Non-uniform Sampling Scheme Research Articles

Identifying Impacts of Contact Tracing on Epidemiological Inference from Phylogenetic Data.

Robust sampling methods are foundational to inferences using phylogenies. Yet the impact of using contact tracing, a type of non-uniform sampling used in public health applications such as infectious disease outbreak investigations, has not been investigated in the molecular epidemiology field. To understand how contact tracing influences a recovered phylogeny, we developed a new simulation tool called SEEPS (Sequence Evolution and Epidemiological Process Simulator) that allows for the simulation of contact tracing and the resulting transmission tree, pathogen phylogeny, and corresponding virus genetic sequences. Importantly, SEEPS takes within-host evolution into account when generating pathogen phylogenies and sequences from transmission histories. Using SEEPS, we demonstrate that contact tracing can significantly impact the structure of the resulting tree, as described by popular tree statistics. Contact tracing generates phylogenies that are less balanced than the underlying transmission process, less representative of the larger epidemiological process, and affects the internal/external branch length ratios that characterize specific epidemiological scenarios. We also examined real data from a 2007-2008 Swedish HIV-1 outbreak and the broader 1998-2010 European HIV-1 epidemic to highlight the differences in contact tracing and expected phylogenies. Aided by SEEPS, we show that the data collection of the Swedish outbreak was strongly influenced by contact tracing even after downsampling, while the broader European Union epidemic showed little evidence of universal contact tracing, agreeing with the known epidemiological information about sampling and spread. Overall, our results highlight the importance of including possible non-uniform sampling schemes when examining phylogenetic trees. For that, SEEPS serves as a useful tool to evaluate such impacts, thereby facilitating better phylogenetic inferences of the characteristics of a disease outbreak. SEEPS is available at github.com/MolEvolEpid/SEEPS.

Imbalanced generative sampling of training data for improving quality of machine learning model

Design exploration in engineering applications often requires a meticulous experimental or numerical study to evaluate performance (Y) of each design, which may require great effort, time or resources. Reducing the number of these tests for finding a good design is of paramount importance in all engineering fields. This study aims at computing a machine learning (ML) model using less number of designs as training data. Uniform sampling (US) in the design space (based on predefined design parameters) to obtain a training data is a promising approach. We further extend this sampling concept to obtain designs in the design space by also employing the ML model.The designs are selected via two non-uniform (imbalanced) sampling methods (namely, height-based sampling - HBS and gradient-based sampling - GBS) while considering their Y and gradient, dY, values. These values are divided into uniform intervals, and we aim at equalizing the number of designs in the training data at each interval as much as possible. This can force designs to have minimum or maximum Y or dY values, which, in fact, lie on small portion of the design space, in general. Therefore, capturing designs from all design space portions can be enabled.Results of the proposed methods are compared against US along with two well studied non-uniform sampling strategies, Stratified Over Sampling (SOS) and Gaussian-Process Based Sampling (GPBS). To reliably investigate quality of ML models obtained using designs sampled via US, SOS, GPBS, HBS and GBS, we utilize standard test (known) functions (such as Easom and Beale) as substitutes for engineering problems. According to the results presented, ML models using HBS and GBS have either better prediction accuracy or wider applicability compared to all other tested sampling methods.

Full-bandwidth anisotropic Migdal-Eliashberg theory and its application to superhydrides

Migdal-Eliashberg theory is one of the state-of-the-art methods for describing conventional superconductors from first principles. However, widely used implementations assume a constant density of states around the Fermi level, which hinders a proper description of materials with distinct features in its vicinity. Here, we present an implementation of the Migdal-Eliashberg theory within the EPW code that considers the full electronic structure and accommodates scattering processes beyond the Fermi surface. To significantly reduce computational costs, we introduce a non-uniform sampling scheme along the imaginary axis. We demonstrate the power of our implementation by applying it to the sodalite-like clathrates YH6 and CaH6, and to the covalently-bonded H3S and D3S. Furthermore, we investigate the effect of maximizing the density of states at the Fermi level in doped H3S and BaSiH8 within the full-bandwidth treatment compared to the constant-density-of-states approximation. Our findings highlight the importance of this advanced treatment in such complex materials.

Deep Adaptive Quadruplet Hashing With Probability Sampling for Large-Scale Image Retrieval

With the preferable efficiency in storage and computation, hashing has shown potential application in large-scale multimedia retrieval. Compared with traditional hashing algorithms using hand-crafted characteristics, deep hashing inherits the representational capacity of deep neural networks to jointly learn semantic features and hash functions, encoding raw data into compact binary codes with significant discrimination. Generally, most of the current multi-wise hashing methods view the similarity margins between image pairs as constant values in training process. When the distance between sample pairs exceeds the fixed margin, the hashing network would not learn anything. Besides, available hashing methods commonly introduce the random sampling strategy to build training batches and ignore the sample distribution, which is harmful to parameter optimization. In this paper, we propose a novel Deep Adaptive Quadruplet Hashing with probability sampling (DAQH) for discriminative binary code learning. Specifically, with exploring the distribution relationship of raw samples, a non-uniform probability sampling strategy is proposed to build more informative and representative training batches, while maintaining the diversity of training samples. By introducing the prior similarity of sample pairs to calculate corresponding margins, an adaptive margin quadruplet loss is designed to dynamically preserve the underlying semantic relationships with its neighbors. To tune the attributes of binary codes, by combining quadruple regularization and orthogonality optimization, binary code constraint is developed to make the learned embedding with significant discrimination. Extensive experimental results on various benchmark datasets demonstrate our proposed DAQH framework achieves state-of-the-art visual similarity search performance.

An Ultra-Low-Power Non-Uniform Derivative-Based Sampling Scheme With Tunable Accuracy

This paper presents an ultra-low-power non-uniform sampling scheme using a derivative-based algorithm that can maintain a comparable accuracy to other non-uniform sampling schemes but with less complexity and lower power consumption. In this method, the change in the derivative of the signal above certain threshold values is used to identify high signal activity for retention of the significant points of the signal. The scheme is implemented using simple building blocks that calculate and compare the change in approximate real-time derivative to a tunable threshed value that can be adjusted to obtain the desired Compression Factor (CF) and Post-Reconstruction Signal-to-Noise plus Distortion Ratio (PR-SNDR) for different signal types. Fabricated in TSMC’s 0.13 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu$</tex-math> </inline-formula> m CMOS technology and tested with real-world biomedical signals, the proposed Derivative Dependent Sampling (DDS) system consumes a maximum power of 155 nW while achieving a CF of more than 6 for an Electrocardiography (ECG) signal. By adding the proposed DDS block to a data acquisition and processing system, the non-uniform sampling can reduce the power dissipation of the entire system.

Enhancing diversity in GANs via non-uniform sampling

Recent advances in Generative Adversarial Networks (GANs) have led to impressive results in generating realistic data. However, GANs training is still challenging, often leading to mode-collapse, where a certain type of samples dominates the generated output. To address this issue, we propose a novel training algorithm based on bidirectional GANs (BiGANs) that can be generalized to any implicit generative model. Our algorithm relies on a non-uniform sampling scheme, where data points in a minibatch are sampled with probability inversely proportional to their log-evidence. However, estimating log-evidence is computationally expensive. Instead, we propose to use the reconstruction error, which directly correlates with the log-evidence and only requires a BiGAN network evaluation. Additionally, we combine the aforementioned method with a regularization in the empirical distribution of the encoder that further boosts the performance. Our empirical results show that the proposed methods improve both the quality and diversity of the generated samples.

Real-Time Stereo 3D Car Detection With Shape-Aware Non-Uniform Sampling

Pseudo-LiDAR based stereo 3D detectors have gained popularity due to their high accuracy. However, these methods need dense depth supervision and suffer from inferior speed. To solve these two issues, a recently introduced RTS3D builds an efficient 4D feature-consistency embedding (FCE) space for the object intermediate representation without depth supervision, where FCE space performs uniform sampling to generate feature sampling points, which ignores the importance of different object regions. In this paper, we observe that, compared with the inner region, the outer region of the object plays a more important role for accurate 3D detection. To fully exploit the useful information from the outer region, we propose a novel shape-aware non-uniform sampling strategy. Instead of uniform sampling, our proposed non-uniform sampling strategy performs dense sampling in outer region and sparse sampling in inner region. Therefore, more points are sampled from the outer region and more useful features are extracted for 3D detection. In addition, we design a high-level semantic enhanced FCE module to exploit more contextual information and suppress noise better. As a result, it further improves feature discrimination of each sampling point. Experimental results on the KITTI dataset show the effectiveness of the proposed method. Compared with the baseline RTS3D, our proposed method has 2.57% improvement on car AP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{3d}$ </tex-math></inline-formula> almost without extra network parameters. Moreover, our proposed method outperforms the state-of-the-art methods without extra supervision at a real-time speed.

Double-objective economic statistical design of () control chart using Linex loss function

PurposeThe purpose of this paper is to develop a double-objective economic statistical design (ESD) of () control chart under Weibull failure properties with the Linex asymmetric loss function. The authors have expressed the probability of type II error (β) as the statistical objective and the expected cost as the economic objective.Design/methodology/approachThe design used in this study is based on a double-objective economic statistical design of () control chart with Weibull shock model via applying Banerjee and Rahim's model for non-uniform and uniform schemes with Linex asymmetric loss function. The results in the least average cost and β in uniform and non-uniform schemes by Linex loss function, compared with the same schemes without loss function.FindingsNumerical results indicate that it is not possible to reduce the second type of error and costs at the same time, which means that by reducing the second type of error, the cost increases, and by reducing the cost, the second type of error increases, both of which are very important. Obtained based on the needs of the industry and which one has more priority has the right to choose. These designs define a Pareto optimal front of solutions that increase the flexibility and adaptability of the control chart in practice. When the authors use non-uniform schemes instead of uniform schemes, the average cost per unit time decreases by an average and when the authors apply loss function, the average cost per unit time increases by an average. Also, this quantity for double-objective schemes with loss function compared to without loss function schemes in cases uniform and non-uniform increases. The reason for this result is that the model underestimated the costs before using the loss function.Practical implicationsThis research adds to the body of knowledge related to flexibility in process quality control. This article may be of interest to quality systems experts in factories where the choice between cost reduction and statistical factor reduction can affect the production process.Originality/valueThe cost functions for double-objective uniform and non-uniform sampling schemes with the Weibull shock model based on the Linex loss function are presented for the first time.

Broadband Signal Digitization Based on Low-Speed Non-Uniform Photonic Sampling

A new non-uniform photonic sampling (NPS) strategy and its special signal reconstruction algorithm are proposed to achieve digital acquisition of broadband periodic signals at a low sampling rate. Compared with the existing schemes, the NPS strategy can largely reduce the sampling number to acquire identical signal information as that obtained by using its equivalent high-speed uniform photonic sampling, which is beneficial for reducing the sampling time and the data volume of the NPS-based analog-to-digital converter (ADC). In addition, the calculation time of the proposed algorithm is millions of times lower than that of the digital alias-free signal processing (DASP) algorithm used before, which benefits from the fast Fourier transform calculation of a one-dimensional data array instead of a two-dimensional data array calculation in the DASP algorithm. A simulation is performed to validate the feasibility of the proposed scheme. In the simulation, a single-channel NPS-based ADC with an average sampling rate of 1 GSa/s is demonstrated by using the proposed NPS strategy and signal reconstruction algorithm. The results indicate the reconstructed signal information for a single-tone microwave signal at 9.9 GHz and a linear frequency modulation signal in the frequency range of 1 GHz to 9 GHz are identical to those obtained by using its equivalent high-speed uniform photonic sampling-based ADC with a sampling rate of 20 GSa/s.

Super-resolution wavefront reconstruction

Context.Cutting-edge, ground-based astronomical instruments are fed by adaptive optics (AO) systems that are aimed at providing high performance down to the visible wavelength domain on 10 m class telescopes and in the near infrared for the first generation instruments of Extremely Large Telescopes (ELTs). Both applications lead to a large ratio between the telescope diameter,D, and the coherence length or Fried parameter,r0, that isD/r0. As the parameter that defines the required number of degrees of freedom of the AO system,D/r0drives the requirement to reconstruct the incoming wavefront with ever-higher spatial resolution. In this context, super-resolution (SR) appears as a potential game changer. Indeed, SR promises to dramatically expand the range of spatial frequencies that can be reconstructed from a set of lower resolution measurements of the wavefront.Aims.As a technique that seeks to upscale the resolution of a set of measured signals, SR retrieves higher-frequency signal content by combining multiple lower resolution sampled data sets. It is well known both in the temporal and spatial domains and widely used in imaging to reduce aliasing and enhance the resolution of coarsely sampled images. This study applies the SR technique to the bidimensional wavefront reconstruction. In particular, we show how SR is intrinsically suited for tomographic multi-wavefront sensor (WFS) AO systems, revealing many of its advantages with minimal design effort.Methods.We provide a direct space and Fourier optics description of the wavefront sensing operation and we demonstrate how SR can be exploited through signal reconstruction, especially within the framework of periodic non-uniform sampling. We investigate both meta-uniform and non-uniform sampling schemes and we show that under some conditions, both sampling schemes enable a perfect reconstruction of band-limited signals. We also provide a SR bi-dimensional model for a Shack-Hartmann (SH) WFS, along with an analysis of the characteristics of the sensitivity function. We validated the SR concept with numerical simulations of representative multi-WFS SH AO systems. Finally, we explored the extension of the method to pyramid WFSs.Results.Our results show that combining several WFS samples in a SR framework grants access to a greater number of modes than the native one offered by a single WFS (despite the fixed sub-aperture size across samples). We show that the wavefront reconstruction achieved with four WFSs can be equivalent to a single WFS providing a sampling resolution that is twice greater (linear across the telescope aperture). We also show that the associated noise propagation is not degraded under SR. Finally, we show that the concept can be extended to the signal produced by single pyramid WFS, with its four re-imaged pupils serving as multiple non-redundant samples.Conclusions.We find that SR applied to wavefront sensing and reconstruction (WFR) offers a new parameter space to explore, as it decouples the size of the sub-aperture from the desired wavefront sampling resolution. By shifting away from outdated assumptions, new and more flexible, better-performing AO designs have now become possible.

Robust Optimization of an Imperfect Process when the Mean and Variance are Jointly Monitored under Dependent Multiple Assignable Causes

Abstract Imperfect processes experience fault productions over time due to specific causes. Integrating the statistical process control, maintenance policy, and economic production quantity has led to more favorable results for the imperfect processes in literature. When monitoring a process, multiple assignable causes (ACs) may shift it to an out-of-control state. As indicated recently, if the interdependency of ACs is neglected, the total cost will be underestimated. Moreover, the mean and variance can simultaneously be affected by the occurrence of ACs. A non-central chi-square (NCS) chart was suggested for its decent performance against X-R chart in detecting the process disturbances and lowering quality loss cost. Besides, the increased occurrence rate of ACs over time leads to higher quality and maintenance costs. Employing a non-uniform sampling (NUS) scheme can significantly reduce costs. In the literature of modeling for imperfect processes under multiple ACs, all input parameters have always been fixed. The effectiveness of the models depends somewhat on the accurate estimates of these parameters. In reality, the estimation of parameters may be associated with uncertainty. For the first time, a robust design approach is proposed for designing NCS chart by considering the interval estimation of uncertain parameters. A particle swarm optimization (PSO) algorithm is used to present solutions. The proposed model is investigated through a real numerical example.

Joint design of control chart and maintenance policy under multiple assignable causes and random failures by considering the statistical constraints

ABSTRACT In modern industries, statistical process monitoring (SPM) and maintenance management are extensively employed to increase the production rate of conforming items. Aiming at minimizing the expected total cost per time unit subject to some statistical constraints, this study proposes a hybrid quality-maintenance model for imperfect short-run process. To bring the proposed model closer to real short-run systems, it is considered that the process mean may shift to an out-of-control condition due to occurrence of several types of assignable causes. Furthermore, it is supposed that the time-to-failure follows a non-homogenous Poisson process implying that the system may suddenly fail with an increasing failure rate function. Moreover, a non-uniform sampling scheme is developed in order to improve the system reliability. Finally, the main advantages of the proposed model are highlighted by conducting two comparative studies. The first one illustrates the efficiency of the non-uniform sampling scheme in increasing the in-control time interval and decreasing the expected total cost. The second one confirms the importance of considering the system failure on both the expected total cost and in-control time interval.

Exploring differential geometry in neural implicits

We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions.To train a neural implicit function, we propose a loss functional that approximates a signed distance function, and allows terms with high-order derivatives, such as the alignment between the principal directions of curvature, to learn more geometric details. During training, we consider a non-uniform sampling strategy based on the curvatures of the point-sampled surface to prioritize points with more geometric details. This sampling implies faster learning while preserving geometric accuracy when compared with previous approaches.We also use the analytical derivatives of a neural implicit function to estimate the differential measures of the underlying point-sampled surface.

An improved compressed sensing method for dynamic impact signals based on cubic spline interpolation.

During the dynamic acquisition of impact signals, a high sampling frequency brings significant challenges to the analog-to-digital converter and other test systems. To address this issue, in this study, an improved compressed sensing (CS) method is proposed for the measurement of impact signals based on cubic spline interpolation (CSI). According to the characteristics of the dynamic impact signal, a random non-uniform sampling strategy combining CS and CSI is presented. The CSI obviously reduces the number of observation points required by the traditional CS. To resolve the problem that the traditional orthogonal matching pursuit (OMP) algorithm can only guarantee the local optimal solution but cannot obtain the global optimal solution, an improved orthogonal matching pursuit (IOMP) algorithm is proposed. First, n atoms related to residuals are selected to build a local atomic dictionary. Subsequently, the atom most relevant to the signal observation result is selected from the local atomic dictionary. The iteration process is repeated until enough atoms are selected. The IOMP algorithm effectively improves the success rate of reconstruction. Finally, an impact signals test platform based on the Machete hammer is established. The results of theoretical simulations and several experiments indicate that the data reconstruction error of the proposed improved CS method for impact signals is approximately 5.0%.

Column $\ell_{2,0}$-Norm Regularized Factorization Model of Low-Rank Matrix Recovery and Its Computation

This paper is concerned with the column $\ell_{2,0}$-regularized factorization model of low-rank matrix recovery problems and its computation. The column $\ell_{2,0}$-norm of factor matrices is introduced to promote column sparsity of factors and low-rank solutions. For this nonconvex discontinuous optimization problem, we develop an alternating majorization-minimization (AMM) method with extrapolation, and a hybrid AMM in which a majorized alternating proximal method is proposed to seek an initial factor pair with less nonzero columns and the AMM with extrapolation is then employed to minimize of a smooth nonconvex loss. We provide the global convergence analysis for the proposed AMM methods and apply them to the matrix completion problem with non-uniform sampling schemes. Numerical experiments are conducted with synthetic and real data examples, and comparison results with the nuclear-norm regularized factorization model and the max-norm regularized convex model show that the column $\ell_{2,0}$-regularized factorization model has an advantage in offering solutions of lower error and rank within less time.

SNIFF: A Scalable Network Inference Framework for Measuring End-to-End Performance

For Internet measurement, a key challenge is how to measure end-to-end performance accurately and effectively. To achieve this goal, several recent studies suggest applying advanced matrix completion techniques to recover the complete matrix using a small percentage of samples. While the low-rank features of matrices are generally utilized in existing studies, important features, which are unique in our domain context and can be used to significantly reduce path sampling overhead with guaranteed recovery accuracy, have not been fully explored. To fill the gap, we propose a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scalable network inference framework</i> , namely, SNIFF, to monitor the end-to-end performance of a set of paths over time. In our framework, we extensively investigate real datasets and identify key features in measurement data, including the low-rank feature of the path-time matrix, the smoothness of performance over a short period, and the pair-wise linear correlation of paths. Based on these features, we develop three non-uniform sampling strategies that increase the sampling rate of important paths while reducing the rate if two paths are highly correlated. Moreover, we formulate two types of optimization problems for matrix completion that take into account important characteristics of data and we develop efficient algorithms to solve the corresponding problems. To evaluate the proposed framework, we conduct extensive numerical experiments for measuring end-to-end delay and throughput performance. The results confirm the feasibility and advantages of the proposed framework and algorithms.

DRI-MVSNet: A depth residual inference network for multi-view stereo images.

Three-dimensional (3D) image reconstruction is an important field of computer vision for restoring the 3D geometry of a given scene. Due to the demand for large amounts of memory, prevalent methods of 3D reconstruction yield inaccurate results, because of which the highly accuracy reconstruction of a scene remains an outstanding challenge. This study proposes a cascaded depth residual inference network, called DRI-MVSNet, that uses a cross-view similarity-based feature map fusion module for residual inference. It involves three improvements. First, a combined module is used for processing channel-related and spatial information to capture the relevant contextual information and improve feature representation. It combines the channel attention mechanism and spatial pooling networks. Second, a cross-view similarity-based feature map fusion module is proposed that learns the similarity between pairs of pixel in each source and reference image at planes of different depths along the frustum of the reference camera. Third, a deep, multi-stage residual prediction module is designed to generate a high-precision depth map that uses a non-uniform depth sampling strategy to construct hypothetical depth planes. The results of extensive experiments show that DRI-MVSNet delivers competitive performance on the DTU and the Tanks & Temples datasets, and the accuracy and completeness of the point cloud reconstructed by it are significantly superior to those of state-of-the-art benchmarks.

An economic-statistical production quantity model under quality-maintenance policy for imperfect manufacturing systems with interaction effect among assignable causes

This study integrates production and maintenance planning with statistical process monitoring in the presence of dependent multiple assignable causes. To adapt the model to the reality, two assumptions are considered: (1) the assignable causes (ACs) are dependent, and (2) the occurrence of ACs can affect both process mean and variability. Given the second assumption, a non-central chi-square (NCS) chart is used to monitor the process. Since the occurrence rate of ACs increases over time, a non-uniform sampling scheme is presented to reduce the out-of-control time period. A sensitivity analysis is presented to explore how the number of AC types influences the cost terms. The results indicate that the more AC types, the higher quality loss and maintenance costs are imposed on the manufacturer. Moreover, three comparative studies are conducted for confirming the effectiveness of the model. The first comparative study shows that the total cost will be less than its real value when the interdependency among the ACs is ignored. The second comparison shows that the NCS chart outperforms the in detecting the process disturbances and leads to a less quality loss cost. Eventually, the last one represents that employing the non-uniform sampling strategy leads to a significant cost savings.

Joint Design of Control Chart, Production Cycle Length, and Maintenance Schedule for Imperfect Manufacturing Systems with Deteriorating Products under Stochastic Shift Size

This paper presents a hybrid model based on the integration of three interrelated topics including statistical process monitoring (SPM), production cycle length, and maintenance scheduling for imperfect production systems. The proposed model takes both process deterioration and product deterioration into account i.e., the process can go out of control and the products can deteriorate over time. In this regard, a nonuniform sampling strategy is presented for calculating the sampling intervals to avoid exceeding the hazard rate from a threshold value. Moreover, in order to make the model more adapted to real industrial systems, the shift magnitude in the mean parameter of quality characteristic is considered as a stochastic variable. To elaborate the model effectiveness, three comparative studies and a sensitivity analysis are presented. The first comparison shows that by using the variable sampling interval scheme instead of the fixed one, the ratio of in-control time interval to the whole production cycle increases dramatically. Moreover, the use of variable sampling interval scheme leads to a significant cost savings and decreases the out-of-control time interval. The second comparative study indicates that although using statistical considerations in establishment of the control chart imposes a higher cost on the manufacturer, both values of the in-control average run length ([Formula: see text]) and out-of-control average run length ([Formula: see text]) improve significantly. In other words, the use of economic-statistical model reduces the amount of non-conforming products as well as the risk of issuing a false alarm by the control chart. The third comparative study indicates that, in terms of total inventory holding cost, the proposed model performs better than the model without considering deterioration possibility due to the significant reduction in the deterioration cost.

Clustered sparsity and Poisson-gap sampling

Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a “flat” pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of ”blue-noise” schedules, such as PG. We call this feature “clustered sparsity”. This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful.