{"title":"Better than the Total Variation Regularization.","authors":"Gengsheng L Zeng","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>The total variation (TV) regularization is popular in iterative image reconstruction when the piecewise-constant nature of the image is encouraged. As a matter of fact, the TV regularization is not strong enough to enforce the piecewise-constant appearance. This paper suggests a different regularization function that is able to discourage some smooth transitions in the image and to encourage the piecewise-constant behavior. This new regularization function involves a Gaussian function. We use the limited-angle tomography problem to illustrate the effectiveness of this new regularization function. The limited-angle tomography situation considered in this paper uses a scanning angular range of <math><mrow><mn>40</mn></mrow> <mrow><mo>°</mo></mrow> </math> . For two-dimensional parallel-beam imaging, the required angular range is supposed to be <math><mrow><mn>180</mn></mrow> <mrow><mo>°</mo></mrow> </math> .</p>","PeriodicalId":520232,"journal":{"name":"International journal of biomedical research & practice","volume":"4 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11423893/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142336206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"One-Step Image Reconstruction for Cine MRI with a Quadratic Constraint.","authors":"Gengsheng L Zeng, Xiaodong Ma, Chun Yuan","doi":"10.33425/2769-6294.1029","DOIUrl":"10.33425/2769-6294.1029","url":null,"abstract":"<p><strong>Motivation: </strong>In cine MRI, the measurements within each timeframe alone are too noisy for image reconstruction. Some information must be 'borrowed' from other time frames and the reconstruction algorithm is a slow iterative procedure.</p><p><strong>Goals: </strong>We set up a constrained objective function, which uses the measurements at other time frames to regularize the image reconstruction. We derive a non-iterative algorithm to minimize this objective function.</p><p><strong>Approach: </strong>The derivation of the algorithm is based on the calculus of variations. The resultant algorithm is in the form of filtered backprojection.</p><p><strong>Results: </strong>The feasibility of the proposed algorithm is demonstrated with a clinical patient brain study.</p><p><strong>Impact: </strong>Non-iterative reconstruction that minimizes a constrained objective function significantly increases the throughput in healthcare institutions. This may translate to reduced healthcare costs. The new reconstruction formula has a closed form that gives an explicit expression of how to incorporate the reference image in dynamic reconstruction.</p>","PeriodicalId":520232,"journal":{"name":"International journal of biomedical research & practice","volume":"4 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11670894/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142901587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}