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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…
An important issue with oversampled FIR analysis filter banks (FBs) is to determine inverse synthesis FBs, when they exist. Given any complex oversampled FIR analysis FB, we first provide an algorithm to determine whether there exists an…
This paper considers the reconstruction of digital complex baseband signals from M-periodically nonuniformly sampled real bandpass signals. With such a sampling, bandpass signals with arbitrary frequency locations can be sampled and…
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…
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…
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…
We turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks), all filters have equal norm, and the essential features of the…
We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original…
A new method for designing non-uniform filter-banks for acoustic echo cancellation is proposed. In the method, the analysis prototype filter design is framed as a convex optimization problem that maximizes the signal-to-alias ratio (SAR) in…
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…
In 2D multi-slice magnetic resonance (MR) acquisition, the through-plane signals are typically of lower resolution than the in-plane signals. While contemporary super-resolution (SR) methods aim to recover the underlying high-resolution…
In this paper, we define a concept of signal matched multirate whitening filter bank which provides an optimum coding gain. This is achieved by whitening the outputs, of the analysis filter bank, within as well as across the channels, by…
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…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of…
We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
In this paper, we propose the construction of critically sampled perfect reconstruction two-channel filterbanks on arbitrary undirected graphs.Inspired by the design of graphQMF proposed in the literature, we propose a general ``spectral…
We investigate time encoding as an alternative method to classical sampling, and address the problem of reconstructing classes of non-bandlimited signals from time-based samples. We consider a sampling mechanism based on first filtering the…
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…