Novel Iterative Truncated Total Least Squares Algorithm for Image Restoration

2013 ◽  
Vol 401-403 ◽  
pp. 1397-1400
Author(s):  
Lei Zhang ◽  
Yue Yun Cao ◽  
Zi Chun Yang
Keyword(s):  
Image Restoration ◽  
Least Squares ◽  
Large Scale ◽  
Total Least Squares ◽  
System Matrix ◽  
Scale Problem ◽  
Truncation Parameter ◽  
Lanczos Bidiagonalization ◽  
Ill Posed ◽  
Truncated Total Least Squares

Image restoration is a typical ill-posed inverse problem, which can be solved by a successful total least squares (TLS) method when not only the observation but the system matrix is also contaminated by addition noise. Considering the image restoration is a large-scale problem in general, project the TLS problem onto a subspace defined by a Lanczos bidiagonalization algorithm, and then the Truncated TLS method is applied on the subspace. Therefore, a novel iterative TTLS method, involving appropriate the choice of truncation parameter, is proposed. Finally, an Image reconstruction example is given to illustrate the effectiveness and robustness of proposed algorithm.

Regularized constrained total least squares image restoration

1995 ◽  
Vol 4 (8) ◽  
pp. 1096-1108 ◽  
Author(s):  
V.Z. Mesarovic ◽  
N.P. Galatsanos ◽  
A.K. Katsaggelos
Keyword(s):  
Image Restoration ◽  
Least Squares ◽  
Total Least Squares

scholarly journals Reply to “Comments on ‘Erroneous Model Field Representations in Multiple Pseudoproxy Studies: Corrections and Implications’”*

2013 ◽  
Vol 26 (10) ◽  
pp. 3485-3486 ◽  
Author(s):  
Jason E. Smerdon ◽  
Alexey Kaplan ◽  
Daniel E. Amrhein
Keyword(s):  
Least Squares ◽  
Northern Hemisphere ◽  
Expectation Maximization ◽  
Strong Influence ◽  
Total Least Squares ◽  
Model Field ◽  
Spatial Skill ◽  
Spatial Performance ◽  
Quantitative Results ◽  
Truncated Total Least Squares

Abstract The commenters confirm the errors identified and discussed in Smerdon et al., which either invalidated or required the reinterpretation of quantitative results from pseudoproxy experiments presented or used in several earlier papers. These errors have a strong influence on the spatial skill assessments of climate field reconstructions (CFRs), despite their small impacts on skill statistics averaged over the Northern Hemisphere. On the basis of spatial performance and contrary to the claim by the commenters, the Regularized Expectation Maximization method using truncated total least squares (RegEM-TTLS) cannot be considered a preferred CFR technique. Moreover, distinctions between CFR methods in the context of the discussion in the original paper are immaterial. Continued investigations using accurately described and faithfully executed pseudoproxy experiments are critical for further evaluation and improvement of CFR methods.

scholarly journals Bayesian Image Restoration Using a Large-Scale Total Patch Variation Prior

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Yang Chen ◽  
Weimin Yu ◽  
Yinsheng Li ◽  
Zhou Yang ◽  
Limin Luo ◽  
...  
Keyword(s):  
Image Restoration ◽  
Large Scale ◽  
Computational Cost ◽  
Real Data ◽  
Inverse Image ◽  
Edge Preserving ◽  
Device Architecture ◽  
Mixture Prior ◽  
Ill Posed ◽  
Improved Performance

Edge-preserving Bayesian restorations using nonquadratic priors are often inefficient in restoring continuous variations and tend to produce block artifacts around edges in ill-posed inverse image restorations. To overcome this, we have proposed a spatial adaptive (SA) prior with improved performance. However, this SA prior restoration suffers from high computational cost and the unguaranteed convergence problem. Concerning these issues, this paper proposes a Large-scale Total Patch Variation (LS-TPV) Prior model for Bayesian image restoration. In this model, the prior for each pixel is defined as a singleton conditional probability, which is in a mixture prior form of one patch similarity prior and one weight entropy prior. A joint MAP estimation is thus built to ensure the iteration monotonicity. The intensive calculation of patch distances is greatly alleviated by the parallelization of Compute Unified Device Architecture(CUDA). Experiments with both simulated and real data validate the good performance of the proposed restoration.

Total Variation Structured Total Least Squares Method for Image Restoration

2013 ◽  
Vol 35 (6) ◽  
pp. B1304-B1320 ◽  
Author(s):  
Xi-Le Zhao ◽  
Wei Wang ◽  
Tie-Yong Zeng ◽  
Ting-Zhu Huang ◽  
Michael K. Ng
Keyword(s):  
Image Restoration ◽  
Least Squares ◽  
Total Variation ◽  
Least Squares Method ◽  
Total Least Squares ◽  
Structured Total Least Squares
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