Stabilized inversion for limited angle tomography

Tim E. Olson

doi:10.1117/12.205441

6 April 1995 Stabilized inversion for limited angle tomography

Tim E. Olson

Proceedings Volume 2491, Wavelet Applications II; (1995) https://doi.org/10.1117/12.205441
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

In this paper we present a method for reconstructing a function f:R² yields R from limited angle tomographic data. This reconstruction problem occurs in may physical systems, where physical limitations prohibit the gathering of tomographic data at certain angles. We begin by reviewing some of the classical work on singular value decompositions and POCS in the context of this problem. We then review some of the classical work by G. Szego and others on finite Toeplitz operators. We consider the implications of this work toward a classical inversion of the problem. We introduce a new inversion technique which utilizes multiresolution analysis, induced correlations caused by non-linear constraints, and non-linear filtering to mollify the reconstruction process. We show that the uncertainty principles generated in recent works of Donoho, Stark et al. guarantee the invertibility of this alternative inversion technique. We also utilize the noise reduction techniques of Donoho and Johnstone to reduce the effects of noise on the process.

Citation Download Citation

Tim E. Olson "Stabilized inversion for limited angle tomography", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); https://doi.org/10.1117/12.205441

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