Yuanjing Feng1, Ye Wu2, Yogesh Rathi3, Carl-Fredrik Westin3. 1. Institute of Information Processing and Automation, College of Information Engineering, Zhejiang University of Technology, 288 Liuhe Road, Hangzhou, Zhejiang Province 310023, China. Electronic address: fyjing@zjut.edu.cn. 2. Institute of Information Processing and Automation, College of Information Engineering, Zhejiang University of Technology, 288 Liuhe Road, Hangzhou, Zhejiang Province 310023, China. 3. Laboratory of Mathematics in Imaging, Brigham and Women's Hospital, Harvard Medical School, 1249 Boylston Street, Boston, MA 02215, United States.
Abstract
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 l2 penalty and the sparsity encouraging effect of the l1 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 l2 or l1 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 l2 regularizer and the reweighted l1 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.
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 l2 penalty and the sparsity encouraging effect of the l1 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 l2 or l1 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 l2 regularizer and the reweighted l1 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.