Related papers: Preconditioning filter bank decompositions using s…

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…

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…

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.…

This paper extends the existing theory of perfect reconstruction two-channel filter banks from bipartite graphs to non-bipartite graphs. By generalizing the concept of downsampling/upsampling we establish the frame of two-channel filter…

A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…

Signal reconstruction from magnitude-only measurements presents a long-standing problem in signal processing. In this contribution, we propose a phase (re)construction method for filter banks with uniform decimation and controlled frequency…

We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…

Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data,…

Dense prediction tasks have enjoyed a growing complexity of encoder architectures, decoders, however, have remained largely the same. They rely on individual blocks decoding intermediate feature maps sequentially. We introduce banks, shared…

Many audio applications rely on filter banks (FBs) to analyze, process, and re-synthesize sounds. To approximate the auditory frequency resolution in the signal chain, some applications rely on perceptually motivated FBs, the gammatone FB…

We propose two-channel critically-sampled filter banks for signals on undirected graphs that utilize spectral domain sampling. Unlike conventional approaches based on vertex domain sampling, our transforms have the following desirable…

This paper explores the perfect reconstruction property of filter banks based on Ramanujan sums and their applications in signal recovery. Originally introduced by Srinivasa Ramanujan, Ramanujan sums serve as powerful tools for extracting…

This paper addresses the important problem of reconstructing a signal from multiple multirate observations. The observations are modeled as the output of an analysis bank, and time-domain analysis is carried out to design an optimal FIR…

We present a novel method to provide efficient and highly detailed reconstructions. Inspired by wavelets, we learn a neural field that decompose the signal both spatially and frequency-wise. We follow the recent grid-based paradigm for…

Regularization techniques are widely used to improve the generality, robustness, and efficiency of deep convolutional neural networks (DCNNs). In this paper, we propose a novel approach of regulating DCNN convolutional kernels by a…

This paper proposes a class of $M$-channel spectral graph filter banks with a symmetric structure, that is, the transform has sampling operations and spectral graph filters on both the analysis and synthesis sides. The filter banks achieve…

Frame is the corner stone for designing decomposition and reconstruction operations in signal processing. Famous frames include wavelets, curvelets,and Gabor. A celebrated result indicates that if a synthesis frame is chosen for…

We propose a generalized convolutional neural network (CNN) architecture that first decomposes the input signal into subbands by an adaptive filter bank structure, and then uses convolutional layers to extract features from each subband…

We propose a simple, interpretable framework for solving a wide range of image reconstruction problems such as denoising and deconvolution. Given a corrupted input image, the model synthesizes a spatially varying linear filter which, when…

The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…