High-resolution image reconstruction with multisensors - Bose, N. K.; Boo, K. J. (International journal of imaging systems and technology, 1998)
This article considers the problem of reconstructing a high‐resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. This leads to a formulation involving a periodically shift‐variant system model. The maximum a posteriori (MAP) estimation scheme is used subject to the assumption that the original high‐resolution image is modeled by a stationary Markov‐Gaussian random field. The resulting MAP formulation is expressed as a complex linear matrix equation, where the characterizing matrix involves the periodic block Toeplitz with Toeplitz block (BTTB) blur matrix and banded‐BTTB inverse covariance matrix associated with the original image. By approximating the periodic‐BTTB and the banded‐BTTB matrices with, respectively, the periodic block circulant with circulant block (BCCB) and the banded‐BCCB matrices, it is shown that the computation‐intensive MAP formulation can be decomposed into a set of smaller matrix equations by using the two‐dimensional discrete Fourier transform. Exact solutions are also considered through the use of the preconditioned conjugate gradient algorithm. Computer simulations are given to illustrate the procedure. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 294–304, 1998