Related papers: Enhanced Multi-Resolution Analysis for Multi-Dimen…
In this article we consider the extension of the (L)SIAC-MRA enhancement procedure to nonuniform meshes. We demonstrate that error reduction can be obtained on perturbed quadrilateral and Delaunay meshes, and investigate the effect of…
Analyzing high-dimensional data presents challenges due to the "curse of dimensionality'', making computations intensive. Dimension reduction techniques, categorized as linear or non-linear, simplify such data. Non-linear methods are…
Multiresolution Analysis (MRA) is a mathematical method that is based on working on a problem at different scales. One of its applications is medical imaging where processing at multiple scales, based on the concept of Gaussian and…
Heuristic search-based planning techniques are commonly used for motion planning on discretized spaces. The performance of these algorithms is heavily affected by the resolution at which the search space is discretized. Typically a fixed…
Recent technical advances in collecting spatial data have been increasing the demand for methods to analyze large spatial datasets. The statistical analysis for these types of datasets can provide useful knowledge in various fields.…
Over the past few decades there has been a strong effort towards the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters for Discontinuous Galerkin (DG) methods, designed to increase the smoothness and improve the…
We propose a novel deep learning framework for fast prediction of boundaries of two-dimensional simply connected domains using wavelets and Multi Resolution Analysis (MRA). The boundaries are modelled as (piecewise) smooth closed curves…
We propose a new approach for 3D shape matching of deformable human shapes. Our approach is based on the joint adoption of three different tools: an intrinsic spectral matching pipeline, a morphable model, and an extrinsic details…
Heuristic search-based motion planning algorithms typically discretise the search space in order to solve the shortest path problem. Their performance is closely related to this discretisation. A fine discretisation allows for better…
We proposed a novel dense line spectrum super-resolution algorithm, the DMRA, that leverages dynamical multi-resolution of atoms technique to address the limitation of traditional compressed sensing methods when handling dense point-source…
Transformers have emerged as a preferred model for many tasks in natural langugage processing and vision. Recent efforts on training and deploying Transformers more efficiently have identified many strategies to approximate the…
Multiple-input multiple-output (MIMO) radar has waveform diversity and large spatial degrees of freedom (DoFs), making it attractive for high-resolution sensing. Scaling MIMO radar to massive arrays can further improve sensing performance,…
Low-Rank Adaptation (LoRA) has emerged as a dominant method in Parameter-Efficient Fine-Tuning (PEFT) for large language models, which augments the transformer layer with one down-projection $A$ and one up-projection $B$. However, LoRA's…
Despite remarkable progress, existing multimodal large language models (MLLMs) are still inferior in granular visual recognition. Contrary to previous works, we study this problem from the perspective of image resolution, and reveal that a…
Large pre-trained models, such as large language models (LLMs), present significant resource challenges for fine-tuning due to their extensive parameter sizes, especially for applications in mobile systems. To address this, Low-Rank…
Low-Rank Adaptation (LoRA) has gained popularity for fine-tuning large foundation models, leveraging low-rank matrices $\mathbf{A}$ and $\mathbf{B}$ to represent weight changes (i.e., $\Delta \mathbf{W} = \mathbf{B} \mathbf{A}$). This…
The multi-resolution approximation (MRA) of Gaussian processes was recently proposed to conduct likelihood-based inference for massive spatial data sets. An advantage of the methodology is that it can be parallelized. We implemented the MRA…
Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…
The multi-reference alignment (MRA) problem entails estimating an image from multiple noisy and rotated copies of itself. If the noise level is low, one can reconstruct the image by estimating the missing rotations, aligning the images, and…
Structured Adaptive Mesh Refinement (Structured AMR) enables simulations to adapt the domain resolution to save computation and storage, and has become one of the dominant data representations used by scientific simulations; however,…