Conventional Uniform Sampling Research Articles

A 0.49–4.34 μW LC-SAR Hybrid ADC with a 10.85-Bit ENOB and 20 KS/s Bandwidth

This paper presents a level-crossing successive-approximation-register (LC-SAR) hybrid analog-to-digital converter (ADC) that combines an LC ADC with an SAR ADC, which may be used for Internet of Things (IoT) random sparse event scenarios. The sampling frequency of a traditional LC ADC is usually proportional to the maximum instantaneous rate of change of the input signal; therefore, a higher input signal frequency inevitably leads to higher system power consumption. However, the proposed hybrid ADC uses the input level difference between the two moments before and after level-crossing detection, thereby ensuring a higher conversion precision and lower power consumption, even at higher input signal frequencies. Compared with traditional LC ADC or SAR ADC, the proposed hybrid ADC combines the ultralow-power advantage of LC ADC with the high-precision advantage of SAR ADC in converting IoT data with sparse characteristics such as ECG, EEG, and brain potential. The LC-SAR hybrid ADC is designed with a 0.18 μm CMOS process and consumes 4.34 μW at a 1.8 V supply voltage, achieving an SNDR of 67.41 dB and a bandwidth of 20 kHz. The spectrum analysis result was 10.85 ENOB when the input sinusoidal signal was 14.975 kHz. When inputted with an ECG signal, the system power consumption was as low as 0.49 μW. Furthermore, the proposed hybrid ADC obtained a good figure of merit, with FoMw and FoMs reaching 58.8 fJ/conv.steps and 164 dB, respectively. Compared to a conventional uniform sampling ADC, approximately 80% of the power savings and an 8x compression ratio can be achieved in physiological signal acquisition applications.

Microvibration streaming measurements using dynamic compressed sensing for satellites

Long-term monitoring of satellite microvibrations generates a significant amount of data streams, placing strain on satellites with limited transmission capacity. To relieve this transmission strain, a dynamic compressed sensing (CS) framework is proposed for measuring satellite microvibrations. Microvibration streams are measured block by block and then reconstructed using a dynamic recovery algorithm. The recovery solution of one block can be used as a priori knowledge for the next block, allowing for faster updates. However, existing dynamic recovery algorithms are only applicable in the real domain and cannot be applied to microvibrations projected on a Fourier basis in the complex domain. In light of this event, the dynamic homotopy algorithm is expanded to the complex domain to deal with microvibration signals that are sparse in the Fourier basis. In comparison to conventional uniform sampling methods, the experimental results show that the dynamic CS with the expanded recovery algorithm can achieve a maximum root-mean-square acceleration (Grms) deviation of 4% in power spectrum density with one-fifth of the sampling points. Compared to recovery algorithms applicable to fixed measurements, the dynamic algorithm can achieve comparable accuracy in about one-third of the computation time. The experimental findings demonstrate the feasibility of satellite microvibrations measurements using dynamic CS.

Time Encoding via Unlimited Sampling: Theory, Algorithms and Hardware Validation

An alternative to conventional uniform sampling is that of time encoding, which converts continuous-time signals into streams of trigger times. This gives rise to Event-Driven Sampling (EDS) models. The data-driven nature of EDS acquisition is advantageous in terms of power consumption and time resolution and is inspired by the information representation in biological nervous systems. If an analog signal is outside a predefined dynamic range, then EDS generates a low density of trigger times, which in turn leads to recovery distortion due to aliasing. In this paper, inspired by the Unlimited Sensing Framework (USF), we propose a new EDS architecture that incorporates a modulo nonlinearity prior to acquisition that we refer to as the modulo EDS or MEDS. In MEDS, the modulo nonlinearity folds high dynamic range inputs into low dynamic range amplitudes, thus avoiding recovery distortion. In particular, we consider the asynchronous sigma-delta modulator (ASDM), previously used for low power analog-to-digital conversion. This novel MEDS based acquisition is enabled by a recent generalization of the modulo nonlinearity called modulo-hysteresis. We design a mathematically guaranteed recovery algorithm for bandlimited inputs based on a sampling rate criterion and provide reconstruction error bounds. We go beyond numerical experiments and also provide a first hardware validation of our approach, thus bridging the gap between theory and practice, while corroborating the conceptual underpinnings of our work.

Coprime Sensing for Airborne Array Interferometric SAR Tomography

In airborne array interferometric SAR (Array-InSAR) tomography, the measurements acquired by conventional uniform sampling array are always restricted by the number of physical baseline elements and the size of baseline aperture. It is desirable to capture new acquisitions and enlarge the aperture with virtual signal processing instead of actually adding array baselines. For this motivation, we utilize the disparity of a pair of coprime sampling sub-arrays to enlarge the baseline aperture and construct new observations virtually. The generation of virtual measurements is equal to estimating cross-correlation matrices in real SAR data. Due to the spatial target variation, we adopted an adaptive filtering method to estimate the cross-correlation matrix. We call the above-mentioned processing of generating virtual measurements as a <i>coprime sensing technique</i>. The newly generated virtual measurements have more degrees of freedom, a larger baseline aperture, and a higher signal-to-noise ratio (SNR) than the physical measurements. These advantages offer the possibility to obtain competitive three-dimensional (3-D) imaging results without increasing the hardware cost of the Array-InSAR. We demonstrate the effectiveness of the proposed method by the coprime acquisitions selected from AIRCAS Array-InSAR data.

Enhanced Off-Policy Reinforcement Learning With Focused Experience Replay

Utilizing the collected experience tuples in the replay buffer (RB) is the primary way of exploiting the experiences in the off-policy reinforcement learning (RL) algorithms, and, therefore, the sampling scheme for the experience tuples in the RB can be critical for experience utilization. In this paper, it is found that a widely used sampling scheme in the off-policy RL suffers from inefficiency due to the inadequate uneven sampling of experience tuples from the RB. In fact, the conventional uniform sampling of the experience tuples in the RB causes a severely unbalanced experience utilization, since experiences stored earlier in the RB is sampled with much higher frequency especially in the early stage of learning. We mitigate this fundamental problem by employing a half-normal sampling probability window that allocates a higher sampling probability to newer experiences in the RB. In addition, we propose general and local size adjustment schemes that determine the standard deviation of the half-normal sampling window to enhance the learning speed and performance and to mitigate the temporary performance degradation during training, respectively. For performance demonstration, we apply the proposed sampling technique to the state-of-the-art off-policy RL algorithms and test for various RL benchmark tasks such as MuJoCo gym and CARLA simulator. As a result, the proposed technique shows considerable learning speed and final performance improvement, especially on the tasks with large state and action space. Furthermore, the proposed sampling technique increases the stability of the considered RL algorithms, verified with less variance of the performance results across different random seeds of network initialization.

Broadening frequency response of a distributed sparse-wideband vibration sensing via a time-division multi-frequency sub-Nyquist sampling.

The maximum detectable vibration frequency response range is inversely related with the sensing fiber length in direct-detection intensity-measuring coherent optical time domain reflectometry (DI-COTDR). Unlike the conventional uniform sampling, the pulse repetition rate is modulated in a time-division manner so that a multi-frequency sub-Nyquist sampling is realized along every point of the sensing fiber. A 24-kHz vibration signal can be detected and recovered by a compressive sensing technique using sampling pulses with repetition rate lower than 5-kHz, which is ten-fold lower compared to that required in the conventional uniform sampling method. Also, a multi-frequency vibration signal can be identified and recovered by this technique. The proposed method can break through the theoretical maximum detection frequency of traditional systems without any hardware modification. Therefore, such a method is of great significance for broadening the frequency response range of the distributed sparse-wideband vibration sensing.

A Method for Energy-Efficient Sampling of Analog to Digital Converters

We present PANDA, a data acquisition technique for energy-constrained sensor nodes that reduces the energy per operation required to sample and preprocess analog sensor data. PANDA takes advantage of the energy consumption patterns of commodity microcontrollers by sampling input signals in short bursts followed by long periods of inactivity. This approach reduces the overhead of repetitively transitioning the CPU and analog components in and out of low-power sleep states. This nonuniformly-spaced input data is then fed to a nonuniform FFT algorithm that computes the frequency spectrum. We show that the spectrum computed with the nonuniform FFT is very close to the spectrum that would be computed from uniformly sampled data preprocessed with a conventional FFT. The output of the nonuniform FFT can be filtered or post-processed with conventional frequency domain analysis techniques, and a uniformly resampled output can be constructed with the conventional inverse FFT. We compare the energy consumption patterns of burst-mode sampling to those of conventional uniform sampling in several real sensor nodes. We demonstrate that for reasonably sized input datasets, burst mode sampling and postprocessing consumes more than 17 percent less energy than conventional uniform sampling, including the additional computations required to compute the nonuniform DFT.

Distributed Dynamic State Estimation and LQG Control in Resource-Constrained Networks

In this paper, the discrete-time distributed dynamic state estimation and linear quadratic Gaussian (LQG) control problems are analyzed for resource-constrained networked systems. Following a holistic approach, we provide a complete system design for the signal processing, communication, and control tasks involved in the problems; and evaluate their performance. In the presence of a controller node and a number of sensor nodes, the sensor nodes, in a resource-efficient way, report their information entities to the controller node using an event-triggered sampling technique called level-crossing sampling. We demonstrate the performance gains due to level-crossing sampling over conventional time-triggered uniform sampling, as well as the advantages of processing data locally before transmitting to the controller. In particular, it is shown that the proposed decentralized schemes with local processing and level-crossing sampling ensure a very close approximation, with a bounded error, to the optimum (centralized) estimation and control schemes, and as a result yield order-2 asymptotic optimality. Moreover, nonideal communication between sensors and the controller is considered, and optimal modulation techniques are provided for different channel models. Simulation results are provided to support the presented discussions.

Zooming in on vibronic structure by lowest-value projection reconstructed 4D coherent spectroscopy.

A fundamental goal of chemical physics is an understanding of microscopic interactions in liquids at and away from equilibrium. In principle, this microscopic information is accessible by high-order and high-dimensionality nonlinear optical measurements. Unfortunately, the time required to execute such experiments increases exponentially with the dimensionality, while the signal decreases exponentially with the order of the nonlinearity. Recently, we demonstrated a non-uniform acquisition method based on radial sampling of the time-domain signal [W. O. Hutson et al., J. Phys. Chem. Lett. 9, 1034 (2018)]. The four-dimensional spectrum was then reconstructed by filtered back-projection using an inverse Radon transform. Here, we demonstrate an alternative reconstruction method based on the statistical analysis of different back-projected spectra which results in a dramatic increase in sensitivity and at least a 100-fold increase in dynamic range compared to conventional uniform sampling and Fourier reconstruction. These results demonstrate that alternative sampling and reconstruction methods enable applications of increasingly high-order and high-dimensionality methods toward deeper insights into the vibronic structure of liquids.

Stable and efficient retrospective 4D-MRI using non-uniformly distributed quasi-random numbers

The purpose of this work is the development of a robust and reliable three-dimensional (3D) Cartesian imaging technique for fast and flexible retrospective 4D abdominal MRI during free breathing. To this end, a non-uniform quasi random (NU-QR) reordering of the phase encoding (ky–kz) lines was incorporated into 3D Cartesian acquisition. The proposed sampling scheme allocates more phase encoding points near the k-space origin while reducing the sampling density in the outer part of the k-space. Respiratory self-gating in combination with SPIRiT-reconstruction is used for the reconstruction of abdominal data sets in different respiratory phases (4D-MRI). Six volunteers and three patients were examined at 1.5 T during free breathing. Additionally, data sets with conventional two-dimensional (2D) linear and 2D quasi random phase encoding order were acquired for the volunteers for comparison. A quantitative evaluation of image quality versus scan times (from 70 s to 626 s) for the given sampling schemes was obtained by calculating the normalized mutual information (NMI) for all volunteers. Motion estimation was accomplished by calculating the maximum derivative of a signal intensity profile of a transition (e.g. tumor or diaphragm).The 2D non-uniform quasi-random distribution of phase encoding lines in Cartesian 3D MRI yields more efficient undersampling patterns for parallel imaging compared to conventional uniform quasi-random and linear sampling. Median NMI values of NU-QR sampling are the highest for all scan times. Therefore, within the same scan time 4D imaging could be performed with improved image quality.The proposed method allows for the reconstruction of motion artifact reduced 4D data sets with isotropic spatial resolution of 2.1 × 2.1 × 2.1 mm3 in a short scan time, e.g. 10 respiratory phases in only 3 min. Cranio-caudal tumor displacements between 23 and 46 mm could be observed.NU-QR sampling enables for stable 4D-MRI with high temporal and spatial resolution within short scan time for visualization of organ or tumor motion during free breathing. Further studies, e.g. the application of the method for radiotherapy planning are needed to investigate the clinical applicability and diagnostic value of the approach.

Ultrafast Four-Dimensional Coherent Spectroscopy by Projection Reconstruction.

Multidimensional coherent spectroscopy provides insights into the vibronic structure and dynamics of complex systems. In general, the higher the dimensionality, the better the spectral discrimination and the more information that may be extracted about the system. A major impediment to widespread implementation of these methods, however, is that the acquisition time generally increases exponentially with dimensionality, prohibiting practical implementation. We demonstrate the use of nonuniform sampling based on the projection-slice theorem and inverse Radon transform within the context of a fifth-order, 4D technique (GAMERS) designed to correlate the vibrational contributions to different electronic states. Projection-reconstruction (PRO GAMERS) greatly reduces the data sampling requirements without sacrificing frequency resolution. The sensitivity of this technique is demonstrated to surpass conventional uniform sampling by orders of magnitude. The incorporation of projection-reconstruction into multidimensional coherent spectroscopy opens up the possibility to study the structure of complex chemical, biological, and physical systems with unprecedented detail.

Identification of FIR Models for LTI Multiscale Systems using Sparse Optimization Techniques

Finite impulse response (FIR) models are very popular in process industries because of their simple model structure, flexibility to explain arbitrary complex stable linear dynamics and finally their ease of implementation in on-line applications. In general, identification of FIR models requires large number of parameters to be estimated. In case of systems with multiple time scales, the length of FIR model structure under conventional uniform sampling becomes arbitrarily high due to simultaneous presence of fast and slow dynamics. This results in more variability in the estimated parameters when the conventional methods such as ordinary least squares are used. In this work, the FIR model estimation problem is formulated as a sparse optimization problem, where the sparse representation of impulse response coefficients for linear-time invariant multiscale systems in the time-frequency domain is exploited in order to explain the overall FIR model effectively with fewer number of coefficients and thereby incurring less variability in the estimated parameters. The effectiveness of proposed methodology is demonstrated by means of simulation case studies.

Intelligent adaptive sampling guided by Gaussian process inference

With the aim of reducing sampling density while having minimal impact on surface reconstruction accuracy, an adaptive sampling method based on Gaussian process inference is proposed. In each iterative step, the current sampling points serve as the training data to predict surface topography and then a new sampling point is adaptively located and inserted at the position where the maximum inference uncertainty is estimated. The updated samples are trained in the next step. By such an iterative training–inference–sampling approach, the reconstructed topography can converge to the expected one efficiently. Demonstrations on different structured, freeform and roughness surfaces ascertain the effectiveness of the sampling strategy. It can lead to an accurate inference of the surface topography and a sufficient reduction of data points compared with conventional uniform sampling. Robustness against random surface features, measurement noise and sharp height changes is further discussed. Such an adaptive sampling method is extremely suitable for discrete point-by-point measurements.

Research into the inversion of the induced polarization relaxation time spectrum based on the uniform amplitude sampling method

The induced polarization relaxation time spectrum (RTS) reflects the distribution of rock pore size, which is a key factor in estimating the oil or water storage capacity of strata. However, as the data acquisition and transmission abilities of well logging instruments are much limited due to the underground environment, it is necessary to explore suitable sampling methods which can be used to obtain an accurate RST with less sampling data. This paper presents a uniform amplitude sampling method (UASM), and compares it with the conventional uniform time sampling method (UTSM) and logarithm time sampling method (LTSM) in terms of the adaptability to different strata, RTS inversion accuracy, and stratum vertical resolution. Numerical simulation results show that the UASM can obtain high inversion accuracy of RTS with different kinds of pore size distribution formation, with high dynamic ranges of pore size, and with a small number of sampling points. The UASM, being able to adapt to the attenuation speed of polarization curve automatically, thus has the highest vertical resolution. The inversion results of rock samples also show that the UASM is superior to the UTSM and LTSM.

Random Sampling Approaches for Implementation of FPGA in Signal Processing

Nowadays, digital front-end devices are widely used in large number of fields such as electronic appliances. Signals must be presented in an appropriate format, for example, the original analog signals must be converted into digital formats that can be recognized and used by digital equipment. In this paper, the random sampling technique is implemented by original design of a Pseudorandom Signal Sampler circuit for controlling ADC to relax constraints of receiver circuits supporting multiband signal processing. This new idea of using non-uniform sampling technique for multiband signals sampling allows the main advantage of suppressing spectral aliases at integer multiples of sampling frequency produced by conventional uniform sampling technique. This approach could reduce the constraints on the anti-aliasing filter, relax the automatic gain control dynamic range, and decrease the ADC dynamic power consumption. Experiments show that this approach achieve good performance and it could be implemented in FPGA in signal processing successfully.

Error-bounded sampling for analytics on big sparse data

Aggregation queries are at the core of business intelligence and data analytics. In the big data era, many scalable shared-nothing systems have been developed to process aggregation queries over massive amount of data. Microsoft's SCOPE is a well-known instance in this category. Nevertheless, aggregation queries are still expensive, because query processing needs to consume the entire data set, which is often hundreds of terabytes. Data sampling is a technique that samples a small portion of data to process and returns an approximate result with an error bound, thereby reducing the query's execution time. While similar problems were studied in the database literature, we encountered new challenges that disable most of prior efforts: (1) error bounds are dictated by end users and cannot be compromised, (2) data is sparse , meaning data has a limited population but a wide range. For such cases, conventional uniform sampling often yield high sampling rates and thus deliver limited or no performance gains. In this paper, we propose error-bounded stratified sampling to reduce sample size. The technique relies on the insight that we may only reduce the sampling rate with the knowledge of data distributions. The technique has been implemented into Microsoft internal search query platform. Results show that the proposed approach can reduce up to 99% sample size comparing with uniform sampling, and its performance is robust against data volume and other key performance metrics.

Toward Time-Quantized Pseudorandom Sampling for Green Communication

In this brief, the authors propose time-quantized pseudorandom sampling (TQ-PRS) as a power-saving solution compared with conventional uniform sampling. Due to its ability to reduce replicas' power levels, TQ-PRS reduces the design constraints on receiver components. Applied on the baseband stage of a multistandard radio receiver, TQ-PRS allows decreasing the antialiasing filter order, as well as reducing the sampling frequency. This feature leads to saving up to 30% of baseband power consumption.

Fast Adaptive Cross-Sampling Scheme for the Sparsified Adaptive Cross Approximation

A fast adaptive cross-sampling (FACS) scheme for the sparsified adaptive cross approximation (SPACA) algorithm is proposed to improve the conventional uniform spatial sampling. The FACS adaptively samples each well-separated block pair in an iterative manner to reach a given sampling error. At each iteration, the FACS first selects a set of initial samples with uniform spatial distribution for each block, and then uses the adaptive cross approximation (ACA) to find the important samples from the initial samples. Compared to the uniform spatial sampling, the FACS is easier to control the sampling error and needs fewer samples for the same sampling error. By reducing the number of samples, the FACS can enhance the efficiency of the SPACA. Numerical results are shown to demonstrate the merits of the proposed scheme.

Compressed sensing for SAR‐based wideband three‐dimensional microwave imaging system using non‐uniform fast Fourier transform

A new compressed sensing (CS) image reconstruction method is proposed for high-resolution wideband threedimensional synthetic aperture radar (SAR) imaging systems. In contrast to existing CS SAR methods that employ only a forward SAR transform in pre- or post-processing, the proposed method employs both forward SAR and reverse SAR (R-SAR) transforms in each CS iteration to improve the quality of reconstructed images. This study proposes a simple and elegant truncation repair method to combat the truncation error and utilises non-uniform fast Fourier transform to reduce the SAR and R-SAR transform errors, thereby ensuring the convergence of the CS algorithm and improving the quality of the reconstructed images. The proposed CS SAR method is applied to microwave and millimeter wave imaging systems for non-destructive evaluation of materials embedded in stratified media. Three different specimens under test are measured by conventional uniform sampling and by random under-sampling with 20% or 30% spatial points of the uniform sampling. The reconstructed images show that, albeit having much less measurement points, the proposed CS method achieves better image quality and lower background artefacts than the images reconstructed from the fullysampled uniform measurements.

Adaptive Angular Sampling for SPECT Imaging.

This paper presents an analytical approach for performing adaptive angular sampling in single photon emission computed tomography (SPECT) imaging. It allows for a rapid determination of the optimum sampling strategy that minimizes image variance in regions-of-interest (ROIs). The proposed method consists of three key components: (a) a set of close-form equations for evaluating image variance and resolution attainable with a given sampling strategy, (b) a gradient-based algorithm for searching through the parameter space to find the optimum sampling strategy and (c) an efficient computation approach for speeding up the search process. In this paper, we have demonstrated the use of the proposed analytical approach with a single-head SPECT system for finding the optimum distribution of imaging time across all possible sampling angles. Compared to the conventional uniform angular sampling approach, adaptive angular sampling allows the camera to spend larger fractions of imaging time at angles that are more efficient in acquiring useful imaging information. This leads to a significantly lowered image variance. In general, the analytical approach developed in this study could be used with many nuclear imaging systems (such as SPECT, PET and X-ray CT) equipped with adaptive hardware. This strategy could provide an optimized sampling efficiency and therefore an improved image quality.