MAP regularized image reconstruction with multisensors

We study the problem of reconstructing high resolution images from multiple undersampled, shifted, degraded frames with subpixel displacement errors. This leads to a formulation involving a spatially-variant imaging system model. The 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 a large linear system, where the coefficient matrix involves block-Toeplitz-Toeplitz-block-like (BTTB-like) blurring matrix and banded BTTB inverse covariance matrix associated with the original image. We find that when there is no subpixel displacement error, the blurring matrix can be diagonalized by the two-dimensional discrete cosine transform matrix. Thus we apply the preconditioned conjugate gradient (PCG) method with cosine transform preconditioners to solve the BTTB-like linear system. Experimental results show that the system can be solved by the cosine transform based PCG method very efficiently.