Synthetic images by subspace transforms. I. Principal components images and related filters

The principal component (PC) approach offers compressions of an image sequence into fewer images and noise suppressing filters. Multiple MR images of the same tomographic slice obtained with different acquisition parameters (i.e., with different TR, TE, and flip angles), time sequences of images in nuclear medicine, and cardiac ultrasound image sequences are examples of such input image sets. In this paper noise relationships of original and linearly transformed image sequences in general, and specifically of original, PC, and PC-filtered images are discussed. As the spinoff, it introduces locally weighted PC transforms and filters, nonlinear PC's, and a single-image based filter for suppression of noise. Examples illustrate increased perceptibility of anatomical/functional structures in PC images and PC-filtered images, including extraction of physiological functional information by PC loading curves. Generally, the more correlated the original images are, the more effective is the PC approach.