Related papers: Excess of Fusion Frames: A Comprehensive Approach
Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the…
A significant challenge in object detection is accurate identification of an object's position in image space, whereas one algorithm with one set of parameters is usually not enough, and the fusion of multiple algorithms and/or parameters…
In this paper, we develop an online basis enrichment method with the mortar mixed finite element method, using the oversampling technique, to solve for flow problems in highly heterogeneous media. We first compute a coarse grid solution…
We study the duality of reconstruction systems, which are $g$-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are…
A complete theory of overmeasurement by measuring refinements of observables is presented. It encompasses a wider set of functions of observ- ables (coarsenings) . Thus the theory has a broad potential application.It is applied to a…
We show that the frame measure function of a frame in certain reproducing kernel Hilbert spaces on metric measure spaces is given by the reciprocal of the Beurling density of its index set. In addition, we show that each such frame with…
In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…
We give some new methods for perfect reconstruction from frame and sampling erasures in finitely many steps. By bridging an erasure set we mean replacing the erased Fourier coefficients of a function with respect to a frame by appropriate…
In LiDAR-based 3D detection, history point clouds contain rich temporal information helpful for future prediction. In the same way, history detections should contribute to future detections. In this paper, we propose a detection enhancement…
K-fusion frames are generalizations of fusion frames in frame theory. This article characterizes various kinds of property of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed.
Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
Cross view feature fusion is the key to address the occlusion problem in human pose estimation. The current fusion methods need to train a separate model for every pair of cameras making them difficult to scale. In this work, we introduce…
We resolve a longstanding open problem by reformulating the Grassmannian fusion frames to the case of mixed dimensions and show that this satisfies the proper properties for the problem. In order to compare elements of mixed dimension, we…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
The prime focus of this paper is the study of optimal duals of a given finite frame as well as optimal dual pairs, in the context of probability modelled erasures of frame coefficients. We characterize optimal dual frames (and dual pairs)…
Redundancy is the qualitative property which makes Hilbert space frames so useful in practice. However, developing a meaningful quantitative notion of redundancy for infinite frames has proven elusive. Though quantitative candidates for…
This work developes a quantitative framework for describing the overcompleteness of a large class of frames. A previous paper introduced notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and…
We discuss the concepts of pseudo-dual frames and approximately dual frames, and illuminate their relationship to classical frames. Approximately dual frames are easier to construct than the classical dual frames, and might be tailored to…
The inherent heavy computation of deep neural networks prevents their widespread applications. A widely used method for accelerating model inference is quantization, by replacing the input operands of a network using fixed-point values.…