Related papers: On Description of Dual Frames
In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing,…
This paper aims to characterize the optimal frame for phase retrieval, defined as the frame whose condition number for phase retrieval attains its minimal value. In the context of the two-dimensional real case, we reveal the connection…
In the present paper, some sufficient and necessary conditions for two frames $\Phi=(\varphi_n)_n$ and $\Psi=(\psi_n)_n$ under which they are approximately or generalized dual frames are determined depending on the properties of their…
Compressed sensing with sparse frame representations is seen to have much greater range of practical applications than that with orthonormal bases. In such settings, one approach to recover the signal is known as $\ell_1$-analysis. We…
Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new…
Given a neighborhood graph representation of a finite set of points $x_i\in\mathbb{R}^d,i=1,\ldots,n,$ we construct a frame (redundant dictionary) for the space of real-valued functions defined on the graph. This frame is adapted to the…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
This paper studies properties of dual probabilistic frames -- in particular in relation to redundancy -- and introduces both approximately dual probabilistic frames and pseudo-dual probabilistic frames. We show that the canonical dual…
Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may…
We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
A theory, graphical notation, mathematical calculus and implementation for finding whether two given expressions can, at execution time, denote references attached to the same object. Intended as the basis for a comprehensive solution to…
This paper looks into the problem of pedestrian tracking using a monocular, potentially moving, uncalibrated camera. The pedestrians are located in each frame using a standard human detector, which are then tracked in subsequent frames.…
The technique requires the epipolar geometry to be pre-estimated between each image pair. It exploits the constraints which the camera movement implies, in order to apply a closed-form correction to the parameters of the input affinities.…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
This paper studies probabilistic dual frames and the associated dual frame potentials from the perspective of optimal mass transport. The main contribution of this work shows that given a probabilistic frame, its associated dual frame…
We study the problem of identifying the parameters of a linear system from its response to multiple unknown waveforms. We assume that the system response is a scaled superposition of time-delayed and frequency-shifted versions of the…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual…
We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a…