Spatio-frequency texture analysis using wavelet increment entropy: Methodology and application to MRI in multiple sclerosis

Texture analysis is crucial for understanding images by extracting features that define spatial patterns. Recently, bi-dimensional extensions of entropy measures have gained attention due to their simplicity and strong theoretical foundations. However, existing methods primarily operate in the spatial domain and thus overlook frequency-domain and multiscale information. To address this, we introduce bidimensional wavelet increment entropy (wavelet IncrEn${}_{2D}$). A one-level discrete wavelet transform (DWT) with the Haar wavelet decomposes each image into approximation (low-frequency) and, for some neuroimaging data, detail (high-frequency) subbands; IncrEn${}_{2D}$ is then applied both to capture global structural patterns and fine, detailed texture variations. We evaluated wavelet IncrEn${}_{2D}$ on synthetic and real datasets, demonstrating its effectiveness in distinguishing between different noise types (white Gaussian, salt-and-pepper, and speckle noise). Comparisons between periodic and synthesized images revealed lower wavelet IncrEn${}_{2D}$ values for periodic textures. Tests on real texture datasets highlight the method's ability to differentiate various patterns. In particular, wavelet IncrEn${}_{2D}$ achieved 86.69% accuracy in distinguishing MRI images of healthy versus multiple sclerosis–affected brains. Overall, wavelet IncrEn${}_{2D}$ offers a robust, frequency-aware descriptor that outperforms existing 2D entropy methods.