple) sampling rates. The algorithm is able to resolve frequency ambiguity and reconstruct signals with an orthogonal frequency basis spanning multiple Nyquist zones, provided that the aggregate information-bearing bandwidth of the signals is less than half the cumulative data converter sampling rates. This manuscript describes the theoretical background for the algorithm and validates it through measurements performed on a test-board comprising of two 10 bit analog-to-digital converters clocked at two different (non-integer multiple) sample rates. Measurements show that even in the presence of aliasing, an orthogonal signal spanning multiple Nyquist zones can be fully reconstructed.

Influence of Neighborhood Size and Cross-Correlation Peak-Fitting Method on Location Accuracy

A known technique to obtain subpixel resolution by using object tracking through cross-correlation consists of interpolating the obtained correlation function and then refining peak location. Although the technique provides accurate results, peak location is usually biased toward the closest integer coordinate. This effect is known as the peak-locking error and it strongly limits this calculation technique’s experimental accuracy. This error may differ depending on the scene and algorithm used to fit and interpolate the correlation peak, but in general, it may be attributed to a sampling problem and the presence of aliasing. Many studies in the literature analyze this effect in the Fourier domain. Here, we propose an alternative analysis on the spatial domain. According to our interpretation, the peak-locking error may be produced by a non-symmetrical sample distribution, thus provoking a bias in the result. According to this, the peak interpolant function, the size of the local domain and low-pass filters play a relevant role in diminishing the error. Our study explores these effects on different samples taken from the DIC Challenge database, and the results show that, in general, peak fitting with a Gaussian function on a relatively large domain provides the most accurate results.

Sparse Bayesian learning with multiple dictionaries

Sparse Bayesian learning (SBL) has emerged as a fast and competitive method to perform sparse processing. The SBL algorithm, which is developed using a Bayesian framework, approximately solves a non-convex optimization problem using fixed point updates. It provides comparable performance and is significantly faster than convex optimization techniques used in sparse processing. We propose a signal model which accounts for dictionary mismatch and the presence of errors in the weight vector at low signal-to-noise ratios. A fixed point update equation is derived which incorporates the statistics of mismatch and weight errors. We also process observations from multiple dictionaries. Noise variances are estimated using stochastic maximum likelihood. The derived update equations are studied quantitatively using beamforming simulations applied to direction-of-arrival (DoA). Performance of SBL using single- and multi-frequency observations, and in the presence of aliasing, is evaluated. SwellEx-96 experimental data demonstrates qualitatively the advantages of SBL.

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.

Correction of Dual-PRF Doppler Velocity Outliers in the Presence of Aliasing

AbstractIn Doppler weather radars, the presence of unfolding errors or outliers is a well-known quality issue for radial velocity fields estimated using the dual–pulse repetition frequency (PRF) technique. Postprocessing methods have been developed to correct dual-PRF outliers, but these need prior application of a dealiasing algorithm for an adequate correction. This paper presents an alternative procedure based on circular statistics that corrects dual-PRF errors in the presence of extended Nyquist aliasing. The correction potential of the proposed method is quantitatively tested by means of velocity field simulations and is exemplified in the application to real cases, including severe storm events. The comparison with two other existing correction methods indicates an improved performance in the correction of clustered outliers. The technique proposed is well suited for real-time applications requiring high-quality Doppler radar velocity fields, such as wind shear and mesocyclone detection algorithms, or assimilation in numerical weather prediction models.

Constraint matrix factorization for space variant PSFs field restoration

In large-scale spatial surveys, the point spread function (PSF) varies across the instrument field of view (FOV). Local measurements of the PSFs are given by the isolated star images. Yet, these estimates may not be directly usable for post-processing because of the observational noise and potentially the aliasing. Given a set of aliased and noisy star images from a telescope, we aim to estimate well-resolved and noise-free PSFs at the observed star positions. In particular, exploiting the spatial correlation of the PSFs across the FOV. We introduce RCA (resolved components analysis) which is a noise-robust dimension reduction and super-resolution method based on matrix-factorization. We propose an original way of using the PSFs spatial correlation in the restoration process through sparsity. The introduced formalism can be applied to correlated data sets with respect to any euclidean parametric space. We tested our method on simulated monochromatic PSFs of Euclid telescope (launch planned for 2020). The proposed method outperforms existing PSFs restoration and dimension reduction methods. We show that a coupled sparsity constraint on individual PSFs and their spatial distribution yields a significant improvement on both the restored PSFs shapes and the PSFs subspace identification, in presence of aliasing. RCA can be naturally extended to account for the wavelength dependency of the PSFs.

Electrical bioimpedance spectroscopy in time-variant systems: Is undersampling always a problem?

Abstract During the last decades, Electrical Bioimpedance Spectroscopy (EBIS) has been applied mainly by using the frequency-sweep technique, across a range of many different applications. Traditionally, the tissue under study is considered to be time-invariant and dynamic changes of tissue activity are ignored by treating the changes as a noise source. A new trend in EBIS is simultaneous electrical stimulation with several frequencies, through the application of a multi-sine, rectangular or other waveform. This method can provide measurements fast enough to sample dynamic changes of different tissues, such as myocard. This high sampling rate comes at a price of reduction in SNR and the increase in complexity of devices. Although the frequency-sweep technique is often inadequate for monitoring the dynamic changes in a variant system, it can be used successfully in applications focused on the time-invariant or slowly-variant part of a system. However, in order to successfully use frequency-sweep EBIS for monitoring time-variant systems, it is paramount to consider the effects of aliasing and especially the folding of higher frequencies, on the desired frequency e.g. DC level. This paper discusses sub-Nyquist sampling of thoracic EBIS measurements and its application in the case of monitoring pulmonary oedema. It is concluded that by considering aliasing, and with proper implementation of smoothing filters, as well as by using random sampling, frequency-sweep EBIS can be used for assessing time-invariant or slowly-variant properties of time-variant biological systems, even in the presence of aliasing. In general, undersampling is not always a problem, but does always require proper consideration.

Maximum likelihood estimation for InSAR image co-registration

This paper presents a closed-form robust phase correlation based algorithm for performing image registration to subpixel accuracy. The subpixel translational shift information is directly obtained from the phase of the normalized cross power spectrum by using Maximum Likelihood Estimation (MLE). The proposed algorithm also has slighter time complexity. Experimental results show that the proposed algorithm yields superior registration precision on the Cramer-Rao Bound (CRB) in the presence of aliasing and noise.

Rely-guarantee references for refinement types over aliased mutable data

Reasoning about side effects and aliasing is the heart of verifying imperative programs. Unrestricted side effects through one reference can invalidate assumptions about an alias. We present a new type system approach to reasoning about safe assumptions in the presence of aliasing and side effects, unifying ideas from reference immutability type systems and rely-guarantee program logics. Our approach, rely-guarantee references, treats multiple references to shared objects similarly to multiple threads in rely-guarantee program logics. We propose statically associating rely and guarantee conditions with individual references to shared objects. Multiple aliases to a given object may coexist only if the guarantee condition of each alias implies the rely condition for all other aliases. We demonstrate that existing reference immutability type systems are special cases of rely-guarantee references. In addition to allowing precise control over state modification, rely-guarantee references allow types to depend on mutable data while still permitting flexible aliasing. Dependent types whose denotation is stable over the actions of the rely and guarantee conditions for a reference and its data will not be invalidated by any action through any alias. We demonstrate this with refinement (subset) types that may depend on mutable data. As a special case, we derive the first reference immutability type system with dependent types over immutable data. We show soundness for our approach and describe experience using rely-guarantee references in a dependently-typed monadic DSL in Coq.

Hemodynamic Changes in Dogs With Diffuse Hepatic Neoplasia Detected by Doppler Ultrasonography

For the purpose of conferring additional information to B-mode ultrasound in the diagnosis of diffuse hepatic diseases, this study aimed to assess liver hemodynamics by Doppler ultrasonography in dogs with diffuse hepatic neoplasia. Were included 11 dogs with histopathologic diagnosis of hepatic neoplasia (7 lymphoma, 4 hepatocellular carcinoma), and diffuse echotexture and echogenicity changes, without detectible nodular lesions in ultrasound. Intrahepatic vascularization, main portal vein and hepatic artery flow were assessed by color and spectral Doppler. A control group of 10 healthy dogs was included. Statistical analysis was performed by Fisher test. Comparing clinical and control group, it was observed that hemodynamic changes associated with diffuse hepatic neoplasia, detected by Doppler ultrasonography, were: common hepatic artery dilation (p = 0.035) and altered intrahepatic vascular pattern by color Doppler mapping (p = 0.001), such as hypervascularity with chaotic distribution of vessels, luminal compression and vascular deviation course, associated or not, with the presence of aliasing. Spectral Doppler showed arterial flow with high systolic peak or low resistivity index. Intrahepatic hemodynamic changes detected by Doppler ultrasonography may help to identify diffuse hepatic neoplasia in dogs, adding information to B-mode exam. More studies with great number of animals are necessary to confirm these data.

Detecting Null-dereference Bugs via a Backward Analysis

Null dereference is a common occurring bug in programming languages such as C. In this paper, we propose a path-sensitive and context-sensitive approach that performs a backward dataflow analysis to identify null-dereference bugs. One novel feature of our approach is that with the help of aliasing predicates, it can perform strong updates in presence of aliasing, thus eliminating false positives. The aliasing predicates are introduced on the premise of a canonical representation for program being analyzed. Moreover, a context-sensitive algorithm for inter-procedural null-dereference analysis is also presented in this paper, which also contributes to improve accuracy. We have implemented this approach, and give an evaluation of it on a set of open source benchmarks. The experimental results verify the effectiveness of our approach, and show that it is suitable for exploring large real programs with reasonable accuracy.

A 3D simultaneous source field test processed using alternating projections: a new active separation method

ABSTRACTIn 2008, a wide azimuth simultaneous source (SimSrc) 3D data set was acquired over an area coinciding with an existing conventional wide azimuth survey. Using two (nearly) simultaneous sources provided twice the number of shots, an increased shot density and twice the fold for essentially the same acquisition time. Although the improved sampling for the SimSrc data was predicted to yield improvements in processes such as 3D multiple attenuation and migration, cross‐talk between the sources was a concern. Cross‐talk can be suppressed by known techniques such as separation algorithms that estimate the individual shots and thereby separate SimSrc records into their constituent shots. However, separation algorithms available at the time suffered from aliasing and were not effective for severely shot‐aliased data such as those encountered in the experimental data set, which had a 75‐m in‐line shot spacing, half that typical for wide azimuth geometries.In this paper we present a new separation technique called the Alternating Projection Method (APM), which is demonstrated to be robust in the presence of aliasing. Through comparisons with conventional wide azimuth data we show that 3D multiple removal and migration are both aided by the increase in shots. Moreover, the high quality of the APM separated data indicates that prestack products such as migration angle gathers will have better quality than was achieved a few years ago using a passive separation approach. We found that by carefully selecting and tailoring the method's projection operators, excellent separation results can be achieved efficiently.

Low-level liquid types

We present Low-Level Liquid Types , a refinement type system for C based on Liquid Types . Low-Level Liquid Types combine refinement types with three key elements to automate verification of critical safety properties of low-level programs: First, by associating refinement types with individual heap locations and precisely tracking the locations referenced by pointers, our system is able to reason about complex invariants of in-memory data structures and sophisticated uses of pointer arithmetic. Second, by adding constructs which allow strong updates to the types of heap locations, even in the presence of aliasing, our system is able to verify properties of in-memory data structures in spite of temporary invariant violations. By using this strong update mechanism, our system is able to verify the correct initialization of newly-allocated regions of memory. Third, by using the abstract interpretation framework of Liquid Types, we are able to use refinement type inference to automatically verify important safety properties without imposing an onerous annotation burden. We have implemented our approach in CSOLVE, a tool for Low-Level Liquid Type inference for C programs. We demonstrate through several examples that CSOLVE is able to precisely infer complex invariants required to verify important safety properties, like the absence of array bounds violations and null-dereferences, with a minimal annotation overhead.

Minimum-phase parts of zero-phase sequences

For more than a decade it has been empirically known that the causal portion of the inverse Fourier transform of the magnitude spectrum of the speech signal behaves like a minimum-phase signal. Later on, this statement has been shown for an all-pole model. In this paper, we consider related results for both discrete-time Fourier and discrete Fourier transforms of arbitrary sequences. We indicate how the presence of aliasing in circular autocorrelation might be detected. The energy concentration property of zero-phase sequences is discussed.

Effective typestate verification in the presence of aliasing

This article addresses the challenge of sound typestate verification, with acceptable precision, for real-world Java programs. We present a novel framework for verification of typestate properties, including several new techniques to precisely treat aliases without undue performance costs. In particular, we present a flow-sensitive, context-sensitive, integrated verifier that utilizes a parametric abstract domain combining typestate and aliasing information. To scale to real programs without compromising precision, we present a staged verification system in which faster verifiers run as early stages which reduce the workload for later, more precise, stages. We have evaluated our framework on a number of real Java programs, checking correct API usage for various Java standard libraries. The results show that our approach scales to hundreds of thousands of lines of code, and verifies correctness for 93% of the potential points of failure.

Optimal Registration Of Aliased Images Using Variable Projection With Applications To Super-Resolution

Accurate registration of images is the most important and challenging aspect of multiframe image restoration problems such as super-resolution. The accuracy of super-resolution algorithms is quite often limited by the ability to register a set of low-resolution images. The main challenge in registering such images is the presence of aliasing. In this paper, we analyse the problem of jointly registering a set of aliased images and its relationship to super-resolution. We describe a statistically optimal approach to multiframe registration which exploits the concept of variable projections to achieve very efficient algorithms. Finally, we demonstrate how the proposed algorithm offers accurate estimation under various conditions when standard approaches fail to provide sufficient accuracy for super-resolution.

Generating precise and concise procedure summaries

We present a framework for generating procedure summaries that are (a) precise - applying the summary in a given context yields the same result as re-analyzing the procedure in that context, and(b) concise - the summary exploits the commonalitiesin the ways the procedure manipulates abstract values, and does not contain superfluous context information. The use of a precise and concise procedure summary inmodular analyses provides a way to capture infinitely many possible contexts in a finite way; in interprocedural analyses, it provides a compact representation of an explicit input-output summary table without loss of precision. We define a class of abstract domains and transformers for which precise and concise summaries can be efficiently generated using our framework. Our framework is rich enough to encode a wide range of problems, including all IFDS and IDE problems. In addition, we show how the framework is instantiated to provide novel solutions to two hard problems: modular linear constant propagation and modular typestate verification, both in the presence of aliasing. We implemented a prototype of our framework that computes summaries for the typestate domain, and report on preliminary experimental results.

BI-hyperdoctrines, higher-order separation logic, and abstraction

We present a precise correspondence between separation logic and a simple notion of predicate BI, extending the earlier correspondence given between part of separation logic and propositional BI. Moreover, we introduce the notion of a BI hyperdoctrine, show that it soundly models classical and intuitionistic first- and higher-order predicate BI, and use it to show that we may easily extend separation logic to higher-order . We also demonstrate that this extension is important for program proving, since it provides sound reasoning principles for data abstraction in the presence of aliasing.

A logical analysis of aliasing in imperative higher-order functions

AbstractWe present a compositional programme logic for call-by-value imperative higher-order functions with general forms of aliasing, which can arise from the use of reference names as function parameters, return values, content of references and parts of data structures. The programme logic extends our earlier logic for alias-free imperative higher-order functions with new operators which serve as building blocks for clean structural reasoning about programms and data structures in the presence of aliasing. This has been an open issue since the pioneering work by Cartwright–Oppen and Morris twenty-five years ago. We illustrate usage of the logic for description and reasoning through concrete examples including a higher-order polymorphic Quicksort. The logical status of the new operators is clarified by translating them into (in)equalities of reference names.

Simplification of Complex EPR Spectra by Cepstral Analysis

As the Fourier transform of time-series data is known as the spectrum, the Fourier transform of the logarithm of the time-series data is called the cepstrum of the data. When cepstral analysis is applied to free induction decay signals of free radicals showing first-order EPR spectra, the identification of nuclear hyperfine coupling constants becomes simple. In a systematic manner, we have examined how the technique of cepstral analysis is affected by the presence of aliasing, noise, uncertainty in the time origin of the free induction decay, the presence of second-order hyperfine couplings, and the applications of various apodization methods. This technique was then applied to analyze the EPR spectrum of anthraquinone anion radical, and anion radicals of porphycene and tetrapropyl-porphycene, and the hyperfine coupling constants thus obtained were compared with published data. A good agreement was always found. We make a case for the usefulness of cepstral analysis in determining the hyperfine coupling constants of complex EPR spectra of organic free radicals.