Band-limited extrapolation on the sphere for signal reconstruction in the presence of noise

2014 ◽  
Author(s):  
Yibeltal F. Alem ◽  
Zubair Khalid ◽  
Rodney A. Kennedy
Keyword(s):  
Signal Reconstruction ◽  
Band Limited

On Derivative Sampling From Image Blur for Reconstruction of Band-Limited Signals

2014 ◽  
Author(s):  
Jacopo Tani ◽  
Sandipan Mishra ◽  
John T. Wen
Keyword(s):  
Numerical Study ◽  
Signal Reconstruction ◽  
Sampling Theorem ◽  
Image Sensors ◽  
Blurred Image ◽  
Derivative Sampling ◽  
Time Averages ◽  
Image Blur ◽  
Band Limited ◽  
Exposure Windows

Image sensors are typically characterized by slow sampling rates, which limit their efficacy in signal reconstruction applications. Their integrative nature though produces image blur when the exposure window is long enough to capture relative motion of the observed object relative to the sensor. Image blur contains more information on the observed dynamics than the typically used centroids, i.e., time averages of the motion within the exposure window. Parameters characterizing the observed motion, such as the signal derivatives at specified sampling instants, can be used for signal reconstruction through the derivative sampling extension of the known sampling theorem. Using slow image based sensors as derivative samplers allows for reconstruction of faster signals, overcoming Nyquist limitations. In this manuscript, we present an algorithm to extract values of a signal and its derivatives from blurred image measurements at specified sampling instants, i.e. the center of the exposure windows, show its application in two signal reconstruction numerical examples and provide a numerical study on the sensitivity of the extracted values to significant problem parameters.

scholarly journals Reconstruction of Periodic Band Limited Signals from Non-Uniform Samples with Sub-Nyquist Sampling Rate

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6246
Author(s):  
Dongxiao Wang ◽  
Xiaoqin Liu ◽  
Xing Wu ◽  
Zhihai Wang
Keyword(s):  
Signal Reconstruction ◽  
Sampling Rate ◽  
Sampling Theorem ◽  
Drive System ◽  
Reconstruction Method ◽  
Robot Arm ◽  
Reconstructed Signal ◽  
Band Limited ◽  
Simulation Signal ◽  
Important State

Important state parameters, such as torque and angle obtained from the servo control and drive system, can reflect the operating condition of the equipment. However, there are two problems with the information obtained through the network from the control and drive system: the low sampling rate, which does not meet the sampling theorem and the nonuniformity of the sampling points. By combing equivalent sampling and nonuniform signal reconstruction theory, this paper proposes a reconstruction method for signal obtained from servo system in periodic reciprocating motion. Equivalent sampling combines the low rate and nonuniform samples from multiple periods into one single period, so that the equivalent sampling rate is far increased. Then, the nonuniform samples with high density are further resampled to meet the reconstruction conditions. This step can avoid the amplitude error in the reconstructed signal and increase the possibility of successful reconstruction. Finally, the reconstruction formula derived from basis theory is applied to recover the signal. This method has been successfully verified by the simulation signal of the robot swing process and the actual current signal collected on the robot arm testbed.

Joint inversion of seismic data for acoustic impedance

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 994-1004 ◽  
Author(s):  
Li‐Yun Fu
Keyword(s):  
Neural Network ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Joint Inversion ◽  
Signal Reconstruction ◽  
Optimal Estimation ◽  
Data Sets ◽  
Seismic Wavelet ◽  
Model Based ◽  
Band Limited

I propose a joint inversion scheme to integrate seismic data, well data, and geological knowledge for acoustic impedance estimation. I examine the problem of recovering acoustic impedance from band‐limited seismic data. Optimal estimation of impedance can be achieved by combined applications of model‐based and deconvolution‐based methods. I incorporate the Robinson seismic convolutional model (RSCM) into the Caianiello neural network for network mapping. The Caianiello neural network provides an efficient approach to decompose the seismic wavelet and its inverse. The joint inversion consists of four steps: (1) multistage seismic inverse wavelets (MSIW) extraction at the wells, (2) the deconvolution with MSIW for initial impedance estimation, (3) multistage seismic wavelets (MSW) extraction at the wells, and (4) the model‐based reconstruction of impedance with MSW for improving the initial impedance model. The Caianiello neural network offers two algorithms for the four‐step process: neural wavelet estimation and input signal reconstruction. The frequency‐domain implementation of the algorithms enables control of the inversion on different frequency scales and facilitates an understanding of reservoir behavior on different resolution scales. The test results show that, with well control, the joint inversion can significantly improve the spatial description of reservoirs in data sets involving complex continental deposits.

Method of estimation of hidden correlation of narrowband noise signals

2019 ◽  
pp. 34-39 ◽  
Author(s):  
E.I. Chernov ◽  
N.E. Sobolev ◽  
A.A. Bondarchuk ◽  
L.E. Aristarhova
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
New Technology ◽  
Digital Signal ◽  
Measuring Instruments ◽  
Central Frequency ◽  
Pearson Criterion ◽  
Useful Signal ◽  
Band Limited ◽  
Narrowband Noise

The concept of hidden correlation of noise signals is introduced. The existence of a hidden correlation between narrowband noise signals isolated simultaneously from broadband band-limited noise is theoretically proved. A method for estimating the latent correlation of narrowband noise signals has been developed and experimentally investigated. As a result of the experiment, where a time frag ent of band-limited noise, the basis of which is shot noise, is used as the studied signal, it is established: when applying the Pearson criterion, there is practically no correlation between the signal at the Central frequency and the sum of signals at mirror frequencies; when applying the proposed method for the analysis of the same signals, a strong hidden correlation is found. The proposed method is useful for researchers, engineers and metrologists engaged in digital signal processing, as well as developers of measuring instruments using a new technology for isolating a useful signal from noise – the method of mirror noise images.

Image Reconstruction with the Fourier Coefficients for Magnetic Induction Tomography

2020 ◽  
Vol 16 (2) ◽  
pp. 156-163
Author(s):  
Jingwen Wang ◽  
Xu Wang ◽  
Dan Yang ◽  
Kaiyang Wang
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Magnetic Induction ◽  
Fourier Coefficients ◽  
Signal Reconstruction ◽  
Reconstruction Algorithm ◽  
Reconstruction Method ◽  
Measurement Equation ◽  
Image Reconstruction Method ◽  
Magnetic Induction Tomography

Background: Image reconstruction of magnetic induction tomography (MIT) is a typical ill-posed inverse problem, which means that the measurements are always far from enough. Thus, MIT image reconstruction results using conventional algorithms such as linear back projection and Landweber often suffer from limitations such as low resolution and blurred edges. Methods: In this paper, based on the recent finite rate of innovation (FRI) framework, a novel image reconstruction method with MIT system is presented. Results: This is achieved through modeling and sampling the MIT signals in FRI framework, resulting in a few new measurements, namely, fourier coefficients. Because each new measurement contains all the pixel position and conductivity information of the dense phase medium, the illposed inverse problem can be improved, by rebuilding the MIT measurement equation with the measurement voltage and the new measurements. Finally, a sparsity-based signal reconstruction algorithm is presented to reconstruct the original MIT image signal, by solving this new measurement equation. Conclusion: Experiments show that the proposed method has better indicators such as image error and correlation coefficient. Therefore, it is a kind of MIT image reconstruction method with high accuracy.

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