Tradeoffs between measurement residual and reconstruction error in inverse problems with prior information
- Lawrence Berkeley Lab., CA (United States). Life Sciences Div.
In many inverse problems with prior information, the measurement residual and the reconstruction error are two natural metrics for reconstruction quality, where the measurement residual is defined as the weighted sum of the squared differences between the data actually measured and the data predicted by the reconstructed model, and the reconstruction error is defined as the sum of the squared differences between the reconstruction and the truth, averaged over some a priori probability space of possible solutions. A reconstruction method that minimizes only one of these cost functions may produce unacceptable results on the other. This paper develops reconstruction methods that control both residual and error, achieving the minimum residual for any fixed error or vice versa. These jointly optimal estimators can be obtained by minimizing a weighted sum of the residual and the error; the weights are determined by the slope of the tradeoff curve at the desired point and may be determined iteratively. These results generalize to other cost functions, provided that the cost functions are quadratic and have unique minimizers; some results are obtained under the weaker assumption that the cost functions are convex. This paper applies these results to a model problem from biomagnetic source imaging and exhibits the tradeoff curve for this problem.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 106621
- Report Number(s):
- LBL-37402; CONF-9507171-1; ON: DE96000120; TRN: AHC29525%%122
- Resource Relation:
- Conference: Experimental and numerical methods for solving ill-posed problems, San Diego, CA (United States), 9-14 Jul 1995; Other Information: PBD: Jun 1995
- Country of Publication:
- United States
- Language:
- English
Similar Records
Alpha image reconstruction (AIR): A new iterative CT image reconstruction approach using voxel-wise alpha blending
Detection geometry and reconstruction error in magnetic source imaging