Sparse Measurements Research Articles

Functional Principal Component Analysis as an Alternative to Mixed-Effect Models for Describing Sparse Repeated Measures in Presence of Missing Data.

Analyzing longitudinal data in health studies is challenging due to sparse and error-prone measurements, strong within-individual correlation, missing data and various trajectory shapes. While mixed-effect models (MM) effectively address these challenges, they remain parametric models and may incur computational costs. In contrast, functional principal component analysis (FPCA) is a non-parametric approach developed for regular and dense functional data that flexibly describes temporal trajectories at a potentially lower computational cost. This article presents an empirical simulation study evaluating the behavior of FPCA with sparse and error-prone repeated measures and its robustness under different missing data schemes in comparison with MM. The results show that FPCA is well-suited in the presence of missing at random data caused by dropout, except in scenarios involving most frequent and systematic dropout. Like MM, FPCA fails under missing not at random mechanism. The FPCA was applied to describe the trajectories of four cognitive functions before clinical dementia and contrast them with those of matched controls in a case-control study nested in a population-based aging cohort. The average cognitive declines of future dementia cases showed a sudden divergence from those of their matched controls with a sharp acceleration 5 to 2.5 years prior to diagnosis.

Preliminary Analysis of Simple Novelty Search.

Novelty search is a powerful tool for finding diverse sets of objects in complicated spaces. Recent experiments on simplified versions of novelty search introduce the idea that novelty search happens at the level of the archive space, rather than individual points. The sparseness measure and archive update criterion create a process that is driven by a two measures: (1) spread out to cover the space while trying to remain as efficiently packed as possible, and (2) metrics inspired by k nearest neighbor theory. In this paper, we generalize previous simplifications of novelty search to include traditional population (μ,λ) dynamics for generating new search points, where the population and the archive are updated separately. We provide some theoretical guidance regarding balancing mutation and sparseness criteria and introduce the concept of saturation as a way of talking about fully covered spaces. We show empirically that claims that novelty search is inherently objectiveless are incorrect. We leverage the understanding of novelty search as an optimizer of archive coverage, suggest several ways to improve the search, and demonstrate one simple improvement-generating some new points directly from the archive rather than the parent population.

Physical constraint flow field reconstruction method for immersion scan-step flow

The lithography immersion flow field is highly sensitive to minor variations due to the precision demands of lithography. The scanning flow induces pressure fluctuations on the lens surface, subsequently impacting the quality of exposure. Previous measurement methods have encountered sparse distribution measurements on the lens surface due to limitations in sensor size and flow field dimensions. In this manuscript, the authors propose a modal fusion flow field reconstruction method, effectively integrating sensor-based experimental methods and equation-based computational methods. This method achieves high-resolution measurements of stress distribution and velocity distribution. Initially, a simulation of the flow field under operational conditions is conducted to acquire a dataset, followed by decomposing the dataset into modes to establish a modal library. Throughout the measurement process, the modal library is dynamically restructured based on sensor signal using a sparse representation method to forecast the flow field, and subsequently, the flow field is corrected in accordance with the Navier-Stokes equation.

A novel data-driven 3D site characterisation method: Tucker decomposition-Bayesian compressive sensing and benchmarking study

ABSTRACT Site characterisation plays a pivotal role in geotechnical design and analysis. With advancements in machine learning and other digital technologies, data-driven site characterisation (DDSC) has garnered substantial interest in data-centric geotechnics. This paper proposes a novel and competitive 3D DDSC method, called Tucker decomposition-Bayesian compressive sensing (TD-BCS), which employs Tucker decomposition to factorise a 3D high-order tensor into a low-rank core tensor along with three associated factor matrices. The method comprises three key components: (1) 3D sparse representation using Tucker decomposition and discrete cosine transform; (2) Bayesian compressive sensing, and its algorithm implementation; and (3) Determination of three effective factor matrices. The proposed TD-BCS method is evaluated through its application to two benchmark examples, involving virtual ground and actual ground scenario based on real CPT data. And the benchmarking results demonstrate that the method not only yields accurate estimates with quantified uncertainty from sparse measurements but also exhibits high computational efficiency compared to other DDSC methods. Indeed, the TD-BCS method can be effectively applied to other 3D geotechnical engineering cases, and its framework is readily extendable to higher dimensions.

Multi-angle speed-of-sound imaging with sparse sampling to characterize medical tissue properties

Medical Speed-of-sound (SoS) imaging, which can characterize medical tissue properties better by quantifying their different SoS, is an effective imaging method compared with conventional B-mode ultrasound imaging. As a commonly used diagnostic instrument, a hand-held array probe features convenient and quick inspection. However, artifacts will occur in the single-angle SoS imaging, resulting in indistinguishable tissue boundaries. In order to build a high-quality SoS image, a number of raw data are needed, which will bring difficulties to data storage and processing. Compressed sensing (CS) theory offers theoretical support to the feasibility that a sparse signal can be rebuilt with random but less sampling data. In this study, we proposed an SoS reconstruction method based on CS theory to process signals obtained from a hand-held linear array probe with a passive reflector positioned on the opposite side. The SoS reconstruction method consists of three parts. Firstly, a sparse transform basis is selected appropriately for a sparse representation of the original signal. Then, considering the mathematical principles of SoS imaging, the ray-length matrix is used as a sparse measurement matrix to observe the original signal, which represents the length of the acoustic propagation path. Finally, the orthogonal matching pursuit algorithm is introduced for image reconstruction. The experimental result of the phantom proves that SoS imaging can clearly distinguish tissues that show similar echogenicity in B-mode ultrasound imaging. The simulation and experimental results show that our proposed method holds promising potential for reconstructing precision SoS images with fewer signal samplings, transmission, and storage.

Spatial-frequency parallel subsampling for distributed compressive sensing in ultrasonic imaging inspection

To address the problem of the high hardware requirements and insufficient data storage capacity in current ultrasonic imaging testing, a novel approach is developed using a programmable device, which combines spatial-frequency parallel subsampling with the distributed compressive sensing simultaneous orthogonal matching pursuit (DCS-SOMP) algorithm to achieve fast and high-quality ultrasonic imaging inspection with a small amount of subsampled data. The spatial sparse measurement method was employed to achieve spatial subsampling and minimize the count of signals. Additionally, frequency subsampling was utilized to significantly reduce the data volume of time-domain signals while ensuring signal quality by truncating the primary testing frequency components. The subsampled data was then reconstructed using distributed compressive sensing (DCS) for multi-channel data reconstruction. The experiment of ultrasonic scanning imaging was conducted on a carbon steel specimen containing six transverse through-holes with a diameter of Ф1.5 mm at different depths. The ultrasonic signals were acquired using the spatial-frequency parallel subsampling method, and subsequently reconstructed using the DCS-SOMP algorithm. The results show that the proposed method achieves comparable image quality to that obtained with complete data, using only 1/8 of the complete data, while accurately locating and quantifying defects.

A pyramid-style neural network model with alterable input for reconstruction of physics field on turbine blade surface from various sparse measurements

Data from turbine cascade experiments typically exhibits low spatial–temporal resolution, along with inevitable noise and local data missing. This paper aims to establish a super-resolution model to reconstruct the complete pressure and temperature fields on the blade surface from limited observations, using the deep learning method. Depending on the three-dimensional geometric complexity of the blade, the required cross-sectional data varies, resulting in input data of different sizes. Conventional surrogate models typically confine themselves to a single input format, leading to limited compatibility with diverse inputs. A pyramid-style model with four optional input ports is proposed, designed to accommodate data with different numbers of span-wise sections. Three training strategies have been evaluated, where distributed training has been proven to be more time-effective and flexible while maintaining high prediction precision, compared to holistic and conventional training. Generally, the average relative error over the whole dataset falls below 0.18%, the average peak signal-to-noise ratio exceeds 52 dB, and the average structural similarity index measurement surpasses 0.999. As the number of span-wise sections and the amount of information in the input increase, the overall performance shows a consistent upward trend. Robustness analyses are conducted by applying artificial noises of varying intensities. The results indicate that the model can tolerate noise intensities of up to 5% with a satisfactory reconstruction accuracy. In addition, the model is quite sensitive to the measurement data noises in complex flow regions such as expansion waves, suggesting that more intensive measurements should be targeted to those regions when conducting cascade experiments. The proposed method satisfies the intended objectives and provides an idea for future applications in digital twin platforms.

Sparse Integer Programming Is Fixed-Parameter Tractable

We study the general integer programming problem where the number of variables n is a variable part of the input. We consider two natural parameters of the constraint matrix A: its numeric measure a and its sparsity measure d. We present an algorithm for solving integer programming in time [Formula: see text], where g is some computable function of the parameters a and d, and L is the binary encoding length of the input. In particular, integer programming is fixed-parameter tractable parameterized by a and d, and is solvable in polynomial time for every fixed a and d. Our results also extend to nonlinear separable convex objective functions. Funding: F. Eisenbrand, C. Hunkenschröder, and K.-M. Klein were supported by the Swiss National Science Foundation (SNSF) within the project “Convexity, geometry of numbers, and the complexity of integer programming” [Grant 163071]. A. Levin and S. Onn are partially supported by the Israel Science Foundation [Grant 308/18]. A. Levin is also partially supported by the Israel Science Foundation [Grant 1467/22]. S. Onn is also partially supported by the Dresner Chair at the Technion. M. Koutecký is partially supported by Charles University project UNCE 24/SCI/008, and by the project 22-22997S of the Grantová Agentura České Republiky (GA ČR).

Online state estimation in water distribution systems via Extended Kalman Filtering

Operators of water distribution systems (WDSs) need continuous and timely information on pressures and flows to ensure smooth operation and respond quickly to unexpected events. While hydraulic models provide reasonable estimates of pressures and flows in WDSs, updating model predictions with real-time sensor data provides clearer insights into true system behavior and enables more effective real-time response. Despite the growing prevalence of distributed sensing within WDSs, standard hydraulic modeling software like EPANET do not support synchronous data assimilation. This study presents a new method for state estimation in WDSs that combines a fully physically-based model of WDS hydraulics with an Extended Kalman Filter (EKF) to estimate system flows and heads based on sparse sensor measurements. To perform state estimation via EKF, a state-space model of the hydraulic system is first formulated based on the 1-D Saint-Venant equations of conservation of mass and momentum. Results demonstrate that the proposed model closely matches steady-state extended-period models simulated using EPANET. Next, through a holdout analysis it is found that fusing sensor data with EKF produces flow and head estimates that closely match ground truth flows and heads at unmonitored locations, indicating that state estimation successfully infers internal hydraulic states from sparse sensor measurements. These findings pave the way towards real-time operational models of WDSs that will enable online detection and mitigation of hazards like pipe leaks, main bursts, and hydraulic transients.

Reconstruction of the turbulent flow field with sparse measurements using physics-informed neural network

Accurate high-resolution flow field prediction based on limited experimental data is a complex task. This research introduces an innovative framework leveraging physics-informed neural network (PINN) to reconstruct high-resolution flow fields using sparse particle image velocimetry measurements for flow over a periodic hill and high-fidelity computational fluid dynamics data for flow over a curved backward-facing step. Model training utilized mean flow measurements, with increased measurement sparsity achieved through various curation strategies. The resulting flow field reconstruction demonstrated marginal error in both test cases, showcasing the ability of the framework to reconstruct the flow field with limited measurement data accurately. Additionally, the study successfully predicted flow fields under two different noise levels, closely aligning with experimental and high-fidelity results (experimental, direct numerical simulation, or large eddy simulation) for both cases. Hyperparameter tuning conducted on the periodic hill case has been applied to the curved backward-facing step case. This research underscores the potential of PINN as an emerging method for turbulent flow field prediction via data assimilation, offering reduced computational costs even with sparse, noisy measurements.

Improved Sparse Representation of Image from Inferred Angles of Steerable Wavelet

Objectives: Presenting images with sparse coefficients has a wide variety of real-time applications in compressive sensing. However, sparse representations of images present challenges due hidden similarities in the higher order moments. Literature suggests that the applications that involve natural images present a high level of similarity. Steerable basis, due to their rotational invariant property, have shown potential in sparse representation of natural images. Hence, the objective of the proposed study is to identify steerable basis that maximize the sparse representation of natural images. Method: Prior studies have used the angle of steerable basis either from the random assignment or derived from Hough transform. In this study, we propose the selection of steerable basis angle derived from maximum a prior method. Exploiting a steerable basis for better sparse representation requires the knowledge of proper steerable angles. Hence, we propose using MAP learning approach to identify this angle. Findings: The proposed method resulted in optimal steerable angle without the need for calculation of Hough Transform. In addition, the method also resulted in almost 10 percent improvement in sparse representation as indicated by higher Kurtosis. Novelty: We compare the measure of sparsity to evaluate the effectiveness of the proposed method. The results indicate the optimal sparsity from the proposed method as indicated from the maximum values of kurtosis compared to the previous related methods. In addition, the proposed method relaxes the requirement of manipulating Hough transform for optimal steerable angle. Keywords: Sparsity, Steerable Basis, Wavelet Pyramid Structure, Image Compression, Hough Transform

A compressed sensing random measurement matrix construction method: block sparse random measurement matrix

A compressed sensing random measurement matrix construction method: block sparse random measurement matrix

An ensemble learning paradigm for subsurface stratigraphy from sparse measurements and augmented training images

The performance of computer vision-based techniques for stratigraphic modeling relies heavily on qualified training images to capture the complex stratigraphic connectivity. In geotechnical engineering, only limited training images are available for a specific site. Stochastic simulation modelling based on limited training data may be biased as the collected images that reflect prior geological knowledge may not encompass all potential stratigraphic patterns. Therefore, it is crucial to establish a high-quality, domain-specific training image database for effective stratigraphic modelling. In this study, an ensemble learning paradigm is proposed to tackle this issue and develop subsurface geological cross-sections from sparse data by reconstruction and redistribution of stratigraphic statistics revealed from limited training images. A domain-specific training image database is first established using generative adversarial networks (GAN) that enable the generation of arbitrary sized image samples from a single training image. Subsequently, multiple qualified image samples that are compatible with site-specific data are adaptively selected and utilized for the ensemble learning of geological cross-sections. The performance of the proposed framework is demonstrated using real geological cross-sections collected from a reclamation site and a tunnelling project in Hong Kong. The results indicate that the proposed method can effectively generate diverse image samples that encompass stratigraphic features beyond those reflected in a single training image. More importantly, the ensemble learning framework can capture the complex spatial stratigraphic connectivity of soil layers with enhanced prediction accuracy.

The Chalmers Cloud Ice Climatology: retrieval implementation and validation

Abstract. Ice clouds are a crucial component of the Earth's weather system, and their representation remains a principal challenge for current weather and climate models. Several past and future satellite missions were explicitly designed to provide observations offering new insights into cloud processes, but these specialized cloud sensors are limited in their spatial and temporal coverage. Geostationary satellites have been observing clouds for several decades and can ideally complement the sparse measurements from specialized cloud sensors. However, the geostationary observations that are continuously and globally available over the full observation record are restricted to a small number of wavelengths, which limits the information they can provide on clouds. The Chalmers Cloud Ice Climatology (CCIC) is a novel cloud-property dataset that aims to provide an improved climate record of ice hydrometeor concentrations by applying state-of-the-art machine-learning techniques to retrieve ice cloud properties from globally gridded, single-channel geostationary observations that are readily available from 1980 onwards. CCIC offers a novel perspective on the record of geostationary IR observations by providing spatially and temporally continuous retrievals of the vertically integrated and vertically resolved concentrations of frozen hydrometeors, typically referred to as ice water path (IWP) and ice water content (IWC). In addition to that, CCIC provides 2D and 3D cloud masks and a 3D cloud classification. A fully convolutional quantile regression neural network constitutes the core of the CCIC retrieval, providing probabilistic estimates of IWP and IWC. The network is trained against CloudSat retrievals using 3.5 years of global collocations. Assessed on a held-out test dataset, the CCIC-provided IWP and IWC estimates achieve correlations exceeding 0.7 and 0.6, respectively, and biases better than −5 % and −2 % demonstrating considerable skill in estimating both IWP and IWC. In addition, CCIC is extensively validated against both in situ and remote sensing measurements from two flight campaign series and a ground-based radar. The results of this independent validation confirm the ability of CCIC to retrieve IWP and IWC. CCIC thus ideally complements temporally and spatially more limited measurements from dedicated cloud sensors by providing spatially and temporally continuous estimates of ice cloud properties. The CCIC network and its associated software are made accessible to the scientific community.

Observation vector reconstruction-based nonparametric nonlinear restoring force identification for granules-structures coupled vibrating system

The nonlinear restoring force (NRF) generated by the collision and friction between particles and structures is the leading cause of the complex dynamic response of the granules-structures coupled vibrating system (GSCVS). Identification of NRF can provide critical information for post-event damage diagnosis and structural design of immersed structures. However, the spatial distribution and dynamic response of the particles near the structures are diverse and complex, making it difficult to describe the NRF with an accurate mathematical model. This paper proposed a data-based nonparametric method to estimate the NRF in the GSCVS. A nonparametric model of NRF that considered the additional effects of particles on both sides of the structures and consisted of system response and undetermined coefficients was developed. The observation vector of the conventional Extended Kalman Filter (EKF) was reconstructed by the sparse measurement of the strain response. The reconstructed observation vector contains three response components: translational displacement, translational acceleration, and rotational acceleration, in which the rotational acceleration response is difficult to measure in engineering applications. The proposed EKF based on observation vector reconstruction (EKF-OVR) can identify the undetermined coefficients in the nonparametric model, and then the NRF can be calculated. Numerical studies showed that EKF-OVR achieved higher accuracy and noise robustness than the conventional EKF and the data fusion based EKF. A dynamic experimental study on granules-beam coupled vibrating system (GBCVS) was conducted, and the proposed algorithm was employed to identify the NRF of the GBCVS. The effects of excitation amplitude, particle size, and immersed depth on NRF are analyzed, and it is found that higher harmonic components in the NRF led to period doubling and chaos of the beam response.

On the accuracy of Prony's method for recovery of exponential sums with closely spaced exponents

In this paper we establish accuracy bounds of Prony's method (PM) for recovery of sparse measures from incomplete and noisy frequency measurements, or the so-called problem of super-resolution, when the minimal separation between the points in the support of the measure may be much smaller than the Rayleigh limit. In particular, we show that PM is optimal with respect to the previously established min-max bound for the problem, in the setting when the measurement bandwidth is constant, with the minimal separation going to zero. Our main technical contribution is an accurate analysis of the inter-relations between the different errors in each step of PM, resulting in previously unnoticed cancellations. We also prove that PM is numerically stable in finite-precision arithmetic. We believe our analysis will pave the way to providing accurate analysis of known algorithms for the super-resolution problem in full generality.

Physics‐Informed Convolutional Decoder (PICD): A Novel Approach for Direct Inversion of Heterogeneous Subsurface Flow

AbstractWe propose a physics‐informed convolutional decoder (PICD) framework for inverse modeling of heterogenous groundwater flow. PICD stands out as a direct inversion method, eliminating the need for repeated forward model simulations. The framework combines data‐driven and physics‐driven approaches by integrating monitoring data and domain knowledge into the inversion process. PICD utilizes a convolutional decoder to effectively approximate the spatial distribution of hydraulic heads, while Karhunen–Loève expansion (KLE) is employed to parameterize hydraulic conductivities. During the training process, the stochastic vector in KLE and the parameters of the convolutional decoder are adjusted simultaneously to minimize the data‐mismatch and the physical violation. The final optimized stochastic vectors correspond to the estimation of hydraulic conductivities, and the trained convolutional decoder can predict the evolution and distribution of hydraulic heads. Various scenarios of groundwater flow are examined and results demonstrate the framework's capability to accurately estimate heterogeneous hydraulic conductivities and to deliver satisfactory predictions of hydraulic heads, even with sparse measurements.

Mitigating Ill-posedness in Parameter Estimation under Sparse measurement for Linear time-varying systems employing Virtual Sensor Responses

Monitoring linear time-varying (LTV) systems using model-based approaches typically requires dense instrumentation and high-fidelity support models, resulting in significant computational and financial costs. Bayesian filtering-based methods adopt a joint state-parameter estimation approach for LTV system monitoring wherein states/parameters are observed as well as inferred from the measurements. Eventually, sparsity in measurement while dealing with high-fidelity models can aggravate the ill-posedness in the estimation diverging the estimation to impractical or no solutions. To enhance estimation resolution and precision, an alternative approach can be supporting estimation with virtual sensor measurements sampled from future time steps. Virtual measurements are in fact measurements sampled from a future time step relative to the time at which estimation is sought. To leverage virtual measurements, the estimation needs to be time-delayed, enabling the observation of states/parameters through measurements taken at both current and subsequent time steps, thereby alleviating the ill-posedness. This method has been explored for an LTV spring-mass-dashpot system, where the numerical investigation utilizes an interacting filtering environment to estimate states and parameters in the presence of sparse measurements. The study has shown how incorporating additional information can stabilize the estimation process, leading to improved estimates for both states and parameters.

Flow field reconstruction from sparse sensor measurements with physics-informed neural networks

In the realm of experimental fluid mechanics, accurately reconstructing high-resolution flow fields is notably challenging due to often sparse and incomplete data across time and space domains. This is exacerbated by the limitations of current experimental tools and methods, which leave critical areas without measurable data. This research suggests a feasible solution to this problem by employing an inverse physics-informed neural network (PINN) to merge available sparse data with physical laws. The method's efficacy is demonstrated using flow around a cylinder as a case study, with three distinct training sets. One was the sparse velocity data from a domain, and the other two datasets were limited velocity data obtained from the domain boundaries and sensors around the cylinder wall. The coefficient of determination (R2) coefficient and mean squared error (RMSE) metrics, indicative of model performance, have been determined for the velocity components of all models. For the 28 sensors model, the R2 value stands at 0.996 with an associated RMSE of 0.0251 for the u component, while for the v component, the R2 value registers at 0.969, accompanied by an RMSE of 0.0169. The outcomes indicate that the method can successfully recreate the actual velocity field with considerable precision with more than 28 sensors around the cylinder, highlighting PINN's potential as an effective data assimilation technique for experimental fluid mechanics.

NSVDNet: Normalized Spatial-Variant Diffusion Network for Robust Image-Guided Depth Completion

Depth images captured by low-cost three-dimensional (3D) cameras are subject to low spatial density, requiring depth completion to improve 3D imaging quality. Image-guided depth completion aims at predicting dense depth images from extremely sparse depth measurements captured by depth sensors with the guidance of aligned Red–Green–Blue (RGB) images. Recent approaches have achieved a remarkable improvement, but the performance will degrade severely due to the corruption in input sparse depth. To enhance robustness to input corruption, we propose a novel depth completion scheme based on a normalized spatial-variant diffusion network incorporating measurement uncertainty, which introduces the following contributions. First, we design a normalized spatial-variant diffusion (NSVD) scheme to apply spatially varying filters iteratively on the sparse depth conditioned on its certainty measure for excluding depth corruption in the diffusion. In addition, we integrate the NSVD module into the network design to enable end-to-end training of filter kernels and depth reliability, which further improves the structural detail preservation via the guidance of RGB semantic features. Furthermore, we apply the NSVD module hierarchically at multiple scales, which ensures global smoothness while preserving visually salient details. The experimental results validate the advantages of the proposed network over existing approaches with enhanced performance and noise robustness for depth completion in real-use scenarios.