Signal Processing Seminar

Image Reconstruction Using Training Images

Per Christian Hansen
Technical University of Denmark

Priors are essential for computing stable solutions to ill-posed problems, and they take many different forms.  Here we consider priors in the form of cross-section images of the object, and this information must be used in a fast, reliable, and computationally efficient manner. We describe an algorithmic framework for this: From a set of training images we use techniques from machine learning to form a dictionary that captures the desired features, and we then compute a reconstruction with a sparse representation in this dictionary. We describe how to stably compute the dictionary through a regularized non-negative matrix factorization, and we study how this dictionary affects the reconstruction quality. Simulations show that for textural images our approach is superior to other methods used for limited-data problems.

About the speaker

Professor Per Christian Hansen has worked with numerical regularization algorithms for 30 years, and he has published 4 books and 100+ papers in leading journals. He has developed a number of software packages, of which Regularization Tools (now in its 4th version) is a popular toolbox for analysis and solution of discrete inverse problems. His current research projects involve algorithms for tomographic reconstruction and iterative image deblurring algorithms. He is a SIAM fellow in recognition of his work on inverse problems and regularization.

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Overview of Signal Processing Seminar