Local Image Reconstruction and Subpixel Restoration Algorithms

This paper introduces a new class of reconstruction algorithms that are fundamentally different from traditional approaches. We deviate from the standard practice that treats images as point samples. In this work, image values are treated as area samples generated by nonoverlapping integrators. This is consistent with the image formation process, particularly for CCD and CID cameras. We show that superior results are obtained by formulating reconstruction as a two-stage process: image restoration followed by application of the point spread function (PSF) of the imaging sensor. By coupling the PSF to the reconstruction process, we satisfy a more intuitive fidelity measure of accuracy that is based on the physical limitations of the sensor. Efficient local techniques for image restoration are derived to invert the effects of the PSF and estimate the underlying image that passed through the sensor. The reconstruction algorithms derived herein are local methods that compare favorably to cubic convolution, a well-known local technique, and they even rival global algorithms such as interpolating cubic splines. Evaluations are made by comparing their passband and stopband performances in the frequency domain, as well as by direct inspection of the resulting images in the spatial domain. A secondary advantage of the algorithms derived with this approach is that they satisfy an imaging-consistency property. This means that they exactly reconstruct the image for some function in the given class of functions. Their error can be shown to be at most twice that of the "optimal" algorithm for a wide range of optimality constraints.