Least squares approach in measurement-dependent filtering for selective medical images

An image-processing method called measurement-dependent filtering has been introduced to improve the SNR (signal-to-noise ratio) of selective images produced by various medical imaging systems. The basic algorithm involves the combination of the low-frequency information of the selective image with the high-frequency information of a nonselective image. A spatially variant control function modulates the amount of high frequency to be added at each point. A least-mean-square (LMS) control function formed from two basis images, namely the high-passed versions of the nonselective image (M(b)) and the selective image (S(b)), is introduced. The original algorithm is now viewed as a two-stage filtering method, including the low-pass filtering noise reduction and least squares filtering for the edge restoration. An appropriate linear transformation is used to convert the original basis images M(b) and S(b) into a new pair with orthogonal noise. This allows the implementation of the LMS and control function with practically obtainable a priori knowledge.