Thursday, October 10

8:30-9:30 AM

Kidd Island & North Cape Rooms

Chair: Gene H. Golub, Stanford University
## IP2

Sparse Matrix Problems in Total Variation Image Restoration

Image restoration refers to the process of recovering an image contaminated by blurring and noise. The problems are computationally intensive and accurate and efficient methods are needed.
Standard restoration methods involve computation in the frequency domain, facilitated by efficient FFT and wavelet algorithms. Recently, there has been a new movement toward a partial differential equation (PDE) based approach, which is motivated by a more systematic approach to restoring images with sharp edges, as well as image segmentation. From a computational standpoint, the PDE formulations call for new techniques. Among the computational difficulties are the highly nonlinear and singular nature of the PDEs that arise and the need to invert ill-conditioned nonlinear differential-integral operators efficiently.

In this presentation, the speaker will first give an introduction to this field and then highlight some sparse matrix problems that arise and some methods that we have found to be successful. He will also try to pose some open problems which he thinks sparse matrix technologies can help to solve.

**Tony F. Chan**

University of California, Los Angeles

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*MMD, 8/15/96*