Aliasing Patterns Research Articles

Multiple-Parallel Morphological Anti-Aliasing Algorithm Implemented in FPGA

During 3D rendering by GPU, jagged patterns will appear at the edge of the image due to the lack of sampling points. To increase the continuity of the image, we use an anti-aliasing technique to process these jagged patterns. In this paper, we review the current anti-aliasing techniques and propose a multi-parallel anti-aliasing algorithm based on Morphological Anti-Aliasing (MLAA). Through an experiment and a comparison of the results, we find that our algorithm achieves better anti-aliasing performance at the edge of the image than Multiple Sampling Anti-Aliasing (MSAA) and MLAA by setting more color gradients. Moreover, our algorithm consumes much less time than MLAA in FPGA implementation by performing edge detection of the image, classification of the aliasing patterns, acquisition of the blend weight coefficients, and calculation of the anti-aliased color in three channels of the image simultaneously. In addition, our algorithm also consumes much less memory than MLAA in FPGA implementation by scaling and optimizing the area texture used by MLAA. A comparison of related works indicates that it is more favorable for the proposed algorithm to perform the anti-aliasing of the image than MSAA and MLAA.

Frames-of-Reference-Based Learning: Overcoming Perceptual Aliasing in Multistep Decision-Making Tasks

Perceptual aliasing challenges reinforcement learning agents. They struggle to learn stable policies by failing to identify and disambiguate perceptually identical states in the environment that require different actions to reach a goal. As the agent often has only a local frame of reference, it cannot represent the global environment. Frame-of-reference-based learning is a feature of vertebrate intelligence that allows multiple simultaneous representations of an environment at different levels of abstraction. This enables the resolution of patterns that are made up of patterns that are made up of features. The evolutionary computation technique of learning classifier systems has shown promise in learning nested patterns in single-step domains. This work uses the frame-of-reference concept within a learning classifier system to learn stable policies in non-Markov multistep domains. Considering aliased states at a constituent level enables the system to place them appropriately in holistic-level policies. Instead of enumerating a huge search space, evolution computation empowers the novel system to evolve fitter rules and policies. The experimental results show that the novel system effectively solves complex aliasing patterns in non-Markov environments that have been challenging to artificial agents. For example, the novel system utilizes only 6.5, 3.71, and 3.22 steps to resolve Maze10, Littman57, and Woods102, respectively.

Sparse DNN Model for Frequency Expanding of Higher Order Ambisonics Encoding Process

The performance of higherorder Ambisonics (HOA) signals obtained using spherical harmonics decomposition method is disturbed by two primary sources of errors, the noise pollution in low-frequency band and the spatial aliasing in high-frequency band. Inspired by the HOA signals upscale method, which is performed using the sparse character of the sound field, this paper propose a sound field decomposition model based on a sparse deep neural network that offers HOA signals with wider frequency bandwidth. We use the frequency domain multi-scale convolutional network to realize the spherical harmonics decomposition, as well as learning the spatial aliasing pattern, based on which the aliasing-free HOA signals can be derived. Besides, we apply a sparse encoding network to cpature the sparse feature of the sound field which will improve the model performance when the sparse condition is satisfied. The experiments results prove that the proposed model can obtain HOA signals with wider frequency range of operation under multiple sources (up to 10 sources) and low reverberant environments (<inline-formula><tex-math notation="LaTeX">$T_{60}\le$</tex-math></inline-formula> 400 ms). When the sparsity feature cannot be satisfied (<inline-formula><tex-math notation="LaTeX">$T_{60} =$</tex-math></inline-formula> 800 ms), the proposed network model still maintain the same performance as the traditional methods.

Fault Diagnosis Based on Tree Heuristic Feature Selection and FS-DFV for Rolling Element Bearings

In order to make up for the deficiency of traditional single diagnosis in rolling element bearing fault diagnosis application, eliminate a large amount of redundant information and improve the classification effect of the aliasing mode, based on comprehensive analysis of the respective advantages of fuzzy set and tree search, this paper presents a joint rolling bearing fault diagnosis method based on tree-inspired feature selection and FS-DFV (Fuzzy Set and Dependent Feature Vector). The dependent feature vectors (DFV) can dig deeper the essential differences of the faults and improve the fault accuracy. By establishing the heuristic tree model, the tree type heuristic feature search strategy is designed, and the excellent feature selection criteria based on the density clustering with noise are proposed, and the conventional feature selection model is improved. In addition, fuzzy set are used to process the problem of extracting aliasing patterns in the DFV, and fuzzy membership is used to guide subsequent feature extraction of the alias modes. The proposed method is compared with the other four fault diagnosis methods. The experimental results show that the proposed method can effectively improve the diagnostic efficiency of the rolling bearing.

Signal aliasing in Gaussian random fields for experiments with qualitative factors

Signal aliasing is an inevitable consequence of using fractional factorial designs. Unlike linear models with fixed factorial effects, for Gaussian random field models advocated in some Bayesian design and computer experiment literature, the issue of signal aliasing has not received comparable attention. In the present article, this issue is tackled for experiments with qualitative factors. The signals in a Gaussian random field can be characterized by the random effects identified from the covariance function. The aliasing severity of the signals is determined by two key elements: (i) the aliasing pattern, which depends only on the chosen design, and (ii) the effect priority, which is related to the variances of the random effects and depends on the model parameters. We first apply this framework to study the signal-aliasing problem for regular fractional factorial designs. For general factorial designs including nonregular ones, we propose an aliasing severity index to quantify the severity of signal aliasing. We also observe that the aliasing severity index is highly correlated with the prediction variance.

Rolling Bearings Fault Diagnosis Based on Tree Heuristic Feature Selection and the Dependent Feature Vector Combined with Rough Sets

Rolling element bearings (REB) are widely used in all walks of life, and they play an important role in the health operation of all kinds of rotating machinery. Therefore, the fault diagnosis of REB has attracted substantial attention. Fault diagnosis methods based on time-frequency signal analysis and intelligent classification are widely used for REB because of their effectiveness. However, there still exist two shortcomings in these fault diagnosis methods: (1) A large amount of redundant information is difficult to identify and delete. (2) Aliasing patterns decrease the methods’ classification accuracy. To overcome these problems, this paper puts forward an improved fault diagnosis method based on tree heuristic feature selection (THFS) and the dependent feature vector combined with rough sets (RS-DFV). In the RS-DFV method, the feature set was optimized through the dependent feature vector (DFV). Furthermore, the DFV revealed the essential difference among different REB faults and improved the accuracy of fault description. Moreover, the rough set was utilized to reasonably describe the aliasing patterns and overcome the problem of abnormal termination in DFV extraction. In addition, a tree heuristic feature selection method (THFS) was devised to delete the redundant information and construct the structure of RS-DFV. Finally, a simulation, four other feature vectors, three other feature selection methods and four other fault diagnosis methods were utilized for the REB fault diagnosis to demonstrate the effectiveness of the RS-DFV method. RS-DFV obtained an effective subset of five features from 100 features, and acquired a very good diagnostic accuracy (100%, 100%, 99.51%, 100%, 99.47%, 100%), which is much higher than all comparative tests. The results indicate that the RS-DFV method could select an appropriate feature set, deeply dig the effectiveness of the features and more exactly describe the aliasing patterns. Consequently, this method performs better in REB fault diagnosis than the original intelligent methods.

Whole-heart spiral simultaneous multi-slice first-pass myocardial perfusion imaging.

To develop and evaluate a simultaneous multislice (SMS) spiral perfusion pulse sequence with whole-heart coverage. An orthogonal set of phase cycling angles following a Hadamard pattern was incorporated into a golden-angle (GA) variable density spiral perfusion sequence to perform SMS imaging at different multiband (MB) factors. Images were reconstructed using an SMS extension of L1-SPIRiT that we have termed SMS-L1-SPIRiT. The proposed sequence was evaluated in 40 subjects (10 each for MB factors of 1, 2, 3, and 4). Images were blindly graded by 2 cardiologists on a 5-point scale (5, excellent). To quantitatively evaluate the reconstruction performance against images acquired without SMS, the MB =1 data were used to retrospectively simulate data acquired at MB factors of 2 to 4. Analysis of the SMS point-spread function for the desired slice showed that the proposed sampling strategy significantly canceled the main-lobe energy of the other slices and has low side-lobe energy resulting in an incoherent temporal aliasing pattern when rotated by the GA. Retrospective experiments demonstrated the SMS-L1-SPIRiT method removed aliasing from the interfering slices and showed excellent agreement with the ground-truth MB =1 images. Clinical evaluation demonstrated high-quality perfusion images with average image-quality scores of 4.3±0.5 (MB =2), 4.2±0.5 (MB =3), and 4.4±0.4 (MB =4) with no significant quality difference in image quality between MB factors (P=0.38). SMS spiral perfusion at MB factors 2, 3, and 4 produces high-quality perfusion images with whole-heart coverage in a clinical setting with high sampling efficiency.

Comparative performance assessment of beam hardening correction algorithms applied on simulated data sets.

Beam hardening artefacts deteriorate the reconstructed image quality in industrial computed tomography. The appearances of beam hardening artefacts can be cupping effects or streaks. They impair the image fidelity to the object being scanned. This work aims at comparing a variety of commonly used beam hardening correction algorithms in the context of industrial computed tomography metrology. We choose four beam hardening correction algorithms of different types for the comparison. They are a single-material linearization algorithm, a multimaterial linearization algorithm, a dual-energy algorithm and an iterative reconstruction algorithm. Each beam hardening correction algorithm is applied to simulated data sets of a dual-material phantom consisting of multiple rods. The comparison is performed on data sets simulated both under ideal conditions and with the addition of quantum noise. The performance of each algorithm is assessed with respect to its effect on the final image quality (contrast-to-noise ratio, spatial resolution), artefact reduction (streaks, cupping effects) and dimensional measurement deviations. The metrics have been carefully designed in order to achieve a robust and quantifiable assessment. The results suggest that the single-material linearization algorithm can reduce beam hardening artefacts in the vicinity of one material. The multimaterial linearization algorithm can further reduce beam hardening artefacts induced by the other material and improve the dimensional measurement accuracy. The dual-energy method can eliminate beam hardening artefacts, and improve the low contrast visibility and dimensional measurement accuracy. The iterative algorithm is able to eliminate beam hardening streaks. However, it induces aliasing patterns around the object edge, and its performance depends critically upon computational power. The contrast-to-noise ratio and spatial resolution are declined by noise. Noise also increases the difficulty of image segmentation and quantitative analysis. LAY DESCRIPTION: X-ray computed tomography (CT) is a major breakthrough in digital imaging technology in the late 20th century. First used as an important tool in medical imaging, CT has gradually introduced to the nonmedical areas (e.g. industrial nondestructive testing). Inherently CT is more prone to artefacts comparing to the conventional real-time X-ray image. Beam hardening artefacts caused by the polychromatic nature of X-ray spectra are known to deteriorate the reconstructed image quality in industrial CT. A number of beam hardening correction algorithms exist and are used across medical CT. However, there is a lack of research on their effectiveness on industrial CT. This study presents an in-depth beam hardening correction algorithm comparison in industrial CT. Since this study takes various factors of the algorithm performance into account, it provides insights of the advantages and disadvantages of each algorithm and assists the choice of algorithm to meet specific needs of industry. Existing beam hardening correction algorithms are divided into the following four categories: linearization, segmentation based linearization, dual-energy and iterative methods. Since the linearization method can only correct single-material objects, we did not include it in the comparative study. Among the remaining categories, we chose one from each category for comparison, for methods in one peer category share similar physical and mathematical principles. The methods are polynomial fit, Joseph segmentation, dual energy and IMPACT iterative method. This study uses a simulated polychromatic data set of a multimaterial phantom. The central slice of the corrected reconstructions is then assessed and the results are presented. In this study, we will compare beam hardening correction methods with respect to their performance on image quality, the removal of image artefacts and the influence on dimensional accuracy.

GRAPPA reconstructed wave-CAIPI MP-RAGE at 7 Tesla.

The aim of this project was to develop a GRAPPA-based reconstruction for wave-CAIPI data. Wave-CAIPI fully exploits the 3D coil sensitivity variations by combining corkscrew k-space trajectories with CAIPIRINHA sampling. It reduces artifacts and limits reconstruction induced spatially varying noise enhancement. The GRAPPA-based wave-CAIPI method is robust and does not depend on the accuracy of coil sensitivity estimations. We developed a GRAPPA-based, noniterative wave-CAIPI reconstruction algorithm utilizing multiple GRAPPA kernels. For data acquisition, we implemented a fast 3D magnetization-prepared rapid gradient-echo wave-CAIPI sequence tailored for ultra-high field application. The imaging results were evaluated by comparing the g-factor and the root mean square error to Cartesian CAIPIRINHA acquisitions. Additionally, to assess the performance of subcortical segmentations (calculated by FreeSurfer), the data were analyzed across five subjects. Sixteen-fold accelerated whole brain magnetization-prepared rapid gradient-echo data (1 mm isotropic resolution) were acquired in 40 seconds at 7T. A clear improvement in image quality compared to Cartesian CAIPIRINHA sampling was observed. For the chosen imaging protocol, the results of 16-fold accelerated wave-CAIPI acquisitions were comparable to results of 12-fold accelerated Cartesian CAIPIRINHA. In comparison to the originally proposed SENSitivity Encoding reconstruction of Wave-CAIPI data, the GRAPPA approach provided similar image quality. High-quality, wave-CAIPI magnetization-prepared rapid gradient-echo images can be reconstructed by means of a GRAPPA-based reconstruction algorithm. Even for high acceleration factors, the noniterative reconstruction is robust and does not require coil sensitivity estimations. By altering the aliasing pattern, ultra-fast whole-brain structural imaging becomes feasible.

FFAST: An Algorithm for Computing an Exactly $ k$ -Sparse DFT in $O( k\log k)$ Time

It is a well-known fact that the Discrete Fourier Transform (DFT) $ \vec {X}$ of an arbitrary $ n$ -length input signal $ \vec {x}$ , can be computed from all the $ n$ time-domain samples in $O( n\log n)$ operations via a Fast Fourier Transform (FFT) algorithm. If the spectrum $ \vec {X}$ is $ k$ -sparse (where $ k\ll n$ ), can we do better? We show that asymptotically in $ k$ and $ n$ , when $ k$ is sub-linear in $ n$ (precisely, $ k= O( n^{ \delta }$ ), where $0 \leq \delta ), and the support of the non-zero DFT coefficients is uniformly random, the fast fourier aliasing-based sparse transform (FFAST) algorithm, proposed in this paper, computes, with asymptotically high probability, the $k$ non-zero DFT coefficients of $\vec {X}$ from $O( k)$ samples of $ \vec {x}$ in $O( k\log k)$ arithmetic operations. Further, the constants in the big Oh notation for both sample and computational cost are small, e.g., when $ \delta , which essentially covers a wide range of sub-linear sparsity cases, the sample cost is less than $4 k$ . Although, in this paper we assume that the samples of the signal $ \vec {x}$ observed by the FFAST are noise-free, a noise-robust extension of the FFAST is provided in a companion (Part II) paper [1] . Our approach is based on filter-less sub-sampling of the input signal using a set of carefully chosen uniform sub-sampling patterns guided by the Chinese Remainder Theorem (CRT) . The idea is to cleverly exploit, rather than avoid, the resulting aliasing artifacts induced by sub-sampling. Specifically, the sub-sampling operation on the time-domain signal $ \vec {x}$ is designed to create aliasing patterns of the non-zero coefficients of the spectrum $ \vec {X}$ to “look like” parity-check constraints of a good erasure-correcting sparse-graph code. Next, we show that computing the sparse DFT $ \vec {X}$ is equivalent to decoding of an appropriate sparse-graph code . The sparse-graph codes further permit a fast peeling-style decoding. Consequently, the resulting DFT computation is low in both the sample and the decoding complexity. We analytically connect our proposed CRT-based aliasing framework to random sparse-graph codes, and analyze the performance of our algorithm using density evolution techniques from coding theory. We provide extensive simulation results, that are in tight agreement with our theoretical findings.

Golden‐ratio rotated stack‐of‐stars acquisition for improved volumetric MRI

To develop and evaluate an improved stack-of-stars radial sampling strategy for reducing streaking artifacts. The conventional stack-of-stars sampling strategy collects the same radial angle for every partition (slice) encoding. In an undersampled acquisition, such an aligned acquisition generates coherent aliasing patterns and introduces strong streaking artifacts. We show that by rotating the radial spokes in a golden-angle manner along the partition-encoding direction, the aliasing pattern is modified, resulting in improved image quality for gridding and more advanced reconstruction methods. Computer simulations were performed and phantom as well as in vivo images for three different applications were acquired. Simulation, phantom, and in vivo experiments confirmed that the proposed method was able to generate images with less streaking artifact and sharper structures based on undersampled acquisitions in comparison with the conventional aligned approach at the same acceleration factors. By combining parallel imaging and compressed sensing in the reconstruction, streaking artifacts were mostly removed with improved delineation of fine structures using the proposed strategy. We present a simple method to reduce streaking artifacts and improve image quality in 3D stack-of-stars acquisitions by re-arranging the radial spoke angles in the 3D partition direction, which can be used for rapid volumetric imaging. Magn Reson Med 78:2290-2298, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Beamforming with Optimal Aliasing Cancellation in Spherical Microphone Arrays

Spherical microphone arrays facilitate three-dimensional processing and analysis of sound fields in applications such as music recording, beamforming and room acoustics. The frequency bandwidth of operation is constrained by the array configuration. At high frequencies, spatial aliasing leads to side-lobes in the array beam pattern, which limits array performance. Previous studies proposed increasing the number of microphones or changing other characteristics of the array configuration to reduce the effect of aliasing. In this paper we present a method to design beamformers that overcome the effect of spatial aliasing by suppressing the undesired side-lobes through signal processing without physically modifying the configuration of the array. This is achieved by modeling the expected aliasing pattern in a maximum-directivity beamformer design, leading to a higher directivity index at frequencies previously considered to be out of the operating bandwidth, thereby extending the microphone array frequency range of operation. Aliasing cancellation is then extended to other beamformers. A simulation example with a 32-element spherical microphone array illustrates the performance of the proposed method. An experimental example validates the theoretical results in practice.

Separation of parallel encoded complex-valued slices (SPECS) from a single complex-valued aliased coil image

PurposeAchieving a reduction in scan time with minimal inter-slice signal leakage is one of the significant obstacles in parallel MR imaging. In fMRI, multiband-imaging techniques accelerate data acquisition by simultaneously magnetizing the spatial frequency spectrum of multiple slices. The SPECS model eliminates the consequential inter-slice signal leakage from the slice unaliasing, while maintaining an optimal reduction in scan time and activation statistics in fMRI studies. Materials and methodsWhen the combined k-space array is inverse Fourier reconstructed, the resulting aliased image is separated into the un-aliased slices through a least squares estimator. Without the additional spatial information from a phased array of receiver coils, slice separation in SPECS is accomplished with acquired aliased images in shifted FOV aliasing pattern, and a bootstrapping approach of incorporating reference calibration images in an orthogonal Hadamard pattern. ResultThe aliased slices are effectively separated with minimal expense to the spatial and temporal resolution. Functional activation is observed in the motor cortex, as the number of aliased slices is increased, in a bilateral finger tapping fMRI experiment. ConclusionThe SPECS model incorporates calibration reference images together with coefficients of orthogonal polynomials into an un-aliasing estimator to achieve separated images, with virtually no residual artifacts and functional activation detection in separated images.

A Fast Hadamard Transform for Signals With Sublinear Sparsity in the Transform Domain

In this paper, we design a new iterative low-complexity algorithm for computing the Walsh-Hadamard transform (WHT) of an N dimensional signal with a K-sparse WHT. We suppose that N is a power of two and K = O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> ), scales sublinearly in N for some α ∈ (0, 1). Assuming a random support model for the nonzero transform-domain components, our algorithm reconstructs the WHT of the signal with a sample complexity O(K log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (N/K)) and a computational complexity O(K log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (K) log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (N/K)). Moreover, the algorithm succeeds with a high probability approaching 1 for large dimension N. Our approach is mainly based on the subsampling (aliasing) property of the WHT, where by a carefully designed subsampling of the time-domain signal, a suitable aliasing pattern is induced in the transform domain. We treat the resulting aliasing patterns as parity-check constraints and represent them by a bipartite graph. We analyze the properties of the resulting bipartite graphs and borrow ideas from codes defined over sparse bipartite graphs to formulate the recovery of the nonzero spectral values as a peeling decoding algorithm for a specific sparse-graph code transmitted over a binary erasure channel. This enables us to use tools from coding theory (belief-propagation analysis) to characterize the asymptotic performance of our algorithm in the very sparse (α ∈ (0, 1/3]) and the less sparse (α ∈ (1/3, 1)) regime. Comprehensive simulation results are provided to assess the empirical performance of the proposed algorithm.

Chemical shift separation with controlled aliasing for hyperpolarized (13) C metabolic imaging.

A chemical shift separation technique for hyperpolarized (13) C metabolic imaging with high spatial and temporal resolution was developed. Specifically, a fast three-dimensional pulse sequence and a reconstruction method were implemented to acquire signals from multiple (13) C species simultaneously with subsequent separation into individual images. A stack of flyback echo-planar imaging readouts and a set of multiband excitation radiofrequency pulses were designed to spatially modulate aliasing patterns of the acquired metabolite images, which translated the chemical shift separation problem into parallel imaging reconstruction problem. An eight-channel coil array was used for data acquisition and a parallel imaging method based on nonlinear inversion was developed to separate the aliased images. Simultaneous acquisitions of pyruvate and lactate in a phantom study and in vivo rat experiments were performed. The results demonstrated successful separation of the metabolite distributions into individual images having high spatial resolution. This method demonstrated the ability to provide accelerated metabolite imaging in hyperpolarized (13) C MR using multichannel coils, tailored readout, and specialized RF pulses.

Motion-corrected compressed-sensing enables robust spiral first-pass perfusion imaging with whole heart coverage

Background First-pass perfusion imaging using CMR is an important tool for diagnosing coronary artery disease (CAD), but most clinical techniques are limited in their spatial coverage. While compressed-sensing (CS) holds promise for highly accelerated perfusion spiral imaging, CS techniques suffer from blurring artifacts in the setting of respiratory motion. Spiral pulse sequences have multiple advantages for myocardial perfusion imaging including high acquisition efficiency, high signal to noise (SNR) and robustness to motion and for CS including a relatively incoherent aliasing pattern. Thus, we develop a whole heart spiral first-pass perfusion sequence combined with robust motion-correction.

A simple method for dealing with aliasing in experimental design

Purpose – The aim of this paper is to proposes a simple and unified method for generating the aliasing pattern of two‐ and three‐level fractional factorial designs be they regular or non‐regular. The paper also demonstrates how the aliasing patterns obtained using the postulated method can be used to render the main measures of aliasing severity.Design/methodology/approach – The proposed method is based on viewing the fractional factorial designs geometrically. It entails regarding the columns of any design as vectors. On the premise that any two vectors are orthogonal if they are at right angle and bearing in mind that aliasing is a form of departure from orthogonality, the proposed method determines the degree of aliasing between any two columns by assessing the extent to which the angle between them differs from 90°.Findings – Three examples were used to illustrate how the proposed method can be applied and to validate its results. The first dealt with a regular two‐level L8 25−2 design whereas the sec...

An optimal selection of two-level regular single arrays for robust parameter experiments

Efforts have been made in the literature to find optimal single arrays which work best for the robust parameter experiments. However, examples show that in many cases the optimal designs obtained by the existing criteria cloud not attain the maximum number of clear interested effects for robust parameter experiments. In this paper, through a similar way of Zhang et al. (2008) (ZLZA, in short), an aliasing pattern to measure the confounding between the interested effects and other effects for the case of robust parameter designs is introduced. A new criterion for selecting optimal two-level regular single arrays is proposed. In the consideration of the criterion, two rank-orders of effects are suggested: one is based on the interest of experimenters and the other is under the usual effect hierarchy principle. The optimal designs are tabulated in the appendix.

Encoding Abstract Syntax Without Fresh Names

This paper introduces a variant of nominal abstract syntax in which bindable names are represented by normal meta-variables as opposed to a separate class of globally fresh names. Distinct meta-variables can be instantiated with the same concrete name, which we call aliasing. The possible aliasing patterns are controlled by explicit constraints on the distinctness (freshness) of names. This approach has already been used in the nominal meta-programming language αML. We recap that language and develop a theory of contextual equivalence for it. The central result of the paper is that abstract syntax trees (ASTs) involving binders can be encoded into αML in such a way that α-equivalence of ASTs corresponds with contextual equivalence of their encodings. This is novel because the encoding does not rely on the existence of globally fresh names and fresh name generation, which are fundamental to the correctness of the pre-existing encoding of abstract syntax into FreshML.

Improvements in multislice parallel imaging using radial CAIPIRINHA

Multislice parallel imaging involves the simultaneous sampling of multiple parallel slices which are subsequently separated using parallel imaging reconstruction. The CAIPIRINHA technique improves this reconstruction by manipulating the phase of the RF excitation pulses to shift the aliasing pattern such that there is less aliasing energy to be reconstructed. In this work, it is shown that combining the phase manipulation used in CAIPIRINHA with a non-Cartesian (radial) sampling scheme further decreases the aliasing energy for the parallel imaging algorithm to reconstruct, thereby further increasing the degree to which a multi-channel receiver array can be utilized for parallel imaging acceleration. In radial CAIPIRINHA, individual bands (slices) in a multislice excitation are modulated with view-dependent phase, causing a destructive interference of entire slices. This destructive interference leads to a reduction in aliasing compared to the coherent shifts one observes when using this same technique with a Cartesian trajectory. Recovery of each individual slice is possible because the applied phase pattern is known, and a conjugate-gradient reconstruction algorithm minimizes the contributions from other slices. Results are presented with a standard 12-channel head coil with acceleration factors up to 14, where radial CAIPIRINHA produces an improved reconstruction when compared with Cartesian CAIPIRINHA.