Linear Estimation with a Size Constraint

Least squares estimation has been used in image processing since Helstrom showed several years ago that Wiener filters could be used to deblur images1. In its most usual application, the technique uses the image data and the object and noise autocorrelation functions to compute the object that corresponds to the minimum of the sum of the squares of the noise values. We show here how least squares techniques can also be used to estimate spectral components when the size and shape of an object are known. Examples of missing components are high frequency Fourier components of an object that has been subjected to low pass filtering (blurring) and transforms of missing projections of an object that is to be restored through computed tomography.