In this chapter, we introduce a whole brain multimodal structural connectivity study in characterizing white matter abnormalities using MRI and DTI. The Jacobian determinant (JD) from MRI and the fractional anisotropy (FA) from DTI over predefined nodes are taken as response vectors in a multivariate general linear model (MGLM). However, when the number of nodes is larger than the number of samples, the covariance matrix estimation is ill-conditioned. So it is necessary to regularize the covariance matrix using various sparse regressions such as compressed sensing, LASSO and sparse likelihood. These sparse regressions are known to cause huge computational bottlenecks. By exploiting hidden persistent homological structure embedded in the sparse regressions, we show how to completely bypass the time consuming L1-optimization and still be able to construct sparse networks and do a network inference. This chapter is based on [75].