scholarly journals Near-Optimal Compressed Sensing Guarantees for Total Variation Minimization

2013 ◽  
Vol 22 (10) ◽  
pp. 3941-3949 ◽  
Author(s):  
Deanna Needell ◽  
Rachel Ward
Keyword(s):  
Compressed Sensing ◽  
Total Variation ◽  
Total Variation Minimization

scholarly journals Optimization of STEM‐HAADF Electron Tomography Reconstructions by Parameter Selection in Compressed Sensing Total Variation Minimization‐Based Algorithms

2020 ◽  
Vol 37 (6) ◽  
pp. 2000070
Author(s):  
Juan M. Muñoz‐Ocaña ◽  
Ainouna Bouziane ◽  
Farzeen Sakina ◽  
Richard T. Baker ◽  
Ana B. Hungría ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Total Variation ◽  
Electron Tomography ◽  
Parameter Selection ◽  
Total Variation Minimization

scholarly journals A General Total Variation Minimization Theorem for Compressed Sensing Based Interior Tomography

2009 ◽  
Vol 2009 ◽  
pp. 1-3 ◽  
Author(s):  
Weimin Han ◽  
Hengyong Yu ◽  
Ge Wang
Keyword(s):  
Compressed Sensing ◽  
Total Variation ◽  
General Theorem ◽  
Region Of Interest ◽  
Delta Function ◽  
Piecewise Constant Function ◽  
Mathematical Tool ◽  
Total Variation Minimization ◽  
Piecewise Constant ◽  
Dirac Delta

Recently, in the compressed sensing framework we found that a two-dimensional interior region-of-interest (ROI) can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant (Yu and Wang, 2009). Here we present a general theorem charactering a minimization property for a piecewise constant function defined on a domain in any dimension. Our major mathematical tool to prove this result is functional analysis without involving the Dirac delta function, which was heuristically used by Yu and Wang (2009).

scholarly journals Removing Stripes, Scratches, and Curtaining with Nonrecoverable Compressed Sensing

2019 ◽  
Vol 25 (3) ◽  
pp. 705-710 ◽  
Author(s):  
Jonathan Schwartz ◽  
Yi Jiang ◽  
Yongjie Wang ◽  
Anthony Aiello ◽  
Pallab Bhattacharya ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Total Variation ◽  
Image Artifacts ◽  
Fourier Space ◽  
Beam Instability ◽  
Signal To Noise ◽  
Total Variation Minimization ◽  
Primary Direction ◽  
Directional Image

AbstractHighly-directional image artifacts such as ion mill curtaining, mechanical scratches, or image striping from beam instability degrade the interpretability of micrographs. These unwanted, aperiodic features extend the image along a primary direction and occupy a small wedge of information in Fourier space. Deleting this wedge of data replaces stripes, scratches, or curtaining, with more complex streaking and blurring artifacts—known within the tomography community as “missing wedge” artifacts. Here, we overcome this problem by recovering the missing region using total variation minimization, which leverages image sparsity-based reconstruction techniques—colloquially referred to as compressed sensing (CS)—to reliably restore images corrupted by stripe-like features. Our approach removes beam instability, ion mill curtaining, mechanical scratches, or any stripe features and remains robust at low signal-to-noise. The success of this approach is achieved by exploiting CS's inability to recover directional structures that are highly localized and missing in Fourier Space.

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