Non-uniform Sampling Scheme Research Articles

Granger causality analysis with nonuniform sampling and its application to pulse-coupled nonlinear dynamics.

The Granger causality (GC) analysis is an effective approach to infer causal relations for time series. However, for data obtained by uniform sampling (i.e., with an equal sampling time interval), it is known that GC can yield unreliable causal inference due to aliasing if the sampling rate is not sufficiently high. To solve this unreliability issue, we consider the nonuniform sampling scheme as it can mitigate against aliasing. By developing an unbiased estimation of power spectral density of nonuniformly sampled time series, we establish a framework of spectrum-based nonparametric GC analysis. Applying this framework to a general class of pulse-coupled nonlinear networks and utilizing some particular spectral structure possessed by these nonlinear network data, we demonstrate that, for such nonlinear networks with nonuniformly sampled data, reliable GC inference can be achieved at a low nonuniform mean sampling rate at which the traditional uniform sampling GC may lead to spurious causal inference.

LORAKS makes better SENSE: Phase-constrained partial fourier SENSE reconstruction without phase calibration.

Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information. The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely used calibrationless uniformly undersampled trajectories. Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches. The SENSE-LORAKS framework provides promising new opportunities for highly accelerated MRI. Magn Reson Med 77:1021-1035, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Segmentation of Thalamus from MR images via Task-Driven Dictionary Learning.

Automatic thalamus segmentation is useful to track changes in thalamic volume over time. In this work, we introduce a task-driven dictionary learning framework to find the optimal dictionary given a set of eleven features obtained from T1-weighted MRI and diffusion tensor imaging. In this dictionary learning framework, a linear classifier is designed concurrently to classify voxels as belonging to the thalamus or non-thalamus class. Morphological post-processing is applied to produce the final thalamus segmentation. Due to the uneven size of the training data samples for the non-thalamus and thalamus classes, a non-uniform sampling scheme is proposed to train the classifier to better discriminate between the two classes around the boundary of the thalamus. Experiments are conducted on data collected from 22 subjects with manually delineated ground truth. The experimental results are promising in terms of improvements in the Dice coefficient of the thalamus segmentation over state-of-the-art atlas-based thalamus segmentation algorithms.

Multi-channel sampling expansion for band-pass signals without channels constraints

The aim of the multi-channel sampling expansion (MSE) is the reconstruction of an unknown continuously defined function ft, from the samples of the responses of m linear time invariant (LTI) systems, each sampled by the 1/m th Nyquist rate. The MSE for band-pass signals in the Fourier transform (FT) domain has recently been presented in the literature under some restricted conditions. To be specific, a necessary condition for perfect reconstruction of a band-pass signals is discussed which requires the number of filters/channels m in the system must be even. Focusing on this issue, first, based on a quadrature representation of the band-pass signal, we propose a new MSE. It is shown that perfect signal reconstruction is possible for any arbitrary number of channels when the upper cutoff frequency is a multiple of the bandwidth. Then, in order to show the importance of the MSE scheme, we apply the recurrent non-uniform sampling scheme to analyze high-rate waveform digitizers. The parallel architecture utilizes the interleaving/multiplexing techniques to extend the capabilities of the monolithic analog/digital (A/D) converter technology. Last, the MSE of band-pass signal is improved which can allow multiple sampling rates in the system.

Superresolution Multipoint Ranging With Optimized Sampling via Orthogonally Designed Golomb Rulers

We consider the problem of performing ranging measurements between a source and multiple receivers efficiently and accurately, as required by distance-based wireless localization systems. To this end, a new multipoint ranging algorithm is proposed, which is obtained by adapting superresolution techniques to the ranging problem, using for the sake of illustration the specific cases of time of arrival (ToA) and phase-difference of arrival (PDoA), unified under the same mathematical framework. The resulting nonparametric algorithm handles multipoint ranging in an efficient manner by employing an orthogonalized nonuniform sampling scheme optimized via Golomb rulers. Since the approach requires the design of mutually orthogonal sets of Golomb rulers with equivalent properties—a problem that founds no solution in current literature—a new genetic algorithm to accomplish this task is presented, which is also found to outperform the best known alternative when used to generate a single ruler. Finally, a Cramer-Rao lower bound (CRLB) analysis of the overall optimized multipoint ranging solution is performed, which together with a comparison against simulation results validates the proposed techniques.

Deterministic multidimensional nonuniform gap sampling

Born from empirical observations in nonuniformly sampled multidimensional NMR data relating to gaps between sampled points, the Poisson-gap sampling method has enjoyed widespread use in biomolecular NMR. While the majority of nonuniform sampling schemes are fully randomly drawn from probability densities that vary over a Nyquist grid, the Poisson-gap scheme employs constrained random deviates to minimize the gaps between sampled grid points. We describe a deterministic gap sampling method, based on the average behavior of Poisson-gap sampling, which performs comparably to its random counterpart with the additional benefit of completely deterministic behavior. We also introduce a general algorithm for multidimensional nonuniform sampling based on a gap equation, and apply it to yield a deterministic sampling scheme that combines burst-mode sampling features with those of Poisson-gap schemes. Finally, we derive a relationship between stochastic gap equations and the expectation value of their sampling probability densities.

Multilayered nonuniform sampling for three-dimensional scene representation

The representation of a three-dimensional (3-D) scene is essential in multiview imaging technologies. We present a unified geometry and texture representation based on global resampling of the scene. A layered data map representation with a distance-dependent nonuniform sampling strategy is proposed. It is capable of increasing the details of the 3-D structure locally and is compact in size. The 3-D point cloud obtained from the multilayered data map is used for view rendering. For any given viewpoint, image synthesis with different levels of detail is carried out using the quadtree-based nonuniformly sampled 3-D data points. Experimental results are presented using the 3-D models of reconstructed real objects.

Uncertainty Quantification for Electromagnetic Systems Using ASGC and DGTD Method

In this paper, an adaptive hierarchical sparse grid collocation (ASGC) method combined with the discontinuous Galerkin time-domain method is leveraged to quantify the impacts of random parameters on the electromagnetics systems. The ASGC method approximates the stochastic observables of interest using interpolation functions over a set of collocation points determined by the Smolyak's algorithm integrated with an adaptive strategy. Instead of resorting to a full-tensor product sense, the Smolyak's algorithm constructs the collocation points in a hierarchical scheme with the interpolation level. Enhanced by an adaptive strategy, the Smolyak's algorithm will sample more points along important dimensions with sharp variations or discontinuities, resulting in a nonuniform sampling scheme. To flexibly handle different stochastic systems, either piecewise linear or Lagrange polynomial basis functions are applied. With these strategies, the number of collocation points is significantly reduced. The statistical knowledge of stochastic observables including the expected value, variance, probability density function, and cumulative distribution function are presented. The accuracy and robustness of the algorithm are demonstrated by various examples.

Optimization of sampling pattern and the design of Fourier ptychographic illuminator.

Fourier ptychography (FP) is a recently developed imaging approach that facilitates high-resolution imaging beyond the cutoff frequency of the employed optics. In the original FP approach, a periodic LED array is used for sample illumination, and therefore, the scanning pattern is a uniform grid in the Fourier space. Such a uniform sampling scheme leads to 3 major problems for FP, namely: 1) it requires a large number of raw images, 2) it introduces the raster grid artefacts in the reconstruction process, and 3) it requires a high-dynamic-range detector. Here, we investigate scanning sequences and sampling patterns to optimize the FP approach. For most biological samples, signal energy is concentrated at low-frequency region, and as such, we can perform non-uniform Fourier sampling in FP by considering the signal structure. In contrast, conventional ptychography perform uniform sampling over the entire real space. To implement the non-uniform Fourier sampling scheme in FP, we have designed and built an illuminator using LEDs mounted on a 3D-printed plastic case. The advantages of this illuminator are threefold in that: 1) it reduces the number of image acquisitions by at least 50% (68 raw images versus 137 in the original FP setup), 2) it departs from the translational symmetry of sampling to solve the raster grid artifact problem, and 3) it reduces the dynamic range of the captured images 6 fold. The results reported in this paper significantly shortened acquisition time and improved quality of FP reconstructions. It may provide new insights for developing Fourier ptychographic imaging platforms and find important applications in digital pathology.

An analog-digital hybrid RX beamformer chip with non-uniform sampling for ultrasound medical imaging with 2D CMUT array.

To reduce the memory area, a two-stage RX beamformer (BF) chip with 64 channels is proposed for the ultrasound medical imaging with a 2D CMUT array. The chip retrieved successfully two B-mode phantom images with a steering angle from -45 (°) to +45 (°), the maximum delay range of 8 μs, and the delay resolution of 6.25 ns. An analog-digital hybrid BF (HBF) is chosen for the proposed chip to utilize the easy beamforming operation in the digital domain and also to reduce chip area by minimizing the number of ADCs. The chip consists of eight analog beamformers (ABF) for the 1st-stage and a digital beamformer (DBF) for the 2nd-stage. The two-stage architecture reduces the memory area of both ABF and DBF by around four times. The DBF circuit is divided into three steps to further reduce the digital FIFO memory area by around twice. Coupled with the non-uniform sampling scheme, the proposed two-stage HBF chip reduces the total memory area by around 40 times compared to the uniform-sampling single-stage BF chip. The chip fabricated in a 0.13- μm CMOS process occupies the area of 19.4 mm(2), and dissipates 1.14 W with the analog supply of 3.3 V and the digital supply of 1.2 V.

Reducing acquisition times in multidimensional NMR with a time-optimized Fourier encoding algorithm.

Speeding up the acquisition of multidimensional nuclear magnetic resonance (NMR) spectra is an important topic in contemporary NMR, with central roles in high-throughput investigations and analyses of marginally stable samples. A variety of fast NMR techniques have been developed, including methods based on non-uniform sampling and Hadamard encoding, that overcome the long sampling times inherent to schemes based on fast-Fourier-transform (FFT) methods. Here, we explore the potential of an alternative fast acquisition method that leverages a priori knowledge, to tailor polychromatic pulses and customized time delays for an efficient Fourier encoding of the indirect domain of an NMR experiment. By porting the encoding of the indirect-domain to the excitation process, this strategy avoids potential artifacts associated with non-uniform sampling schemes and uses a minimum number of scans equal to the number of resonances present in the indirect dimension. An added convenience is afforded by the fact that a usual 2D FFT can be used to process the generated data. Acquisitions of 2D heteronuclear correlation NMR spectra on quinine and on the anti-inflammatory drug isobutyl propionic phenolic acid illustrate the new method's performance. This method can be readily automated to deal with complex samples such as those occurring in metabolomics, in in-cell as well as in in vivo NMR applications, where speed and temporal stability are often primary concerns.

Towards automatic protein backbone assignment using proton-detected 4D solid-state NMR data.

We introduce an efficient approach for sequential protein backbone assignment based on two complementary proton-detected 4D solid-state NMR experiments that correlate Hi(N)/Ni with CAi/COi or CAi-1/COi-1. The resulting 4D spectra exhibit excellent sensitivity and resolution and are amenable to (semi-)automatic assignment approaches. This strategy allows to obtain sequential connections with high confidence as problems related to peak overlap and multiple assignment possibilities are avoided. Non-uniform sampling schemes were implemented to allow for the acquisition of 4D spectra within a few days. Rather moderate hardware requirements enable the successful demonstration of the method on deuterated type III secretion needles using a 600 MHz spectrometer at a spinning rate of 25 kHz.

Backward Adaptation for Power Efficient Sampling

Advances in sampling and coding theory have contributed significantly towards lowering power consumption of resource-constrained devices, e.g. battery-operated sensor nodes, enabling them to operate for extended periods of time. In this paper, rate and energy efficiency of a recently proposed adaptive nonuniform sampling framework by Feizi <etal xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> , called Time-Stampless Adaptive Nonuniform Sampling (TANS), is examined and compared against state-of-the-art methods. TANS addresses one of the main limitations of nonuniform sampling schemes: sampling times do not need to be stored/transmitted since they can be computed using a function of previously taken samples. The sampling rate is adapted continuously with the aim of reducing the rate and therefore the energy consumption of the sampling process when the signal is varying slowly. Three TANS methods are proposed for different signal models and sampling requirements: i) TANS by polynomial extrapolation, which only assumes the third derivative of the signal is bounded but requires no other specific knowledge of the signal; ii) TANS by incremental variation, where the sampling time intervals are chosen from a lattice; and iii) TANS constrained to a finite set of sampling rates. Practical implementation details of TANS are discussed, and its rate and energy performance are compared with uniform sampling followed by a transformation-based compression, nonuniform sampling, and compressed sensing. Our results demonstrate that TANS provides significant improvements in terms of both the rate-distortion performance and the energy consumption compared against the other approaches.

Accurate scoring of non-uniform sampling schemes for quantitative NMR

Non-uniform sampling (NUS) in NMR spectroscopy is a recognized and powerful tool to minimize acquisition time. Recent advances in reconstruction methodologies are paving the way for the use of NUS in quantitative applications, where accurate measurement of peak intensities is crucial. The presence or absence of NUS artifacts in reconstructed spectra ultimately determines the success of NUS in quantitative NMR. The quality of reconstructed spectra from NUS acquired data is dependent upon the quality of the sampling scheme. Here we demonstrate that the best performing sampling schemes make up a very small percentage of the total randomly generated schemes. A scoring method is found to accurately predict the quantitative similarity between reconstructed NUS spectra and those of fully sampled spectra. We present an easy-to-use protocol to batch generate and rank optimal Poisson-gap NUS schedules for use with 2D NMR with minimized noise and accurate signal reproduction, without the need for the creation of synthetic spectra.

A novel quadrature clutter rejection approach based on the multivariate empirical mode decomposition for bidirectional Doppler ultrasound signals

A novel quadrature clutter rejection approach based on multivariate empirical mode decomposition (MEMD), which is an extension of empirical mode decomposition (EMD) to multivariate for processing multichannel signals, is proposed in this paper to suppress the quadrature clutter signals induced by the vascular wall and the surrounding stationary or slowly moving tissues in composite Doppler ultrasound signals, and extract more blood flow components with low velocities. In this approach, the MEMD algorithms, which include the bivariate empirical mode decomposition with a nonuniform sampling scheme for adaptive selection of projection directions (NS_BEMD) and the trivariate empirical mode decomposition with noise assistance (NA_TEMD), are directly employed to adaptively decompose the complex-valued quadrature composite signals echoed from both bidirectional blood flow and moving wall into a small number of zero-mean rotation components, which are defined as complex intrinsic mode functions (CIMFs). Then the relevant CIMFs contributed to blood flow components are automatically distinguished in terms of the break of the CIMFs’ power, and then directly added up to give the quadrature blood flow signal. Specific simulation and human subject experiments are taken up to demonstrate the advantages and limitations of this novel method for quadrature clutter rejection in bidirectional Doppler ultrasound signals. Due to eliminating the extra errors induced by the Hilbert transform or complex FIR filter algorithms used in the traditional clutter rejection approaches based on the directional separation process, the proposed method provides improved accuracy for clutter rejection, and preserve more slow blood blow components, which could be helpful to early diagnose arterial diseases.

Sequential Decentralized Parameter Estimation Under Randomly Observed Fisher Information

We consider the problem of decentralized scalar parameter estimation using wireless sensor networks with Gaussian noise. Specifically, we propose a novel framework based on level-triggered sampling, a non-uniform sampling strategy, and sequential estimation. The proposed estimator can be used as an asymptotically optimal fixed-sample-size decentralized estimator when the observed Fisher information, i.e., Fisher information without expectation, is deterministic, as an alternative to the one-shot estimators commonly found in the literature. It can also be used as an asymptotically optimal sequential decentralized estimator when the observed Fisher information is random. We show that the optimal centralized estimator under Gaussian noise, which is the maximum likelihood estimator, is characterized by two processes, namely the observed Fisher information Ut and the observed correlation Vt. It is noted that Vt is always random even when Ut is not. In the proposed scheme, each sensor computes its local random processes, and sends a single bit to the fusion center (FC) whenever the local random processes passes certain predefined levels. The FC, upon receiving a bit from a sensor, updates its approximation to the corresponding global random process and, accordingly, its estimate. The sequential estimation process terminates when Ut (or the approximation to it) reaches a target value. We provide an asymptotic analysis for the proposed estimator and the one based on conventional uniform-in-time sampling under both deterministic and random Ut, and determine the conditions under which they are asymptotically optimal, consistent, and asymptotically unbiased. Analytical results, together with simulation results, demonstrate the superiority of the proposed estimator based on level-triggered sampling over the traditional decentralized estimator based on uniform sampling.

Nonuniform Sampling and Maximum Entropy Reconstruction in Multidimensional NMR

NMR spectroscopy is one of the most powerful and versatile analytic tools available to chemists. The discrete Fourier transform (DFT) played a seminal role in the development of modern NMR, including the multidimensional methods that are essential for characterizing complex biomolecules. However, it suffers from well-known limitations: chiefly the difficulty in obtaining high-resolution spectral estimates from short data records. Because the time required to perform an experiment is proportional to the number of data samples, this problem imposes a sampling burden for multidimensional NMR experiments. At high magnetic field, where spectral dispersion is greatest, the problem becomes particularly acute. Consequently multidimensional NMR experiments that rely on the DFT must either sacrifice resolution in order to be completed in reasonable time or use inordinate amounts of time to achieve the potential resolution afforded by high-field magnets. Maximum entropy (MaxEnt) reconstruction is a non-Fourier method of spectrum analysis that can provide high-resolution spectral estimates from short data records. It can also be used with nonuniformly sampled data sets. Since resolution is substantially determined by the largest evolution time sampled, nonuniform sampling enables high resolution while avoiding the need to uniformly sample at large numbers of evolution times. The Nyquist sampling theorem does not apply to nonuniformly sampled data, and artifacts that occur with the use of nonuniform sampling can be viewed as frequency-aliased signals. Strategies for suppressing nonuniform sampling artifacts include the careful design of the sampling scheme and special methods for computing the spectrum. Researchers now routinely report that they can complete an N-dimensional NMR experiment 3(N-1) times faster (a 3D experiment in one ninth of the time). As a result, high-resolution three- and four-dimensional experiments that were prohibitively time consuming are now practical. Conversely, tailored sampling in the indirect dimensions has led to improved sensitivity. Further advances in nonuniform sampling strategies could enable further reductions in sampling requirements for high resolution NMR spectra, and the combination of these strategies with robust non-Fourier methods of spectrum analysis (such as MaxEnt) represent a profound change in the way researchers conduct multidimensional experiments. The potential benefits will enable more advanced applications of multidimensional NMR spectroscopy to study biological macromolecules, metabolomics, natural products, dynamic systems, and other areas where resolution, sensitivity, or experiment time are limiting. Just as the development of multidimensional NMR methods presaged multidimensional methods in other areas of spectroscopy, we anticipate that nonuniform sampling approaches will find applications in other forms of spectroscopy.

Compressive sampling photoacoustic tomography based on edge expander codes and TV regularization

A new photoacoustic (PA) signal sampling and image reconstruction method, called compressive sampling PA tomography (CSPAT), is recently proposed to make low sampling rate and high-resolution PA tomography possible. A key problem within the CSPAT framework is the design of optic masks. We propose to use edge expander codes-based masks instead of the conventional random distribution masks, and efficient total variation (TV) regularization-based model to formulate the associated problem. The edge expander codes-based masks, corresponding to non-uniform sampling schemes, are validated by both theoretical analysis and results from computer simulations. The proposed method is expected to enhance the capability of CSPAT for reducing the number of measurements and fast data acquisition.

Adaptive Sampling for ECG Detection Based on Compression Dictionary

This paper presents an adaptive sampling method for electrocardiogram (ECG) signal detection. First, by employing the strings matching process with compression dictionary, we recognize each segment of ECG with different characteristics. Then, based on the non-uniform sampling strategy, the sampling rate is determined adaptively. As the results of simulation indicated, our approach reconstructed the ECG signal at an optimized sampling rate with the guarantee of ECG integrity. Compared with the existing adaptive sampling technique, our approach acquires an ECG signal at a 30% lower sampling rate. Finally, the experiment exhibits its superiority in terms of energy efficiency and memory capacity performance.

Scene surface light field representation for realistic lighting

Existing light field-based lighting follows the representation on plane, such as the commonly used light slab. A novel light field representation on scene surface is proposed. The illumination is captured by a panorama camera on translation stage with a nonuniform sampling and calibration strategy. Sampled light rays are reprojected on the reconstructed scene to generate the scene surface light field representations for both direct light source and indirect light. This representation is more consistent with the actual emission and reflection of light transport than the existing ones. An accurate light source estimation and a practical indirect light resampling approach are presented based on the representation. The rendering results illustrate the realistic lighting effect, especially in spatially varying illumination.