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A quadratic programming approach for joint image reconstruction: mathematical and geophysical examples. (English) Zbl 1070.65050

Summary: Although a comparative analysis of multiple images of a physical target can be useful, a joint image reconstruction approach should provide better interpretative elements for multi-spectral images. We present a generalized image reconstruction algorithm for the simultaneous reconstruction of bandlimited images based on the novel cross-gradients concept developed for geophysical imaging.
The general problem is formulated as the search for those images that stay within their band limits, are geometrically similar and satisfy their respective data in a least-squares sense. A robust iterative quadratic programming scheme is used to minimize the resulting objective function. We apply the algorithm to synthetic data generated using linear mathematical functions and to comparative geophysical test data. The resulting images recovered the test targets and show improved structural semblance between the reconstructed images in comparison to the results from two other conventional approaches.
(Some figures in this article are in colour only in the electronic version).

MSC:

65K10 Numerical optimization and variational techniques
49J20 Existence theories for optimal control problems involving partial differential equations
49M37 Numerical methods based on nonlinear programming
86A15 Seismology (including tsunami modeling), earthquakes
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory

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