{"componentChunkName":"component---src-templates-course-unit-page-tsx","path":"/en/courseunit/802676s/","result":{"data":{"translations":{"edges":[{"node":{"context":{"locale":"fi","code":"802676S","title":"Introduction to Inverse Problems"},"path":"/fi/opintojakso/802676s/"}},{"node":{"context":{"locale":"en","code":"802676S","title":"Introduction to Inverse Problems"},"path":"/en/courseunit/802676s/"}}]},"SISU":{"courseUnit":[{"id":"otm-3a2987b9-0b8d-36ca-a2d1-2eaaf2ef3186","code":"802676S","name":{"en":"Introduction to Inverse Problems","fi":"Introduction to Inverse Problems"},"credits":{"max":5,"min":5},"studyLevel":null,"possibleAttainmentLanguages":[{"name":{"en":"English","fi":"englanti","sv":"engelska"}}],"responsibleOrganisations":[],"coordinatingOrganisations":[],"curriculumPeriods":[],"cooperationNetworkDirection":"INBOUND","cooperationNetworks":[{"targetGroups":[{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["jy-DP-15471","jy-DP-21321","jy-DP-13215","otm-157daa3c-6f87-4d1d-86e2-5f2ed9872b58","jy-DP-13221","jy-DP-21280","jy-DP-30241"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":null,"phase2OptionGroupIds":["jy-DP-15471","jy-DP-13215","jy-DP-30241"],"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null}],"description":{"en":"

This course is offered through the Network for Inverse Problems. These studies are available for the following degree students:

","fi":"

Tämä opintojakso on tarjolla Inversio-ongelmien verkostossa. Verkoston opinnot ovat tarjolla seuraavien tutkinto-ohjelmien opiskelijoille:

"},"cooperationNetwork":{"abbreviation":"inversio","name":{"en":"Education network on Inverse Problems","fi":"Inversio-ongelmien koulutusverkosto"}}}],"gradeScaleId":"sis-0-5","outcomes":{"en":"After successful completion of the course the student can identify linear ill-posed inverse problems and their severity. Furthermore, the students will be able to analyze and solve such problems with direct and indirect solution methods, identify necessary regularization, is able to implement such methods and work with basic simulated and experimental data.","fi":"After successful completion of the course the student can identify linear ill-posed inverse problems and their severity. Furthermore, the students will be able to analyze and solve such problems with direct and indirect solution methods, identify necessary regularization, is able to implement such methods and work with basic simulated and experimental data."},"tweetText":null,"content":{"en":"Theory of ill-posed inverse problems, singular value decomposition, Generalized-Inverse and Normal equations, Landweber iterations and Tikhonov regularization, Morozov discrepancy principle. Examples include convolutions, Fourier and Radon transform, corresponding to applications in image processing, X-ray and Magnetic Resonance Tomography. Use of Matlab/Python for implementation.","fi":"Theory of ill-posed inverse problems, singular value decomposition, Generalized-Inverse and Normal equations, Landweber iterations and Tikhonov regularization, Morozov discrepancy principle. Examples includeconvolutions, Fourier and Radon transform, corresponding to applications in image processing, X-ray and Magnetic Resonance Tomography. Use of Matlab/Python for implementation."},"additional":{"en":"Language of instruction English Timing 3rd/last year during B.Sc. studies, 1st or 2nd year of Master, 3rd period. Target group Students having mathematics, applied mathematics, or statistics as the major or a minor subject.","fi":"Opetuskieli Englanti Ajoitus 3rd/last year during B.Sc. studies, 1st or 2nd year of Master, 3rd period. Kohderyhmä Students having mathematics, applied mathematics, or statistics as the major or a minor subject."},"prerequisites":{"en":"Prerequisites and co-requisites Core courses in the B.Sc curriculum of mathematical sciences, especially linear algebra; Numerical Analysis, Fourier analysis (beneficial, but not necessary), Functional analysis (beneficial, but not necessary).","fi":"Esitietovaatimukset Core courses in the B.Sc curriculum of mathematical sciences, especially linear algebra; Numerical Analysis, Fourier analysis (beneficial,but not necessary), Functional analysis (beneficial, but not necessary)."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Introduction to Inverse Problems","id":"otm-3a2987b9-0b8d-36ca-a2d1-2eaaf2ef3186","code":"802676S","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}}}