Compressed Sensing Based Interior Tomography

By Hengyong Yu, Ge Wang. Physics in Medicine and Biology, 2009

592 citations recorded by the source corpus.

While conventional wisdom is that the interior problem does not have a unique solution, by analytic continuation we recently showed that the interior problem can be uniquely and stably solved if we have a known sub-region inside a region of interest (ROI). However, such a known sub-region is not always readily available, and it is even impossible to find in some cases. Based on compressed sensing theory, here we prove that if an object under reconstruction is essentially piecewise constant, a local ROI can be exactly and stably reconstructed via the total variation minimization. Because many objects in computed tomography (CT) applications can be approximately modeled as piecewise constant, our approach is practically useful and suggests a new research direction for interior tomography. To illustrate the merits of our finding, we develop an iterative interior reconstruction algorithm that minimizes the total variation of a reconstructed image and evaluate the performance in numerical simulation.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/a0cb0baf2d663202cc2c39b3e3a344000d12393e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Ge Wang
2. Guang-Hong Chen
3. Jie Tang
4. Brian Nett
5. Xin Jin
6. Liang Li
7. Zhiqiang Chen
8. Jesse Railo

In Computer Vision and Pattern Recognition

1. Guang-Hong Chen
2. Jie Tang
3. Brian Nett
4. Xin Jin
5. Liang Li
6. Zhiqiang Chen
7. Ge Wang

In Radiology, Nuclear Medicine and Imaging

1. Xin Jin
2. Liang Li
3. Zhiqiang Chen
4. Ge Wang
5. Jie Tang
6. Brian Nett
7. Guang-Hong Chen
8. Hengyong Yu

Citations in the corpus

• Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms (2009, methodology): “The second feature is that iterative methods are more forgiving for data truncation at a given view angle and / or view truncation as in limited view angle problems (e.g. tomosynthesis imaging) (Persson et al 2001, Li et al 2002, Kolehmainen et al 2003, Yu and Wang 2009).”
• Low-Dose X-ray CT Reconstruction via Dictionary Learning (2012, unknown): “Yu andWang proved that a piecewise constant interior region of interest (ROI ) can be uniquely reconstructed by a TV minimizing technique [15], [16].”
• Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems (2020, background): “nd the values of f in an arbitrarily small open set inside the ROI, then f is uniquely determined everywhere [12, 40]. For practical applications of ROI tomography in medical imaging, see for example [82, 83]. See also [43, 60, 61] for a discussion of the diculties of obtaining stable reconstruction”
• A limited-angle CT reconstruction method based on anisotropic TV minimization (2013, methodology): “…2009, Bian et al 2010), PICCS (Chen et al 2008, 2009, Tang et al 2009), simultaneous algebraic reconstruction technique (SART) with TV (SART + TV) (Yu and Wang 2009), soft-thresholding algorithms (Yu and Wang 2010, Xu et al 2011), iTV (Ritschl et al 2011) and split-Bregman reconstruction…”
• CT artifacts: Causes and reduction techniques (2012, unknown): “There is still a small error at the edge of the field of view, which can be reduced using more sophisticated methods [38, 39], or by scanning a slightly larger field of view.”
• RODEO: Robust DE-aliasing autoencOder for real-time medical image reconstruction (2017, unknown): “CS exploits the sparsity of the image in order to reconstruct it from lower number of sinogram samples than was deemed necessary previously [35-37].”