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On the Optimality of Operator-Like Wavelets for Sparse AR(1) Processes

Related publications (80)

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Enhanced change detection using nonlinear feature extraction

Devis Tuia, Giona Matasci

This paper presents an application of the kernel principal component analysis aiming at aligning optical images before the application of change detection techniques. The approach relies on the extraction of nonlinear features from a selected subset of pix ...

2012

Optimally Localized Wavelets and Smoothing Kernels

Kunal Narayan Chaudhury

It is well-known that the Gaussian functions and, more generally, their modulations-translations (the Gabor functions) have the unique property of being optimally localized in space and frequency in the sense of Heisenberg's uncertainty principle. In this ...

EPFL2011

A Dual-Tree Rational-Dilation Complex Wavelet Transform

Ilker Bayram

In this correspondence, we introduce a dual-tree rational-dilation complex wavelet transform for oscillatory signal processing. Like the short-time Fourier transform and the dyadic dual-tree complex wavelet transform, the introduced transform employs quadr ...

2011

Wavelets on graphs via spectral graph theory

Pierre Vandergheynst, Rémi Gribonval

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral deco ...

Elsevier2011

A Musically Motivated Mid-Level Representation for Pitch Estimation and Musical Audio Source Separation

When designing an audio processing system, the target tasks often influence the choice of a data representation or transformation. Low-level time-frequency representations such as the short-time Fourier transform (STFT) are popular, because they offer a me ...

2011

Steerable Pyramids and Tight Wavelet Frames in L_2(R^d)

Michaël Unser, Dimitri Nestor Alice Van De Ville

We present a functional framework for the design of tight steerable wavelet frames in any number of dimensions. The 2-D version of the method can be viewed as a generalization of Simoncelli's steerable pyramid that gives access to a larger palette of steer ...

Institute of Electrical and Electronics Engineers2011

Multiscale analysis of high resolution digital elevation models using the wavelet transform

Michaël Kalbermatten

At the end of the nineties the emergence of high resolution (1 m) digital elevation models (DEMs) settled the context of high precision geomorphological analysis. These new elevation models permitted to reveal structures that remained heretofore undetectab ...

EPFL2010

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

On the Shiftability of Dual-Tree Complex Wavelet Transforms

Michaël Unser, Kunal Narayan Chaudhury

The dual-tree complex wavelet transform (DT-ℂWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-ℂWT which, among other things, offers a direct explanation ...

IEEE2010

Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010