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These studies are available for the following degree students:<br><br></p><ul><li>Bachelor's Degree Programme in Mathematics</li><li>Bachelor's Degree Programme in Mathematics (Subject Teacher)</li><li>Master’s Degree Programme in Mathematics</li><li>Master's degree Programme in Mathematics (Subject Teacher)</li><li>Doctoral Degree Programme in Mathematics and Statistics</li></ul>","fi":"<p>Tämä opintojakso on tarjolla Inversio-ongelmien verkostossa. Verkoston opinnot ovat tarjolla seuraavien tutkinto-ohjelmien opiskelijoille:<br><br></p><ul><li>Matematiikan kandidaattiohjelma</li><li>Matematiikan aineenopettajan kandidaattiohjelma</li><li>Matematiikan maisteriohjelma</li><li>Matematiikan aineenopettajan&nbsp;maisteriohjelma</li><li>Matematiikan\nja tilastotieteen tohtoriohjelma</li></ul>"},"cooperationNetwork":{"abbreviation":"inversio","name":{"en":"Education network on Inverse Problems","fi":"Inversio-ongelmien koulutusverkosto"}}}],"gradeScaleId":"sis-0-5","outcomes":{"en":"Students will be familiar with basic operations to analyse, process, and understand images. Identify suitable presentations for different classes of images. Learn suitable analytical models for denoising and segmentation of images. Methods will be implemented using Matlab/Python.","fi":"Students will be familiar with basic operations to analyse, process, and understand images. Identify suitable presentations for different classes of images. Learn suitable analytical models for denoising and segmentation of images. Methods will be implemented using Matlab/Python."},"tweetText":null,"content":{"en":"Basics of representing images and signals using Fourier and wavelet transforms. Variational models for image denoising and nonlinear diffusion. Deconvolution, denoising, and inpainting as examples for classic inverse problems arising in imaging. Segmentation and the Mumford-Shah functional.","fi":"Basics of representing images and signals using Fourier and wavelet transforms. Variational models for image denoising and nonlinear diffusion. Deconvolution, denoising, and inpainting as examples for classic inverse problems arising in imaging. Segmentation and the Mumford-Shah functional."},"additional":{"en":"Timing 3rd/last year during B.Sc., 1st or 2nd year of Master Target group Students having mathematics, applied mathematics, or statistics as the major or a minor subject.","fi":"Timing 3rd/last year during B.Sc., 1st or 2nd year of Master Target group Students having mathematics, applied mathematics, or statistics as the major or a minor subject."},"prerequisites":{"en":"Core courses in the B.Sc curriculum of mathematical sciences, especially Analysis 1 NM00BD54, Analysis 2 NM00BD55, Measure and Integral 802651S. Additionally as recommended: optimization (recommended), Introduction to Inverse Problems (beneficial, but not necessary).","fi":"Core courses in the B.Sc curriculum of mathematical sciences, especially Analysis 1 NM00BD54, Analysis 2 NM00BD55, Measure and Integral 802651S. Additionally as recommended: optimization (recommended), Introduction to Inverse Problems (beneficial, but not necessary)."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Mathematics of Imaging and Vision","id":"otm-debcc029-8a03-3ed9-ad1d-55b5a9d56502","code":"802678S","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-71fd8cc0-9fb4-38e1-bbb0-d1d63f911ddf"],"organisations":[],"attainmentLanguages":["en"],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}