Related papers: A new shift strategy for the implicitly restarted …

In this paper, we propose an implicit gradient descent algorithm for the classic $k$-means problem. The implicit gradient step or backward Euler is solved via stochastic fixed-point iteration, in which we randomly sample a mini-batch…

Differentially private (stochastic) gradient descent is the workhorse of DP private machine learning in both the convex and non-convex settings. Without privacy constraints, second-order methods, like Newton's method, converge faster than…

A recently introduced framework of semidiscretisations for hyperbolic conservation laws known as correction procedure via reconstruction (CPR, also known as flux reconstruction) is considered in the extended setting of summation-by-parts…

High-resolution magnetic resonance imaging (MRI) is essential in clinical diagnosis. However, its long acquisition time remains a critical issue. Parallel imaging (PI) is a common approach to reduce acquisition time by periodically skipping…

We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce…

An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…

In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…

Magnetic Resonance Imaging (MRI) is widely used in clinical practice, but suffered from prolonged acquisition time. Although deep learning methods have been proposed to accelerate acquisition and demonstrate promising performance, they rely…

3D reconstruction of high-resolution target remains a challenge task due to the large memory required from the large input image size. Recently developed learning based algorithms provide promising reconstruction performance than…

We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields.…

Recovering high quality surfaces from noisy triangulated surfaces is a fundamental important problem in geometry processing. Sharp features including edges and corners can not be well preserved in most existing denoising methods except the…

We propose two new algebraic reconstruction techniques based on Kaczmarz's method that produce a regularized solution to noisy tomography problems. Tomography problems exhibit semi-convergence when iterative methods are employed, and the…

Parallel imaging is a widely-used technique to accelerate magnetic resonance imaging (MRI). However, current methods still perform poorly in reconstructing artifact-free MRI images from highly undersampled k-space data. Recently, implicit…

We present an algorithm for low rank decomposition of tensors of any symmetry type, from fully asymmetric to fully symmetric. It recovers the decomposition one summand at a time via the higher-order power method. This approach is known to…

This work presents a generalized period decomposition approach, significantly improving the practical reliability of Shor's quantum factoring algorithm. Although Shor's algorithm theoretically enables polynomial-time integer factorization,…

Reconstructing high-quality magnetic resonance images (MRI) from undersampled raw data is of great interest from both technical and clinical point of views. To this date, however, it is still a mathematically and computationally challenging…

In this paper, we propose a new algorithm to make a novel spatial image transformation. The proposed approach aims to reduce the bit depth used for image storage. The basic technique for the proposed transformation is based of the modulus…

The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…

We present Hybrid-CSR, a geometric deep-learning model that combines explicit and implicit shape representations for cortical surface reconstruction. Specifically, Hybrid-CSR begins with explicit deformations of template meshes to obtain…

Recent medical image segmentation methods apply implicit neural representation (INR) to the decoder for achieving a continuous coordinate decoding to tackle the drawback of conventional discrete grid-based data representations. However, the…