A quadratic programming approach for joint image reconstruction: mathematical and geophysical examples

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 band-limited 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.