{"id":50992,"date":"2025-01-17T11:51:06","date_gmt":"2025-01-17T16:51:06","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=tribe_events&p=50992"},"modified":"2025-03-24T09:25:09","modified_gmt":"2025-03-24T13:25:09","slug":"ams-weekly-seminar-anne-gelb","status":"publish","type":"tribe_events","link":"https:\/\/engineering.jhu.edu\/ams\/event\/ams-weekly-seminar-anne-gelb\/","title":{"rendered":"Applied Mathematics and Statistics presents the Duncan Lecture Series w\/Anne Gelb"},"content":{"rendered":"

Location:\u00a0<\/strong>Gilman 50<\/p>\n

When:<\/strong>\u00a0March 27th at 1:30 p.m.<\/p>\n

Title:\u00a0<\/strong>Image recovery for linear inverse problems from multiple measurements: From point estimates to uncertainty quantification<\/p>\n

Abstract:<\/strong> Numerical algorithms for image recovery from linear inverse problems that are designed to recover point estimates typically involve solving a convex optimization problem that includes a regularization term \u00a0used to promote some prior belief about the underlying image. Compressive sensing (CS) provides a well-known example for which the regularization term encourages sparsity in some presumably sparse domain (e.g. edges, gradient). \u00a0Although the CS approach has been used successfully in a broad range of applications, it can be difficult to choose the appropriate regularization parameters, as well as the appropriate regularization operator, and the results are not always robust to increased amounts of noise or additional under-sampling.<\/p>\n

The Bayesian approach casts the inverse problem in terms of random variables, \u00a0and is often used to formulate the recovery as the posterior distribution of the unknown, from which it is possible to sample. \u00a0The main (hypothetical) advantages to using the Bayesian approach are (1) the hierarchical structure of the prior in the Bayesian framework (as compared to the regularization term parameter in CS methods) reduces the amount of hand-tuning required and (2) sampling from the posterior distribution allows for uncertainty quantification, which can be important especially in applications where it crucial to know how reliable the recovery is. \u00a0 However, as is the case for CS methods, it is important to choose a good prior, which is not always easy to do, with the \u201cbest\u201d priors sometimes leading to various computational complexities.<\/p>\n

In some applications we are given multiple measurement vectors (MMV) of \u00a0noisy observable (indirect) data. \u00a0This talk discusses how both the CS and Bayesian approaches can exploit the redundant information to improve the accuracy of approximation, limit the amount of hand tuning of parameters, reduce the uncertainty of the sampled posterior mean, \u00a0all while being mindful of computational complexities.<\/p>\n

This work involves many collaborators:<\/strong> Jan Glaubitz, Dylan Green, Jonathan Lindbloom, Theresa Scarnati, Guohui Song, Yao Xiao, and Jack Zhang.<\/p>\n

Zoom link:<\/strong> https:\/\/wse.zoom.us\/j\/93287142219?pwd=z9fqWnRMzmzS0SGijRiie5yN3kHRSZ.1<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Location:\u00a0Gilman 50 When:\u00a0March 27th at 1:30 p.m. Title:\u00a0Image recovery for linear inverse problems from multiple measurements: From point estimates to uncertainty quantification Abstract: Numerical algorithms for image recovery from 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