A Self-Referencing Level-Set Method for Image Reconstruction from Sparse Fourier Samples

Authors:
Jong Chul Ye;Yoram Bresler;Pierre Moulin
Affiliations:
Philips Research - USA, 345 Scarborough Road, Briarcliff Manor, New York 10510, USA. jong.ye@philips.com;Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1308 W. Main Street, Urbana, IL 61801, USA;Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1308 W. Main Street, Urbana, IL 61801, USA
Venue:
International Journal of Computer Vision
Year:
2002

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Abstract

We address an ill-posed inverse problem of image estimation from sparse samples of its Fourier transform. The problem is formulated as joint estimation of the supports of unknown sparse objects in the image, and pixel values on these supports. The domain and the pixel values are alternately estimated using the level-set method and the conjugate gradient method, respectively. Our level-set evolution shows a unique switching behavior, which stabilizes the level-set evolution. Furthermore, the trade-off between the stability and the speed of evolution can be easily controlled by the number of the conjugate gradient steps, thus avoiding the re-initialization steps in conventional level set approaches.