Diffusion tensor tractography studies on mechanisms of recovery of injured fornix

The fornix,which connects the medial temporal lobe and the medial diencephalon,is involved in episodic memory as an important part of the Papez circuit.The mechanisms of recovery of an injured fornix revealed by diffusion tensor tractography in the five studies are summarized as follows：1） recovery through the nerve tract from an injured fornical crus to the medial temporal lobe via the normal pathway of the fornical crus;2）recovery through the nerve tract originating from an ipsi-lesional fornical body connected to the ipsi-lesional medial temporal lobe via the splenium of the corpus callosum;3） recovery through the nerve tract from the ipsi-lesional fornical body extending to the contra-lesional medial temporal lobe via the splenium of the corpus callosum;4） recovery through the nerve tract originating from the ipsi-lesional fornical column connected to the ipsi-lesional medial temporal lobe;and 5） recovery through the nerve tract originating from the contra-lesional fornical column connected to the ipsi-lesional medial temporal lobe via the contra-lesional medial temporal lobe and the splenium of the corpus callosum.These diffusion tensor tractography studies on mechanisms of recovery of injured fornical crus appeared to provide useful information for clinicians caring for patients with brain injury,however,studies on this topic are still in the beginning stages.

Higher-order principal component pursuit via tensor approximation and convex optimization

Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit （PCP）. This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit （HOPCP）, since it is critical in multi-way data analysis. Unlike the convexification （nuclear norm） for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme： the augmented Lagrangian alternating direction method （ALADM） and its truncated higher-order singular value decomposition （ALADM-THOSVD） version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.

Medial reorganization of motor function in corona radiata following middle cerebral artery infarction A case report

Peri-lesional reorganization is one of the motor recovery mechanisms following stroke. A 23-year-old female who presented with complete paralysis of the right extremities at the onset of infarct in the left middle cerebral artery territory was included. She slowly recovered some function, and could extend the affected knee with resistance after 9 months. Diffusion tensor tractography, functional MRI, and transcranial magnetic stimulation testing were performed at 7 years after onset. Results showed that diffusion tensor tractography of the affected （left） hemisphere passed through the medial corona radiata at, or around, the wall of the lateral ventricle. The contralateral primary sensorimotor cortex was activated during affected knee movements. The motor-evoked potential, which was obtained from the affected leg, exhibited corticospinal tract characteristics. Results indicated that motor function of the affected leg recovered via the corticospinal tract, which descended through the corona radiata medial to the infarct. The motor function of the affected leg was reorganized to the medial corona radiata following infarct to the middle cerebral artery territory.

Robust tensor decomposition via orientation invariant tubal nuclear norms

Aiming at recovering an unknown tensor(i.e.,multi-way array)corrupted by both sparse outliers and dense noises,robust tensor decomposition(RTD)serves as a powerful pre-processing tool for subsequent tasks like classification and target detection in many computer vision and machine learning applications.Recently,tubal nuclear norm(TNN)based optimization is proposed with superior performance as compared with other tensorial nuclear norms for tensor recovery.However,one major limitation is its orientation sensitivity due to low-rankness strictly defined along tubal orientation and it cannot simultaneously model spectral low-rankness in multiple orientations.To this end,we introduce two new tensor norms called OITNN-O and OITNN-L to exploit multi-orientational spectral low-rankness for an arbitrary K-way(K≥3)tensors.We further formulate two RTD models via the proposed norms and develop two algorithms as the solutions.Theoretically,we establish non-asymptotic error bounds which can predict the scaling behavior of the estimation error.Experiments on real-world datasets demonstrate the superiority and effectiveness of the proposed norms.