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This paper presents a multiscale decomposition algorithm. Unlike standard wavelet transforms, the proposed operator is both linear and shift invariant. The central idea is to obtain shift invariance by averaging the aligned wavelet…
This paper expands on the previously described reflectionless filters - that is, filters having, in principle, identically-zero reflection coefficient at all frequencies - by introducing a wide variety of new reflectionless structures that…
The 2-D discrete wavelet transform (DWT) can be found in the heart of many image-processing algorithms. Until recently, several studies have compared the performance of such transform on various shared-memory parallel architectures,…
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…
This article describes a series of new results outlining equivalences between certain "rewirings" of filterbank system block diagrams, and the corresponding actions of convolution, modulation, and downsampling operators. This gives rise to…
The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…
Like the continous shearlet transform and their relatives, discrete transformations based on the interplay between several filterbanks with anisotropic dilations provide a high potential to recover directed features in two and more…
In this work, a scalable and modular architecture for massive MIMO base stations with distributed processing is proposed. New antennas can readily be added by adding a new node as each node handles all the additional involved processing.…
This work introduces a wavelet neural network to learn a filter-bank specialized to fit non-stationary signals and improve interpretability and performance for digital signal processing. The network uses a wavelet transform as the first…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
The field of molecular programming allows for the programming of the structure and behavior of matter at the molecular level, even to the point of encoding arbitrary computation. However, current approaches tend to be wasteful in terms of…
The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a…
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.…
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…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
In this paper, we introduce several new schemes for calculation of discrete wavelet transforms of images. These schemes reduce the number of steps and, as a consequence, allow to reduce the number of synchronizations on parallel…
In this paper a two channel paraunitary filter bank is proposed, which is based on linear canonical transform, instead of discrete Fourier transform. Input-output relation for such a filter bank are derived in terms of polyphase matrices…
Perfect reconstruction filter banks can be used to generate a variety of wavelet bases. Using IIR linear phase filters one can obtain symmetry properties for the wavelet and scaling functions. In this paper we describe all possible IIR…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
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…