Diffusion-Weighted MR Signal Sparsity Indicates Impaired White Matter Organization in Lissencephaly

We demonstrate a novel technique for studying white matter pathology by examining the statistical properties of the DWI signal. We apply a sparse coding method, K-SVD, to decompose a diffusion-weighted series. We then quantify the efficiency of the resulting encoding by computing the Gini coefficient. We show that this measure is abnormally decreased in a cohort of lissencephaly patients compared to age-matched control subjects. Our results support the hypotheses that more organized white matter can be more sparsely encoded and that the sparsity of the encoding may thus be used to infer pathological white matter states.