Related papers: Preconditioning filter bank decompositions using s…
The decomposition of large unitary matrices into smaller ones is important, because it provides ways to realization of classical and quantum information processing schemes. Today, most of the methods use planar meshes of tunable two-channel…
Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the…
In the companion paper, we proposed a concept of signal matched whitening filter bank and developed a time and order recursive, fast least squares algorithm for the same. Objective of part II of the paper is two fold: first is to define a…
Tight framelets on a smooth and compact Riemannian manifold $\mathcal{M}$ provide a tool of multiresolution analysis for data from geosciences, astrophysics, medical sciences, etc. This work investigates the construction, characterizations,…
So far there has not been paid attention to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames, in finite dimensional Hilbert spaces.…
We train a bank of complex filters that operates on the raw waveform and is fed into a convolutional neural network for end-to-end phone recognition. These time-domain filterbanks (TD-filterbanks) are initialized as an approximation of…
We design a critically-sampled compact-support biorthogonal transform for graph signals, via graph filterbanks. Instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations, the…
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…
Sparse representation of images under certain transform domain has been playing a fundamental role in image restoration tasks. One such representative method is the widely used wavelet tight frame systems. Instead of adopting fixed filters…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
Key to successfully deal with complex contemporary datasets is the development of tractable models that account for the irregular structure of the information at hand. This paper provides a comprehensive and unifying view of several…
The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…
We study the feasibility of short finite impulse response (FIR) synthesis for perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis banks, we focus on the one with the minimum filter length. For filter banks with…
Group lifting structures are introduced to provide an algebraic framework for studying lifting factorizations of two-channel perfect reconstruction finite-impulse-response (FIR) filter banks. The lifting factorizations generated by a group…
Classical image filters, such as those for averaging or differencing, are carefully normalized to ensure consistency, interpretability, and to avoid artifacts like intensity shifts, halos, or ringing. In contrast, convolutional filters…
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…
Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process…
In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available.…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…