scholarly journals Scalable signal reconstruction for a broad range of applications

2021 ◽  
Vol 64 (2) ◽  
pp. 106-115
Author(s):  
Abolfazl Asudeh ◽  
Jees Augustine ◽  
Saravanan Thirumuruganathan ◽  
Azade Nazi ◽  
Nan Zhang ◽  
...  
Keyword(s):  
Traffic Engineering ◽  
Optimization Problem ◽  
Signal Reconstruction ◽  
Linear Equations ◽  
Synthetic Data ◽  
Scalable Algorithm ◽  
Underdetermined System ◽  
Medical Image Reconstruction ◽  
The Common ◽  
Similarity Joins

Signal reconstruction problem (SRP) is an important optimization problem where the objective is to identify a solution to an underdetermined system of linear equations that is closest to a given prior. It has a substantial number of applications in diverse areas, such as network traffic engineering, medical image reconstruction, acoustics, astronomy, and many more. Unfortunately, most of the common approaches for solving SRP do not scale to large problem sizes. We propose a novel and scalable algorithm for solving this critical problem. Specifically, we make four major contributions. First, we propose a dual formulation of the problem and develop the DIRECT algorithm that is significantly more efficient than the state of the art. Second, we show how adapting database techniques developed for scalable similarity joins provides a substantial speedup over DIRECT. Third, we describe several practical techniques that allow our algorithm to scale---on a single machine---to settings that are orders of magnitude larger than previously studied. Finally, we use the database techniques of materialization and reuse to extend our result to dynamic settings where the input to the SRP changes. Extensive experiments on real-world and synthetic data confirm the efficiency, effectiveness, and scalability of our proposal.

scholarly journals Linear Program Relaxation of Sparse Nonnegative Recovery in Compressive Sensing Microarrays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Linxia Qin ◽  
Naihua Xiu ◽  
Lingchen Kong ◽  
Yu Li
Keyword(s):  
Compressive Sensing ◽  
Unique Solution ◽  
Linear Equations ◽  
Group Testing ◽  
Extreme Points ◽  
System Of Linear Equations ◽  
Underdetermined System ◽  
The Common ◽  
Property Condition ◽  
Sparsest Solutions

Compressive sensing microarrays (CSM) are DNA-based sensors that operate using group testing and compressive sensing principles. Mathematically, one can cast the CSM as sparse nonnegative recovery (SNR) which is to find the sparsest solutions subjected to an underdetermined system of linear equations and nonnegative restriction. In this paper, we discuss thel1relaxation of the SNR. By defining nonnegative restricted isometry/orthogonality constants, we give a nonnegative restricted property condition which guarantees that the SNR and thel1relaxation share the common unique solution. Besides, we show that any solution to the SNR must be one of the extreme points of the underlying feasible set.

scholarly journals Introducing a Conditional Ghost Correction Into the Vector Method

1984 ◽  
Vol 6 (2) ◽  
pp. 117-123 ◽  
Author(s):  
H. Schaeben
Keyword(s):  
Mathematical Model ◽  
Quadratic Programming ◽  
Optimization Problem ◽  
Linear Equations ◽  
Singular System ◽  
Orientation Distribution ◽  
Mathematical Approach ◽  
System Of Linear Equations ◽  
Vector Method ◽  
The Mathematical Model

The concept of conditional ghost correction is introduced into the vector method of quantitative texture analysis. The mathematical model actually chosen here reduces the texture problem to one of quadratic programming. Thus, a well defined optimization problem has to be solved, the singular system of linear equations governing the correspondence between pole and orientation distribution being reduced to a set of equality constraints of the restated texture problem. This new mathematical approach in terms of the vector method reveals the modeling character of the solution of the texture problem provided by the vector method completely.

scholarly journals Parameterized Nonlinear Least Squares for Unsupervised Nonlinear Spectral Unmixing

2019 ◽  
Vol 11 (2) ◽  
pp. 148 ◽  
Author(s):  
Risheng Huang ◽  
Xiaorun Li ◽  
Haiqiang Lu ◽  
Jing Li ◽  
Liaoying Zhao
Keyword(s):  
Least Squares ◽  
Optimization Problem ◽  
Nonnegative Matrix Factorization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Nonlinear Least Squares ◽  
Hyperspectral Data ◽  
Spectral Unmixing

This paper presents a new parameterized nonlinear least squares (PNLS) algorithm for unsupervised nonlinear spectral unmixing (UNSU). The PNLS-based algorithms transform the original optimization problem with respect to the endmembers, abundances, and nonlinearity coefficients estimation into separate alternate parameterized nonlinear least squares problems. Owing to the Sigmoid parameterization, the PNLS-based algorithms are able to thoroughly relax the additional nonnegative constraint and the nonnegative constraint in the original optimization problems, which facilitates finding a solution to the optimization problems . Subsequently, we propose to solve the PNLS problems based on the Gauss–Newton method. Compared to the existing nonnegative matrix factorization (NMF)-based algorithms for UNSU, the well-designed PNLS-based algorithms have faster convergence speed and better unmixing accuracy. To verify the performance of the proposed algorithms, the PNLS-based algorithms and other state-of-the-art algorithms are applied to synthetic data generated by the Fan model and the generalized bilinear model (GBM), as well as real hyperspectral data. The results demonstrate the superiority of the PNLS-based algorithms.

Euclid and the art of wavelet estimation, Part II: Robust algorithm and field‐data examples

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1939-1946 ◽  
Author(s):  
Eike Rietsch
Keyword(s):  
Field Data ◽  
Synthetic Data ◽  
Noise Resistance ◽  
Zero Eigenvalue ◽  
Seismic Line ◽  
Robust Algorithm ◽  
Seismic Wavelet ◽  
Time Zones ◽  
The Common ◽  
Common Signal

In this second part of a two‐part work, a more robust algorithm is derived and used for the estimation of the seismic wavelet as the common signal of two or more seismic traces. It is based on the properties of the eigenvectors with zero eigenvalue of a matrix derived in the first part, whose elements are the samples of the autocorrelation functions and crosscorrelation functions of these seismic traces for a number of lags. The noise resistance of this algorithm is illustrated by means of a synthetic‐data example and then demonstrated on field data. In one field‐data example, the so‐called Euclid wavelet is compared with one derived deterministically by means of an impedance log. The other example relates three quite different Euclid wavelets determined in three different time zones on a seismic line to one another by showing that their differences can be explained by absorption.

Feasibility of approximate broadband estimation of acoustic impedance profile from first principles and band-limited reflection data

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. R57-R74 ◽  
Author(s):  
Santi Kumar Ghosh ◽  
Animesh Mandal
Keyword(s):  
First Principles ◽  
Acoustic Impedance ◽  
Linear Equations ◽  
Synthetic Data ◽  
Reflection Coefficients ◽  
Limited Data ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Impedance Profile ◽  
Band Limited

Because seismic reflection data are band limited, acoustic impedance profiles derived from them are nonunique. The conventional inversion methods counter the nonuniqueness either by stabilizing the answer with respect to an initial model or by imposing mathematical constraints such as sparsity of the reflection coefficients. By making a nominal assumption of an earth model locally consisting of a stack of homogeneous and horizontal layers, we have formulated a set of linear equations in which the reflection coefficients are the unknowns and the recursively integrated seismic trace constitute the data. Drawing only on first principles, the Zoeppritz equation in this case, the approach makes a frontal assault on the problem of reconstructing reflection coefficients from band-limited data. The local layer-cake assumption and the strategy of seeking a singular value decomposition solution of the linear equations counter the nonuniqueness, provided that the objective is to reconstruct a smooth version of the impedance profile that includes only its crude structures. Tests on synthetic data generated from elementary models and from measured logs of acoustic impedance demonstrated the efficacy of the method, even when a significant amount of noise was added to the data. The emergence of consistent estimates of impedance, approximating the original impedance, from synthetic data generated for several frequency bands has inspired our confidence in the method. The other attractive outputs of the method are as follows: (1) an accurate estimate of the impedance mean, (2) an accurate reconstruction of the direct-current (DC) frequency of the reflectivity, and (3) an acceptable reconstruction of the broad outline of the original impedance profile. These outputs can serve as constraints for either more refined inversions or geologic interpretations. Beginning from the restriction of band-limited data, we have devised a method that neither requires a starting input model nor imposes mathematical constraints on the earth reflectivity and still yielded significant and relevant geologic information.

scholarly journals AN ENERGY-BASED APPROACH FOR DETECTION AND CHARACTERIZATION OF SUBTLE ENTITIES WITHIN LASER SCANNING POINT-CLOUDS

2016 ◽  
Vol XLI-B3 ◽  
pp. 167-171
Author(s):  
Reuma Arav ◽  
Sagi Filin
Keyword(s):  
Laser Scanning ◽  
Optimization Problem ◽  
Point Clouds ◽  
Urban Environments ◽  
Natural Environments ◽  
Detection Scheme ◽  
Airborne Laser ◽  
The Common ◽  
Geomorphological Features

Airborne laser scans present an optimal tool to describe geomorphological features in natural environments. However, a challenge arises in the detection of such phenomena, as they are embedded in the topography, tend to blend into their surroundings and leave only a subtle signature within the data. Most object-recognition studies address mainly urban environments and follow a general pipeline where the data are partitioned into segments with uniform properties. These approaches are restricted to man-made domain and are capable to handle limited features that answer a well-defined geometric form. As natural environments present a more complex set of features, the common interpretation of the data is still manual at large. In this paper, we propose a data-aware detection scheme, unbound to specific domains or shapes. We define the recognition question as an energy optimization problem, solved by variational means. Our approach, based on the level-set method, characterizes geometrically local surfaces within the data, and uses these characteristics as potential field for minimization. The main advantage here is that it allows topological changes of the evolving curves, such as merging and breaking. We demonstrate the proposed methodology on the detection of collapse sinkholes.

scholarly journals Estimation of the Relative Arrival Time of Microseismic Events Based on Phase-Only Correlation

Energies ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2527 ◽  
Author(s):  
Peng Wang ◽  
Xu Chang ◽  
Xiyan Zhou
Keyword(s):  
Arrival Time ◽  
Linear Equations ◽  
Time Lag ◽  
Synthetic Data ◽  
Information Criterion ◽  
Peak Position ◽  
Arrival Times ◽  
Time Frequency ◽  
Microseismic Events ◽  
Microseismic Event

The arrival time of a microseismic event is an important piece of information for microseismic monitoring. The accuracy and efficiency of arrival time identification is affected by many factors, such as the low signal-to-noise ratio (SNR) of the records, the vast amount of real-time monitoring records, and the abnormal situations of monitoring equipment. In order to eliminate the interference of these factors, we propose a method based on phase-only correlation (POC) to estimate the relative arrival times of microseismic events. The proposed method includes three main steps: (1) The SNR of the records is improved via time-frequency transform, which is used to obtain the time-frequency representation of each trace of a microseismic event. (2) The POC functions of all pairs of time-frequency representations are calculated. The peak value of the POC function indicates the similarity of the traces, and the peak position in the time lag axis indicates the relative arrival times between the traces. (3) Using the peak values as weighting coefficients of the linear equations, consistency processing is used to exclude any abnormal situations and obtain the optimal relative arrival times. We used synthetic data and field data to validate the proposed method. Comparing with Akaike information criterion (AIC) and cross-correlation, the proposed method is more robust at estimating the relative arrival time and excluding the influence of abnormal situations.

scholarly journals On Randomized Sampling Kaczmarz Method with Application in Compressed Sensing

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Mei-Lan Sun ◽  
Chuan-Qing Gu ◽  
Peng-Fei Tang
Keyword(s):  
Compressed Sensing ◽  
Signal Reconstruction ◽  
Linear Equations ◽  
Residual Vector ◽  
Randomized Sampling ◽  
Kaczmarz Algorithm ◽  
Systems Of Linear Equations ◽  
Large Systems ◽  
Kaczmarz Method ◽  
Control Criterion

We propose a randomized sampling Kaczmarz algorithm for the solution of very large systems of linear equations by introducing a maximal sampling probability control criterion, which is aimed at grasping the largest entry of the absolute sampling residual vector at each iteration. This new method differs from the greedy randomized Kaczmarz algorithm, which needs not to compute the residual vector of the whole linear system to determine the working rows. Numerical experiments show that the proposed algorithm has the most significant effect when the selected row number, i.e, the size of samples, is equal to the logarithm of all rows. Finally, we extend the randomized sampling Kaczmarz to signal reconstruction problems in compressed sensing. Signal experiments show that the new extended algorithm is more effective than the randomized sparse Kaczmarz method for online compressed sensing.

scholarly journals Tree-Based Backtracking Orthogonal Matching Pursuit for Sparse Signal Reconstruction

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yigang Cen ◽  
Fangfei Wang ◽  
Ruizhen Zhao ◽  
Lihong Cui ◽  
Lihui Cen ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Optimization Problem ◽  
Selection Process ◽  
Matching Pursuit ◽  
Signal Reconstruction ◽  
Search Space ◽  
Orthogonal Matching Pursuit ◽  
Superior Performance ◽  
Sparse Signal ◽  
Tree Model

Compressed sensing (CS) is a theory which exploits the sparsity characteristic of the original signal in signal sampling and coding. By solving an optimization problem, the original sparse signal can be reconstructed accurately. In this paper, a new Tree-based Backtracking Orthogonal Matching Pursuit (TBOMP) algorithm is presented with the idea of the tree model in wavelet domain. The algorithm can convert the wavelet tree structure to the corresponding relations of candidate atoms without any prior information of signal sparsity. Thus, the atom selection process will be more structural and the search space can be narrowed. Moreover, according to the backtracking process, the previous chosen atoms’ reliability can be detected and the unreliable atoms can be deleted at each iteration, which leads to an accurate reconstruction of the signal ultimately. Compared with other compressed sensing algorithms, simulation results show the proposed algorithm’s superior performance to that of several other OMP-type algorithms.

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