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Toward sparse and geometry adapted video approximations

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The perception that we have about the world is influenced by elements of diverse nature. Indeed humans tend to integrate information coming from different sensory modalities to better understand their environment. Following this observation, scientists hav ...

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Mohammadjavad Faraji

In this report we extend the ideas behind classical multiscale signal processing techniques in order to analyze data residing on graphs. In particular, we extend the notions of filtering, downsampling, and upsampling to functions defined on graphs. We then ...

2011

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Martin Vetterli, Yue Lu

Spectral factorization is a classical tool in signal processing and communications. It also plays a critical role in X-ray crystallography, in the context of phase retrieval. In this work, we study the problem of sparse spectral factorization, aiming to re ...

2011

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Pascal Frossard, Ivana Tosic, Dimitri Palaz

This paper proposes a framework for stereo image coding with effective representation of geometry in 3D scenes. We propose a joint sparse approximation framework for pairs of perspective images that are represented as linear expansions of atoms selected fr ...

2011

Guaranteed recovery of a low-rank and joint-sparse matrix from incomplete and noisy measurements

Pierre Vandergheynst, Mohammad Golbabaee

Assume a multichannel data matrix, which due to the column-wise dependencies, has low-rank and joint-sparse representation. This matrix wont have many degrees of freedom. Enormous developments over the last decade in areas of compressed sensing and low-ran ...

2011

Compressive sensing meets game theory

Volkan Cevher, Sina Jafarpour

We introduce the Multiplicative Update Selector and Estimator (MUSE) algorithm for sparse approximation in under-determined linear regression problems. Given ƒ = Φα* + μ, the MUSE provably and efficiently finds a k-sparse vector α̂ such that ∥Φα̂ − ƒ∥∞ ≤ ∥ ...

IEEE2011

A procedure based on proper orthogonal decomposition for time-frequency analysis of time series

Giacomo Valerio Iungo

A procedure for time-frequency analysis of time series is described, which is mainly inspired by singular-spectrum analysis, but it presents some modifications that allow checking the convergence of the results and extracting the detected spectral componen ...

Springer Verlag2011

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In this paper we present a novel nonlinear video diffusion approach based on the fusion of information in audio and video channels. Both modalities are efficiently combined into a diffusion coefficient that integrates the basic assumption in this domain, i ...

Institute of Electrical and Electronics Engineers2011

Sensing and Recovery under Sparsity Constraints

Ali Hormati

Popular transforms, like the discrete cosine transform or the wavelet transform, owe their success to the fact that they promote sparsity. These transforms are capable of extracting the structure of a large class of signals and representing them by a few t ...

EPFL2010

Sparse Image Representation by Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

Despite the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation are limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertic ...

Elsevier2010