I was recently talking to both
Dick Gordon, one of the person who devised the ART algorithm and
Ramesh Raskar in different discussions on fast algorithms, hardware and compressive sensing and the following occurred to me. We have
Xiaochuan Pan,
Emil Sidky and
Michael Vannier making the case in
Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction? that faster algorithms cannot seem to be adopted by the larger CT engineering community. It seems to me that while dose reduction might be a selling point for changing this status-quo
as advocated by Dick, the other argument might come from the fact that not much is known with regards to actual guarantees of convergence of the ART, SART,.... algorithm. However, I personally think that the real reason you have not seen faster algorithms taking over
large sections of the CT world, stems from the fact that the faster algorithms do not require a
change in hardware configuration. This might seem a little counter intuitive but when you change the hardware configuration, you change many processes at the engineering level that necessarily enable new type of thinking. In the meantime, after
reading this paper on
SART-type Image Reconstruction from a Limited Number of Projections with the Sparisity Constraint by
Hengyong Yu and
Ge Wang a while back I just came across this new paper on the convergence of the ART and related algorithms:
Convergence Analysis of SART by Bregman Iteration and Dual Gradient Descent by
Ming Yan. The abstract reads:
In this paper, we provide two approaches to prove the convergence of simultaneous algebraic reconstruction technique (SART): linearized Bregman iteration and dual gradient descent. These proofs can be applied to other Landweber-like schemes such as Cimmino's algorithm and component averaging (CAV). The numerical experiments of these three algorithms are provided to demonstrate the convergence results. In addition, conjugate gradient method based on dual problem is utilized to compare with SART.
I was recently talking to both Dick Gordon, one of the person who devised the ART algorithm and Ramesh Raskar in different discussions on fast algorithms, hardware and compressive sensing and the following occurred to me. We have Xiaochuan Pan, Emil Sidky and Michael Vannier making the case in Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction? that faster algorithms cannot seem to be adopted by the larger CT engineering community. It seems to me that while dose reduction might be a selling point for changing this status-quo as advocated by Dick, the other argument might come from the fact that not much is known with regards to actual guarantees of convergence of the ART, SART,.... algorithm. However, I personally think that the real reason you have not seen faster algorithms taking over large sections of the CT world, stems from the fact that the faster algorithms do not require a change in hardware configuration. This might seem a little counter intuitive but when you change the hardware configuration, you change many processes at the engineering level that necessarily enable new type of thinking. In the meantime, after reading this paper on SART-type Image Reconstruction from a Limited Number of Projections with the Sparisity Constraint by Hengyong Yu and Ge Wang a while back I just came across this new paper on the convergence of the ART and related algorithms: Convergence Analysis of SART by Bregman Iteration and Dual Gradient Descent by Ming Yan. The abstract reads:
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