Related papers: Low-Coherence Frames from Group Fourier Matrices
Inspired by the concept of coherent frozen waves, this paper introduces one possible theoretical framework of its partially coherent version, a frozen spatial coherence, in which a desired two-point correlation structure of an optical field…
Weight optimization of frame structures with continuous cross-section parametrization is a challenging non-convex problem that has traditionally been solved by local optimization techniques. Here, we exploit its inherent semi-algebraic…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
We introduce a general technique to construct tight fusion frames with prescribed symmetries. Applying this technique with a prescription for "all the symmetries", we construct a new family of equi-isoclinic tight fusion frames (EITFFs),…
Tight wavelet frames are computationally and theoretically attractive, but most existing multivariate constructions have various drawbacks, including low vanishing moments for the wavelets, or a large number of wavelet masks. We further…
While most existing sparse recovery results allow only minimal structure within the measurement scheme, many practical problems possess significant structure. To address this gap, we present a framework for structured measurements that are…
In this work, we propose a joint collaboration-compression framework for sequential estimation of a random vector parameter in a resource constrained wireless sensor network (WSN). Specifically, we propose a framework where the local…
We study the properties of a set of vectors called tight frames that obtained as the orthogonal projection of some orthonormal basis of $\R^n$ onto $\R^k.$ We show that a set of vectors is a tight frame if and only if the set of all cross…
A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that…
In this paper we combine many of the standard and more recent algebraic techniques for testing isomorphism of finite groups (GpI) with combinatorial techniques that have typically been applied to Graph Isomorphism. In particular, we show…
Decoherence-free subsystems have been successfully developed as a tool to preserve fragile quantum information against noises. In this letter, we develop a structure theory for decoherence-free subsystems. Based on it, we present an…
The quantum mechanical harmonic oscillator Hamiltonian generates a one-parameter unitary group W(\theta) in L^2(R) which rotates the time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When W(\theta) is applied to any…
We develop a new compressive sensing (CS) inversion algorithm by utilizing the Gaussian mixture model (GMM). While the compressive sensing is performed globally on the entire image as implemented in our lensless camera, a low-rank GMM is…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
In the present work we introduce a unified framework that allows for the very first systematic construction of symmetric resonance-based integrators to approximate a wide class of nonlinear dispersive equations at low-regularity. The…
In this paper we propose a tool for high-dimensional approximation based on trigonometric polynomials where we allow only low-dimensional interactions of variables. In a general high-dimensional setting, it is already possible to deal with…
Mechanical vibration monitoring often requires high sampling rates and generates large data volumes, posing challenges for storage, transmission, and power efficiency. Compressive Sensing (CS) offers a promising approach to overcome these…
We study the rigidity properties of Grassmannian frames: basis-like sets of unit vectors that correspond to optimal Grassmannian line packings. It is known that Grassmannian frames characterized by the Welch bound must satisfy the…