Diffusion spectrum imaging (DSI) from multiple diffusion-weighted images (DWI) allows to image the complex geometry of water diffusion in biological tissue. To capture the structure of DSI data, we propose to use sparse coding constrained by physical properties of the signal, namely symmetry and positivity, to learn a dictionary of diffu- sion profiles. Given this estimated model of the signal, we can extract better estimates of the signal from noisy measurements and also speed up acquisition by reducing the number of acquired DWI while giving access to high resolution DSI data. The method learns jointly for all the acquired DWI and scales to full brain data. Working with two sets of 515 DWI images acquired on two different subjects we show that using just half of the data (258 DWI) we can better predict the other 257 DWI than the classic symmetry procedure. The observation holds even if the diffusion profiles are estimated on a different subject dataset from an undersampled q-space of 40 measurements.