Accelerated Dynamic MRI Using Kernel-Based Low Rank Constraint.

We present a novel reconstruction method for dynamic MR images from highly under-sampled k-space measurements. The reconstruction problem is posed as spectrally regularized matrix recovery problem, where kernel-based low rank constraint is employed to effectively utilize the non-linear correlations between the images in the dynamic sequence. Unlike other kernel-based methods, we use a single-step regularized reconstruction approach to simultaneously learn the kernel basis functions and the weights. The objective function is optimized using variable splitting and alternating direction method of multipliers. The framework can seamlessly handle additional sparsity constraints such as spatio-temporal total variation. The algorithm performance is evaluated on a numerical phantom and in vivo data sets and it shows significant improvement over the comparison methods.

Tracking using motion estimation with physically motivated inter-region constraints.

We propose a method for tracking structures (e.g., ventricles and myocardium) in cardiac images (e.g., magnetic resonance) by propagating forward in time a previous estimate of the structures using a new physically motivated motion estimation scheme. Our method estimates motion by regularizing only within structures so that differing motions among different structures are not mixed. It simultaneously satisfies the physical constraints at the interface between a fluid and a medium that the normal component of the fluid's motion must match the normal component of the medium's motion and the No-Slip condition, which states that the tangential velocity approaches zero near the interface. We show that these conditions lead to partial differential equations with Robin boundary conditions at the interface, which couple the motion between structures. We show that propagating a segmentation across frames using our motion estimation scheme leads to more accurate segmentation than traditional motion estimation that does not use physical constraints. Our method is suited to interactive segmentation, prominently used in commercial applications for cardiac analysis, where segmentation propagation is used to predict a segmentation in the next frame. We show that our method leads to more accurate predictions than a popular and recent interactive method used in cardiac segmentation.

Kernel map compression for speeding the execution of kernel-based methods.

The use of Mercer kernel methods in statistical learning theory provides for strong learning capabilities, as seen in kernel principal component analysis and support vector machines. Unfortunately, after learning, the computational complexity of execution through a kernel is of the order of the size of the training set, which is quite large for many applications. This paper proposes a two-step procedure for arriving at a compact and computationally efficient execution procedure. After learning in the kernel space, the proposed extension exploits the universal approximation capabilities of generalized radial basis function neural networks to efficiently approximate and replace the projections onto the empirical kernel map used during execution. Sample applications demonstrate significant compression of the kernel representation with graceful performance loss.

Buphthalmos in the setting of persistent hyperplastic primary vitreous cataract.

PURPOSE: To report a case of unilateral persistent hyperplastic primary vitreous cataract presenting with ipsilateral buphthalmos. DESIGN: Retrospective case report. METHODS: The patient chart was reviewed, and a relevant literature search was performed. RESULTS: A four-month-old child presented with persistent hyperplastic primary vitreous cataract in the right eye and ipsilateral buphthalmos with no discernable angle abnormalities. He underwent lensectomy, anterior vitrectomy, and limited transscleral diode cyclodestruction in the right eye. CONCLUSIONS: This appears to be the first report of buphthalmos presenting with unilateral persistent hyperplastic primary vitreous. Despite two comorbidities, the patient has thus far responded well to initial treatment and visual rehabilitation.