Purpose Higher order tensor (HOT) imaging approaches based on the spherical deconvolution framework have attracted much interest for their effectiveness in estimating fiber orientation distribution (FOD). However, sparse regularization techniques are still needed to obtain stable FOD in solving the deconvolution problem, particularly in very high orders. Our goal is to adequately characterize the actual sparsity lying in the FOD domain to develop accurate estimation approach for fiber orientation in HOT framework. Materials and methods We propose a sparse HOT regularization model by enforcing the sparse constraint directly on the representation of FOD instead of imposing it on coefficients of basis function. Then, we incorporate both the stabilizing effect of the l 2 penalty and the sparsity encouraging effect of the l 1 penalty in the sparse model to adequately characterize the actual sparsity lying in the FOD domain. Furthermore, a weighted regularization scheme is developed to iteratively solve the deconvolution problem. The deconvolution technique is compared against existing methods using l 2 or l 1 regularizer and tested on synthetic data and real human brain. Results Experiments were conducted on synthetic data and real human brain data. The synthetic experimental results indicate that crossing fibers are more easily detected and the angular resolution limit is improved by our method by approximately 20°–30° compared to existing HOT method. The detection accuracy is considerably improved compared with that of spherical deconvolution approaches using the l 2 regularizer and the reweighted l 1 scheme. Conclusions Results of testing the deconvolution technique demonstrate that it allows HOTs to obtain increasingly clean and sharp FOD, which in turn significantly increases the angular resolution of current HOT methods. With sparsity on FOD domain, this method efficiently improves the ability of HOT in resolving crossing fibers. 
Sparse deconvolution of higher order tensor for fiber orientation distribution estimation