Blind deconvolution and structured matrix computations with applications to array imaging

In this chapter, we study using total least squares (TLS) methods for solving blind deconvolution problems arising in image recovery. Here, the true image is to be estimated using only partial information about the blurring operator, or point spread function, which is also subject to error and noise. Iterative, regularized, and constrained TLS methods are discussed and analyzed. As an application, we study TLS methods for the reconstruction of high-resolution images from multiple undersampled images of a scene that is obtained by using a charge-coupled device (CCD) or a CMOS detector array of sensors which are shifted relative to each other by subpixel displacements. The objective is improving the performance of the signal-processing algorithms in the presence of the ubiquitous perturbations of displacements around the ideal subpixel locations because of imperfections in fabrication and so on, or because of shifts designed to enable superresolution reconstructions in array imaging. The target architecture consists of a regular array of identical lenslets whose images are grouped, combined, and then digitally processed. Such a system will have the resolution, ?eld of view, and sensitivity of a camera with an e?ective aperture that would be considerably larger than the single-lenslet aperture, yet with a short focal length typical of each lenslet. As a means for solving the resulting blind deconvolution problems, the errors-in-variables (or the TLS) method is applied.