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Stochastic First-Order Minimization Techniques Using Jensen Surrogates for X-Ray Transmission Tomography
Optimization and Control · Submitted 26 Oct 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Using measured data, we show that the stochastic variant we propose outperforms other algorithms, including the gradient descent counterparts.
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The abstract, sentence by sentence
Image reconstruction in X-ray transmission tomography has been an important research field for decades. In light of data volume increasing faster than processor speeds, one needs accelerated iterative algorithms to solve the optimization problem in the X-ray CT application. Incremental methods, in which a subset of data is being used at each iteration to accelerate the computations, have been getting more popular lately in the machine learning and mathematical optimization fields. The most popular member of this family of algorithms in the X-ray CT field is ordered-subsets. Even though it performs well in earlier iterations, the lack of convergence in later iterations is a known phenomenon. In this paper, we propose two incremental methods that use Jensen surrogates for the X-ray CT application, one stochastic and one ordered-subsets type. Using measured data, we show that the stochastic variant we propose outperforms other algorithms, including the gradient descent counterparts.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Image reconstruction in X-ray transmission tomography has been an important research field for decades. | background 1.00 | 0.03 | 0.01 | asserted 1.00 |
| s1 | In light of data volume increasing faster than processor speeds, one needs accelerated iterative algorithms to solve the optimization problem in the X-ray CT application. | background 0.90 | 0.06 | 0.02 | asserted 0.97 |
| s2 | Incremental methods, in which a subset of data is being used at each iteration to accelerate the computations, have been getting more popular lately in the machine learning and mathematical optimization fields. | background 1.00 | 0.04 | 0.02 | asserted 0.97 |
| s3 | The most popular member of this family of algorithms in the X-ray CT field is ordered-subsets. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s4 | Even though it performs well in earlier iterations, the lack of convergence in later iterations is a known phenomenon. | background 0.60 | 0.05 | 0.03 | asserted 1.00 |
| s5 | In this paper, we propose two incremental methods that use Jensen surrogates for the X-ray CT application, one stochastic and one ordered-subsets type. | contribution 0.99 | 0.92 | 0.11 | asserted 1.00 |
| s6 | Using measured data, we show that the stochastic variant we propose outperforms other algorithms, including the gradient descent counterparts. | result 1.00 | 0.96 | 0.84 | asserted 1.00 |
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The paper
Original abstract
Image reconstruction in X-ray transmission tomography has been an important research field for decades. In light of data volume increasing faster than processor speeds, one needs accelerated iterative algorithms to solve the optimization problem in the X-ray CT application. Incremental methods, in which a subset of data is being used at each iteration to accelerate the computations, have been getting more popular lately in the machine learning and mathematical optimization fields. The most popular member of this family of algorithms in the X-ray CT field is ordered-subsets. Even though it performs well in earlier iterations, the lack of convergence in later iterations is a known phenomenon. In this paper, we propose two incremental methods that use Jensen surrogates for the X-ray CT application, one stochastic and one ordered-subsets type. Using measured data, we show that the stochastic variant we propose outperforms other algorithms, including the gradient descent counterparts.
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