{"year":"2020","scopus_import":"1","date_updated":"2024-10-15T10:43:38Z","_id":"18252","article_processing_charge":"No","title":"Overparameterized models for vector fields","issue":"3","abstract":[{"text":"Vector fields arise in a variety of quantity measure and visualization techniques, such as fluid flow imaging, motion estimation, deformation measures, and color imaging, leading to a better understanding of physical phenomena. Recent progress in vector field imaging technologies has emphasized the need for efficient noise removal and reconstruction algorithms. A key ingredient in the successful extraction of signals from noisy measurements is prior information, which can often be represented as a parameterized model. In this work, we extend the overparameterization variational framework in order to perform model-based reconstruction of vector fields. The overparameterization methodology combines local modeling of the data with global model parameter regularization. By considering the vector field as a linear combination of basis vector fields and appropriate scale and rotation coefficients, we can reduce the denoising problem to a simpler form of coefficient recovery. We introduce two versions of the overparameterization framework: a total variation-based method and a sparsity-based method, which relies on the cosparse analysis model. We demonstrate the efficiency of the proposed frameworks for two- and three-dimensional vector fields with linear and quadratic overparameterization models.","lang":"eng"}],"author":[{"full_name":"Rotker, Keren","last_name":"Rotker","first_name":"Keren"},{"full_name":"Bashat, Dafna Ben","first_name":"Dafna Ben","last_name":"Bashat"},{"first_name":"Alexander","orcid":"0000-0001-9699-8730","last_name":"Bronstein","full_name":"Bronstein, Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6"}],"language":[{"iso":"eng"}],"status":"public","publication_status":"published","citation":{"ieee":"K. Rotker, D. B. Bashat, and A. M. Bronstein, “Overparameterized models for vector fields,” <i>SIAM Journal on Imaging Sciences</i>, vol. 13, no. 3. Society for Industrial &#38; Applied Mathematics, pp. 1386–1414, 2020.","ista":"Rotker K, Bashat DB, Bronstein AM. 2020. Overparameterized models for vector fields. SIAM Journal on Imaging Sciences. 13(3), 1386–1414.","mla":"Rotker, Keren, et al. “Overparameterized Models for Vector Fields.” <i>SIAM Journal on Imaging Sciences</i>, vol. 13, no. 3, Society for Industrial &#38; Applied Mathematics, 2020, pp. 1386–414, doi:<a href=\"https://doi.org/10.1137/19m1280697\">10.1137/19m1280697</a>.","apa":"Rotker, K., Bashat, D. B., &#38; Bronstein, A. M. (2020). Overparameterized models for vector fields. <i>SIAM Journal on Imaging Sciences</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/19m1280697\">https://doi.org/10.1137/19m1280697</a>","ama":"Rotker K, Bashat DB, Bronstein AM. Overparameterized models for vector fields. <i>SIAM Journal on Imaging Sciences</i>. 2020;13(3):1386-1414. doi:<a href=\"https://doi.org/10.1137/19m1280697\">10.1137/19m1280697</a>","chicago":"Rotker, Keren, Dafna Ben Bashat, and Alex M. Bronstein. “Overparameterized Models for Vector Fields.” <i>SIAM Journal on Imaging Sciences</i>. Society for Industrial &#38; Applied Mathematics, 2020. <a href=\"https://doi.org/10.1137/19m1280697\">https://doi.org/10.1137/19m1280697</a>.","short":"K. Rotker, D.B. Bashat, A.M. Bronstein, SIAM Journal on Imaging Sciences 13 (2020) 1386–1414."},"date_published":"2020-01-01T00:00:00Z","month":"01","article_type":"original","OA_type":"closed access","page":"1386-1414","volume":13,"publication_identifier":{"eissn":["1936-4954"]},"quality_controlled":"1","extern":"1","date_created":"2024-10-08T13:06:25Z","intvolume":"        13","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","publication":"SIAM Journal on Imaging Sciences","publisher":"Society for Industrial & Applied Mathematics","oa_version":"None","doi":"10.1137/19m1280697"}