On the Relationship Between Feature‐Recognizing MRI and MRI Encoded by Singular Value Decomposition

This paper describes the similarity between two methods of non‐Fourier MRI: feature‐recognizing MRI (FR MRI) and MRI with encoding by singular value decomposition (SVD MRI). Both methods represented images as truncated expansions of non‐Fourier basis functions; these basis images were derived from prior image data by using closely‐related mathematical techniques: the Karhunen‐Loeve decomposition (or principal components analysis) and singular value decomposition, respectively. We demonstrate that FR and SVD MRI are equivalent in the following sense: given the same prior image data, they lead to exactly the same basis functions. FR MRI utilized prior images of the same body part in many “training” subjects, thought to be similar to the “unknown” subject to be imaged. SVD MRI utilized a single prior image of one subject in order to perform dynamic imaging of that subject. We demonstrate that the basis function expansion derived from a single prior image may not be capable of representing new features (features not found in the prior image). Therefore, the SVD basis functions may be inappropriate for dynamic imaging.