Multichannel restoration with limited a priori information [electron microscopy of biological macromolecules]

We introduce a method for multichannel restoration of images in which there is severely limited knowledge about the undegraded signal, and possibly the noise. We assume that we know the channel degradations and that there will be a significant noise reduction in a postprocessing stage in which multiple realizations are combined. This post-restoration noise reduction is often performed when working with micrographs of biological macromolecules. The restoration filters are designed to enforce a projection constraint upon the entire system. This projection constraint results in a system that provides an oblique projection of the input signal into the subspace defined by the reconstruction device in a direction orthogonal to a space defined by the channel degradations and the restoration filters. The approach achieves noise reduction without distorting the signal by exploiting the redundancy of the measurements.