A new method to collapse the S-transform into local spectra by integrating in squares

The two-dimensional S-transform (2D-ST) is a promising technique for identifying texture characteristics of brain pathology in magnetic resonance images. Previous work has obtained "texture curves" from the four-dimensional ST domain by integrating the local Fourier domain for each pixel in concentric rings of constant width. Using this approach, previous studies have shown that specific spatial frequency bands can discriminate between active and inactive lesions in multiple sclerosis and between brain tumor genotypes. However, integration in rings produces an artificial drop in spectral power at the Nyquist frequency, potentially masking true high-frequency information. We present a new method of producing texture curves by integrating the ST domain in squares. We compare the two methods on synthetic and clinical multiple sclerosis data and show that our method is simple to implement and produces spectra localized to frequencies below the Nyquist frequency. Integration in squares may produce spectra that are more sensitive to subtle high-frequency changes.