Publications by Lorenzo Granai

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On the Use of A Priori Information for Sparse Signal Approximations

Pierre Vandergheynst, Lorenzo Granai, Oscar Divorra Escoda

This report is the extension to the case of sparse approximations of our previous study on the effects of introducing a priori knowledge to solve the recovery of sparse representations when overcomplete dictionaries are used. Greedy algorithms and Basis Pu ...

2004

Sparse decomposition over multi-component redundant dictionaries

Pierre Vandergheynst, Lorenzo Granai

In many applications - such as compression, de-noising and source separation - a good and efficient signal representation is characterized by sparsity. This means that many coefficients are close to zero, while only few ones have a non-negligible amplitude ...

IEEE2004

Very low bit rate image coding using redundant dictionaries

Pierre Vandergheynst, Lorenzo Granai, Lorenzo Peotta

Very low bit rate image coding is an important problem regarding applications such as storage on low memory devices or streaming data on the internet. The state of the art in image compression is to use 2-D wavelets. The advantages of wavelet bases lie in ...

SPIE2003

Hybrid video coding using bi-dimensional matching pursuit

Pierre Vandergheynst, Lorenzo Granai, Lorenzo Peotta, Emilio Maggio

In this report we propose a new coding scheme based on the Matching Pursuit algorithm and exploiting some of the new features introduced by H.264 for motion estimation. Main points of this work are the design of a redundant dictionary suitable for coding d ...

2003

Ridgelet transform applied to motion compensated images

Pierre Vandergheynst, Lorenzo Granai

Wavelet transform is a powerful instrument in catching zero-dimensional singularities. Ridgelets are a powerful instrument in catching and representing mono-dimensional singularities in bidimensional space. In this paper we propose a hybrid video coder sch ...

SPIE2003

New Dictionary and Fast Atom Searching Methods for Matching Pursuit Representation of Displaced Frame Difference

Pascal Frossard, Pierre Vandergheynst, Lorenzo Granai

Matching pursuit decomposes a signal into a linear expansion of functions selected from a redundant dictionary, isolating the signal structures that are coherent with respect to a given dictionary. In this paper we focus on the Matching Pursuit representat ...

IEEE2002

A generalized Rate-Distortion limit for edge representation

Pierre Vandergheynst, Lorenzo Granai

This paper presents a rate-distortion analysis for a simple horizon edge image model. A quadtree with anisotropy and rotation is performed in this kind of image, giving a toy model for a non-linear adaptive coding technique, and its rate-distortion behavio ...

2002

R-D Analysis of Adaptive Edge Representations

Pierre Vandergheynst, Lorenzo Granai

This paper presents a Rate-Distortion analysis for a simple horizon edge image model. A quadtree with anisotropy and rotation is performed on this kind of image, giving a toy model for a non-linear adaptive coding technique, and its Rate-Distortion behavio ...

IEEE2002