Texture quantification of medical images using a novel complex space-frequency transform

Objective: To develop an efficient space-frequency transform for texture analysis and demonstrate its application on magnetic resonance (MR) images of multiple sclerosis (MS) patients. Materials and methods: We applied our new transform to MR images of three enhancing lesions from two relapsing-remitting MS patients acquired serially over 9 months. Local spectra of the images were generated using our new technique, and spatial frequencies corresponding to MS lesion activity were extracted by applying a band-pass filter and inverting. We examined the changes in T2 intensity and low-frequency energy (LFE) over time within the lesion, surrounding tissue and a region of normal-appearing white matter (NAWM). Results: We calculated complex local spectra of 428 × 428 images in approximately 1 min and achieved a spatial frequency resolution of 0.05 cm^-1. We observed an increase in LFE within the lesion and a drop in LFE in the hyperintense border of tissue surrounding the lesion. Conclusion: We have developed an efficient, invertible transform that produces high-resolution local frequency spectra of an MR image in approximately 1 min. Negative LFE values in the boundaries of an active lesion may help discriminate between the core lesion undergoing demyelination and a border of inflammation.