Let the Data Speak for Itself: Data-Driven Learning of Sparse Signal Models

SpeakerYoram Bresler
Organization University of Illinois at Urbana-Champaign
LocationEngineering Building II Room 1230
DateNovember 30, 2012 12:50 PM

Abstract

The sparsity of signals and images in a certain transform domain or dictionary has been exploited in many applications in signal and image processing, including compression, denoising, and  notably in compressed sensing, which enables accurate reconstruction from undersampled data.  These various applications used sparsifying transforms such as DCT, wavelets, curvelets, and finite differences, all of which had a fixed, analytical form. Recently, sparse representations that are directly adapted to the data have become popular, especially in applications such as image denoising, and inpainting.

We describe two contributions to this new framework. First, we describe a novel approach for simultaneously learning the dictionary and reconstructing the image from highly undersampled data.  Numerical experiments on magnetic resonance images of several anatomies demonstrate dramatic improvements on the order of 4-18 dB in reconstruction error and doubling of the acceptable undersampling factor compared to previous compressed sensing methods. Second, we describe a new formulation for data-driven learning of sparsifying transforms. While there has been extensive research on learning synthesis dictionaries and some recent work on learning analysis dictionaries, the idea of learning sparsifying transforms has received no attention. We show the superiority of our learned transforms over analytical sparsifying transforms such as the DCT for signal and image representation. We also show promising performance in image denoising using the learnt transforms, which compares favorably with approaches involving learnt synthesis dictionaries, but at orders of magnitude lower computational cost.

Biosketch

Yoram Bresler received the B.Sc. (cum laude) and M.Sc. degrees from the Technion, Israel Institute of Technology, in 1974 and 1981 respectively, and the Ph.D degree from Stanford University, in 1986, all in Electrical Engineering. In 1987 he joined the University of Illinois at Urbana-Champaign, where he is currently a Professor at the Departments of Electrical and Computer Engineering and Bioengineering, and at the Coordinated Science Laboratory. Yoram Bresler is also President and Chief Technology Officer at InstaRecon, Inc., a startup he co-founded to commercialize breakthrough technology for tomographic reconstruction developed in his academic research. His current research interests include multi dimensional and statistical signal processing and their applications to inverse problems in imaging, and in particular compressed sensing, computed tomography, and magnetic resonance imaging. Dr. Bresler has served on the editorial board of a number of journals, and currently he serves on the editorial boards for the SIAM Journal on Imaging Science. Dr. Bresler is a fellow of the IEEE and of the AIMBE. He received two Senior Paper Awards from the IEEE Signal Processing society, and a paper he coauthored with one of his students received the Young Author Award from the same society in 2002. He is the recipient of a 1991 NSF Presidential Young Investigator Award, the Technion (Israel Inst. of Technology) Fellowship in 1995, and the Xerox Senior Award for Faculty Research in 1998. He was named a University of Illinois Scholar in 1999, appointed as an Associate at the Center for Advanced Study of the University in 2001-2, and Faculty Fellow at NCSA in 2006.

 

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