Related papers: Hybrid ABBA-GMRES for Unmatched Backprojectors in …
We propose inexact subspace iteration for solving high-dimensional eigenvalue problems with low-rank structure. Inexactness stems from low-rank compression, enabling efficient representation of high-dimensional vectors in a low-rank tensor…
Magnetic resonance imaging (MRI) can present multi-contrast images of the same anatomical structures, enabling multi-contrast super-resolution (SR) techniques. Compared with SR reconstruction using a single-contrast, multi-contrast SR…
Neural Radiance Fields (NeRFs) have shown impressive results for novel view synthesis when a sufficiently large amount of views are available. When dealing with few-shot settings, i.e. with a small set of input views, the training could…
The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to…
We propose a new family of subgradient- and gradient-based methods which converges with optimal complexity for convex optimization problems whose feasible region is simple enough. This includes cases where the objective function is…
Recent efforts in using 3D Gaussians for scene reconstruction and novel view synthesis can achieve impressive results on curated benchmarks; however, images captured in real life are often blurry. In this work, we analyze the robustness of…
A randomized Gram-Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization. The proposed process can be less computationally expensive than the classical Gram-Schmidt process while being at least…
An iterative method LSMR is presented for solving linear systems $Ax=b$ and least-squares problem $\min \norm{Ax-b}_2$, with $A$ being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is…
The High Energy X-ray telescope (HE) on-board the Hard X-ray Modulation Telescope (\textit{Insight}-HXMT) can serve as a wide Field of View (FOV) gamma-ray monitor with high time resolution ($\mu$s) and large effective area (up to thousands…
Purpose: Handheld gamma cameras with coded aperture collimators are under investigation for intraoperative imaging in nuclear medicine. Coded apertures are a promising collimation technique for applications such as lymph node localization…
Krylov subspace methods are among the most efficient solvers for large scale linear algebra problems. Nevertheless, classic Krylov subspace algorithms do not scale well on massively parallel hardware due to synchronization bottlenecks.…
Communication, i.e., data movement, is a critical bottleneck for the performance of classical Krylov subspace method solvers on modern computer architectures. Variants of these methods which avoid communication have been introduced, which,…
The GMRES method is used to solve sparse, non-symmetric systems of linear equations arising from many scientific applications. The solver performance within a single node is memory bound, due to the low arithmetic intensity of its…
Tomographic image sizes keep increasing over time and while the GPUs that compute the tomographic reconstruction are also increasing in memory size, they are not doing so fast enough to reconstruct the largest datasets. This problem is…
Many inverse problems and signal processing problems involve low-rank regularizers based on the nuclear norm. Commonly, proximal gradient methods (PGM) are adopted to solve this type of non-smooth problems as they can offer fast and…
Purpose: The expanded encoding model incorporates spatially- and time-varying field perturbations for correction during reconstruction. So far, these reconstructions have used the conjugate gradient method with early stopping used as…
A wide range of applications necessitates solving large-scale ill-posed problems contaminated by noise. Krylov subspace regularization methods are particularly advantageous in this context, as they rely solely on matrix-vector…
Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order execution often…
In this work, we propose new variants of Anderson acceleration and nonlinear GMRES for general fixed-point iterations, based on modified least-squares problems associated with the methods. To solve the underlying linear systems, we apply…
3D Gaussian Splatting (3DGS) has recently enabled real-time photorealistic rendering in compact scenes, but scaling to large urban environments introduces severe aliasing artifacts and optimization instability, especially under…