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Given a lowpass filter, finding a dual lowpass filter is an essential step in constructing non-redundant wavelet filter banks. Obtaining dual lowpass filters is not an easy task. In this paper, we introduce a new method called committee…
A multivariate biorthogonal wavelet system can be obtained from a pair of multivariate biorthogonal refinement masks in Multiresolution Analysis setup. Some multivariate refinement masks may be decomposed into lower dimensional refinement…
Interpolatory filters are of great interest in subdivision schemes and wavelet analysis. Due to the high-order linear-phase moment property, interpolatory refinement filters are often used to construct wavelets and framelets with high-order…
In this paper, we present a new method for designing wavelet filter banks for any dilation matrices and in any dimension. Our approach utilizes extended Laplacian pyramid matrices to achieve this flexibility. By generalizing recent tight…
We introduce a method for high-quality 3D reconstruction from multi-view images. Our method uses a new point-based representation, the regularized dipole sum, which generalizes the winding number to allow for interpolation of per-point…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
Constructing tight wavelet filter banks with prescribed directions is challenging. This paper presents a systematic method for designing a tight wavelet filter bank, given any prescribed directions. There are two types of wavelet filters in…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
We introduce a fast algorithm for generating long self-affine profiles. The algorithm, which is based on the fast wavelet transform, is faster than the conventional Fourier filtering algorithm. In addition to increased performance for large…
For any symmetry group $H$ and any appropriate matrix dilation we give an explicit method for the construction of $H$-symmetric refinable interpolatory refinable masks which satisfy sum rule of arbitrary order $n$. For each such mask we…
Decomposing discrete signals such as images into components is vital in many applications, and this paper propose a framework to produce filtering banks to accomplish this task. The framework is an equation set which is ill-posed, and thus…
It is of interest to study a wavelet system with a minimum number of generators. It has been showed by X. Dai, D. R. Larson, and D. M. Speegle in [11] that for any $d\times d$ real-valued expansive matrix M, a homogeneous orthonormal…
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…
Cell-free massive MIMO systems consist of many distributed access points with simple components that jointly serve the users. In millimeter wave bands, only a limited set of predetermined beams can be supported. In a network that…
For a given symmetric refinable mask obeying the sum rule of order $n$, an explicit method is suggested for the construction of mutually symmetric almost frame-like wavelet system providing approximation order $n$. A transformation based on…
A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function.…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
We reconsider the problem of joint power control and beamforming design to maximize the weighted sum rate in large and potentially cell-free massive MIMO networks. In contrast to the available short-term methods, where an iterative…
We here use notions from the theory linear shift-invariant dynamical systems to provide an easy-to-compute characterization of all rational wavelet filters. For a given N bigger or equql to 2, the number of inputs, the construction is based…
The volume of data and the velocity with which it is being generated by com- putational experiments on high performance computing (HPC) systems is quickly outpacing our ability to effectively store this information in its full fidelity.…