A method for structured linear total least norm on blind deconvolution problem

2005 ◽  
Vol 19 (1-2) ◽  
pp. 151-164 ◽  
Author(s):  
SeYoung Oh ◽  
SunJoo Kwon ◽  
Jae Heon Yun
Keyword(s):  
Blind Deconvolution ◽  
Deconvolution Problem ◽  
Total Least Norm

scholarly journals Multichannel blind deconvolution of seismic signals

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2093-2107 ◽  
Author(s):  
Kjetil F. Kaaresen ◽  
Tofinn Taxt
Keyword(s):  
Blind Deconvolution ◽  
A Priori ◽  
Optimization Method ◽  
Earth Model ◽  
Moderate Increase ◽  
Wavelet Estimation ◽  
A Posteriori Estimate ◽  
Least Squares Fit ◽  
Deconvolution Problem ◽  
Priori Information

A new algorithm for simultaneous wavelet estimation and deconvolution of seismic reflection signals is given. To remove the inherent ambiguity in this blind deconvolution problem, we introduce relevant a priori information. Our major assumption is sparseness of the reflectivity, which corresponds to a layered‐earth model. This allows nonminimum‐phase wavelets to be recovered reliably and closely spaced reflectors to be resolved. To combine a priori knowledge and data, we use a Bayesian framework and derive a maximum a posteriori estimate. Computing this estimate is a difficult optimization problem solved by a suboptimal iterative procedure. The procedure alternates steps of wavelet estimation and reflectivity estimation. The first step only requires a simple least‐squares fit, while the second step is solved by the iterated window maximization algorithm proposed by Kaaresen. This enables better efficiency and optimality than established alternatives. The resulting optimization method can easily handle multichannel models with only a moderate increase of the computational load. Lateral continuity of the reflectors is achieved by modeling local dependencies between neighboring traces. Major improvements in both wavelet and reflectivity estimates are obtained by taking the wavelet to be invariant across several traces. The practicality of the algorithm is demonstrated on synthetic and real seismic data. An application to multivariate well‐log segmentation is also given.

scholarly journals Phase retrieval of low-rank matrices by anchored regression

2020 ◽  
Author(s):  
Kiryung Lee ◽  
Sohail Bahmani ◽  
Yonina C Eldar ◽  
Justin Romberg
Keyword(s):  
Phase Retrieval ◽  
Blind Deconvolution ◽  
Accurate Estimate ◽  
Optimal Number ◽  
Low Rank ◽  
Partial Result ◽  
Linear Measurements ◽  
Target Matrix ◽  
Deconvolution Problem ◽  
General Rank

Abstract We study the low-rank phase retrieval problem, where our goal is to recover a $d_1\times d_2$ low-rank matrix from a series of phaseless linear measurements. This is a fourth-order inverse problem, as we are trying to recover factors of a matrix that have been observed, indirectly, through some quadratic measurements. We propose a solution to this problem using the recently introduced technique of anchored regression. This approach uses two different types of convex relaxations: we replace the quadratic equality constraints for the phaseless measurements by a search over a polytope and enforce the rank constraint through nuclear norm regularization. The result is a convex program in the space of $d_1 \times d_2$ matrices. We analyze two specific scenarios. In the first, the target matrix is rank-$1$, and the observations are structured to correspond to a phaseless blind deconvolution. In the second, the target matrix has general rank, and we observe the magnitudes of the inner products against a series of independent Gaussian random matrices. In each of these problems, we show that anchored regression returns an accurate estimate from a near-optimal number of measurements given that we have access to an anchor matrix of sufficient quality. We also show how to create such an anchor in the phaseless blind deconvolution problem from an optimal number of measurements and present a partial result in this direction for the general rank problem.

scholarly journals On Sequential Learning for Parameter Estimation in Particle Algorithms for State-Space Models

2016 ◽  
Vol 6 (1) ◽  
pp. 13
Author(s):  
Chunlin Ji
Keyword(s):  
State Space ◽  
Blind Deconvolution ◽  
State Space Model ◽  
The State ◽  
State Space Models ◽  
Sequential Learning ◽  
Model Parameters ◽  
Learning Method ◽  
Space Model ◽  
Deconvolution Problem

Particle methods, also known as Sequential Monte Carlo, have been ubiquitous for Bayesian inference for state-space models, particulary when dealing with nonlinear non-Gaussian scenarios. However, in many practical situations, the state-space model contains unknown model parameters that need to be estimated simultaneously with the state. In this paper, We discuss a sequential analysis for combined parameter and state estimation. An online learning method is proposed to approach the distribution of the model parameter by tuning a flexible proposal mixture distribution to minimize their Kullback-Leibler divergence. We derive the sequential learning method by using a truncated Dirichlet processes normal mixture and present a general algorithm under a framework of the auxiliary particle filtering. The proposed algorithm is verified in a blind deconvolution problem, which is a typical state-space model with unknown model parameters. Furthermore, in a more challenging application that we call meta-modulation, which is a more complex blind deconvolution problem with sophisticated system evolution equations, the proposed method performs satisfactorily and achieves an exciting result for high efficiency communication.

Projection-based approach to the blind deconvolution problem

1993 ◽  
Author(s):  
Yongyi Yang ◽  
Henry Stark ◽  
Nikolas P. Galatsanos
Keyword(s):  
Blind Deconvolution ◽  
Deconvolution Problem

scholarly journals Regularized Deblurring using Directional Prior with Sparse Representation

2019 ◽  
Vol 9 (1S3) ◽  
pp. 206-210
Keyword(s):  
Optimization Problem ◽  
Blind Deconvolution ◽  
Augmented Lagrangian Method ◽  
Real Data ◽  
Performance Comparison ◽  
Simultaneous Estimation ◽  
Deconvolution Problem ◽  
Ill Posed ◽  
Regularized Optimization ◽  
Well Posed

Blind deconvolution defined as simultaneous estimation and removal of blur is an ill-posed problem that can be solved with well-posed priors. In this paper we focus on directional edge prior based on orientation of gradients. Then the deconvolution problem is modeled as L2-regularized optimization problem which seeks a solution through constraint optimization. The constrained optimization problem is done in frequency domain with an Augmented Lagrangian Method (ALM). The proposed algorithm is tested on various synthetic as well as real data taken from various sources and the performance comparison is carried out with other state of the art existing methods.

scholarly journals Adaptive Operator-Based Spectral Deconvolution With the Levenberg-Marquardt Algorithm

2019 ◽  
Vol 10 (3) ◽  
pp. 242-253 ◽  
Author(s):  
Chan Huang ◽  
Feinan Chen ◽  
Yuyang Chang ◽  
Lin Han ◽  
Shuang Li ◽  
...  
Keyword(s):  
Noise Suppression ◽  
Blind Deconvolution ◽  
Light Emitting Diode ◽  
Spectral Deconvolution ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Deconvolution Problem ◽  
Different Color ◽  
Restoration Method ◽  
Mean Square Errors

AbstractSpectral distortion often occurs in spectral data due to the influence of the bandpass function of the spectrometer. Spectral deconvolution is an effective restoration method to solve this problem. Based on the theory of the maximum posteriori estimation, this paper transforms the spectral deconvolution problem into a multi-parameter optimization problem, and a novel spectral deconvolution method is proposed on the basis of Levenberg-Marquardt algorithm. Furthermore, a spectral adaptive operator is added to the method, which improves the effect of the regularization term. The proposed methods, Richardson-Lucy (R-L) method and Huber-Markov spectroscopic semi-blind deconvolution (HMSBD) method, are employed to deconvolute the white light-emitting diode (LED) spectra with two different color temperatures, respectively. The correction errors, root mean square errors, noise suppression ability, and the computation speed of above methods are compared. The experimental results prove the superiority of the proposed algorithm.

Sign in / Sign up

Export Citation Format

Share Document