Zhiwei Qiao, Gage Redler, Boris Epel, Howard Halpern
{"title":"A fully linearized ADMM algorithm for optimization based image reconstruction.","authors":"Zhiwei Qiao, Gage Redler, Boris Epel, Howard Halpern","doi":"10.3233/XST-240029","DOIUrl":null,"url":null,"abstract":"<p><strong>Background and objective: </strong>Optimization based image reconstruction algorithm is an advanced algorithm in medical imaging. However, the corresponding solving algorithm is challenging because the model is usually large-scale and non-smooth. This work aims to devise a simple and convergent solver for optimization model.</p><p><strong>Methods: </strong>The alternating direction method of multipliers (ADMM) algorithm is a simple and effective solver of the optimization model. However, there always exists a sub-problem that has not close-form solution. One may use gradient descent algorithm to solve this sub-problem, but the step-size selection via line search is time-consuming. Or, one may use fast Fourier transform (FFT) to get a close-form solution if the sparse transform matrix is of special structure. In this work, we propose a fully linearized ADMM (FL-ADMM) algorithm that avoids line search to determine step-size and applies to sparse transform of any structure.</p><p><strong>Results: </strong>We derive the FL-ADMM algorithm instances for three total variation (TV) models in 2D computed tomography (CT). Further, we validate and evaluate one FL-ADMM algorithm and explore how two important factors impact convergence rate. These studies show that the FL-ADMM algorithm may accurately solve the optimization model.</p><p><strong>Conclusion: </strong>The FL-ADMM algorithm is a simple, effective, convergent and universal solver of optimization model in image reconstruction. Compared to the standard ADMM algorithm, the new algorithm does not need time-consuming step-size line-search or special demand to sparse transform. It is a rapid prototyping tool for optimization based image reconstruction.</p>","PeriodicalId":49948,"journal":{"name":"Journal of X-Ray Science and Technology","volume":" ","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of X-Ray Science and Technology","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.3233/XST-240029","RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"INSTRUMENTS & INSTRUMENTATION","Score":null,"Total":0}
引用次数: 0
Abstract
Background and objective: Optimization based image reconstruction algorithm is an advanced algorithm in medical imaging. However, the corresponding solving algorithm is challenging because the model is usually large-scale and non-smooth. This work aims to devise a simple and convergent solver for optimization model.
Methods: The alternating direction method of multipliers (ADMM) algorithm is a simple and effective solver of the optimization model. However, there always exists a sub-problem that has not close-form solution. One may use gradient descent algorithm to solve this sub-problem, but the step-size selection via line search is time-consuming. Or, one may use fast Fourier transform (FFT) to get a close-form solution if the sparse transform matrix is of special structure. In this work, we propose a fully linearized ADMM (FL-ADMM) algorithm that avoids line search to determine step-size and applies to sparse transform of any structure.
Results: We derive the FL-ADMM algorithm instances for three total variation (TV) models in 2D computed tomography (CT). Further, we validate and evaluate one FL-ADMM algorithm and explore how two important factors impact convergence rate. These studies show that the FL-ADMM algorithm may accurately solve the optimization model.
Conclusion: The FL-ADMM algorithm is a simple, effective, convergent and universal solver of optimization model in image reconstruction. Compared to the standard ADMM algorithm, the new algorithm does not need time-consuming step-size line-search or special demand to sparse transform. It is a rapid prototyping tool for optimization based image reconstruction.
期刊介绍:
Research areas within the scope of the journal include:
Interaction of x-rays with matter: x-ray phenomena, biological effects of radiation, radiation safety and optical constants
X-ray sources: x-rays from synchrotrons, x-ray lasers, plasmas, and other sources, conventional or unconventional
Optical elements: grazing incidence optics, multilayer mirrors, zone plates, gratings, other diffraction optics
Optical instruments: interferometers, spectrometers, microscopes, telescopes, microprobes