Related papers: Expansions from frame coefficients with erasures
One of a key problems in signal reconstruction process with the use of frames is to find a dual frame. Typically, a canonical dual frame is used. However, there are many applications where this choice appears to be unfortunate. Due to that…
Fusion frames are extensively studied due to their effectiveness in recovering signals from large-scale data. They are applicable in distributed processing, wireless sensor networks, and packet encoding systems due to their robustness and…
We consider the recovery of a continuous domain piecewise constant image from its non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero levelset of…
This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination…
We describe a hidden surface removal algorithm for two-dimensional layered scenes built from arbitrary primitives, particularly suited to interaction and animation in rich scenes (for example, in illustration). The method makes use of a…
Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging. For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be…
In this paper we study the compressive sensing effects on 2D signals exhibiting sparsity in 2D DFT domain. A simple algorithm for reconstruction of randomly under-sampled data is proposed. It is based on the analytically determined…
We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of the Fourier phase information, this problem is ill-posed. Therefore,…
Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real or complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…
Sparse signal recovery algorithms like sparse Bayesian learning work well but the complexity quickly grows when tackling higher dimensional parametric dictionaries. In this work we propose a novel Bayesian strategy to address the two…
We study sparsity and spectral properties of dual frames of a given finite frame. We show that any finite frame has a dual with no more than $n^2$ non-vanishing entries, where $n$ denotes the ambient dimension, and that for most frames no…
This paper extends the concepts of Minimal Redundancy Condition (MRC) and robustness of erasures for infinite frames in Hilbert spaces. We begin by establishing a comprehensive framework for the MRC, emphasizing its importance in ensuring…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing…
Frame theory provides a robust method for recovering vectors in a Hilbert space from inner product data, though the associated decomposition formula can be computationally demanding. We relax the frame condition by studying sequences that…
The paper explores the problem of \emph{spectral compressed sensing}, which aims to recover a spectrally sparse signal from a small random subset of its $n$ time domain samples. The signal of interest is assumed to be a superposition of $r$…
The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate…