Publications related to Discrete-Time Wavelet Extrema Representation - Design and Consistent Reconstruction

Sensing and Recovery under Sparsity Constraints

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

A Time-Domain Wavelet-Based Approach for Fluorescence Diffuse Optical Tomography

Michaël Unser, Chandra Sekhar Seelamantula

Purpose: In the context of fluorescence diffuse optical tomography, determining the optimal way to exploit the time-resolved information has been receiving much attention and different features of the time-resolved signals have been introduced. In this art ...

AAPM2010

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

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-value ...

Institute of Electrical and Electronics Engineers2009

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Michaël Unser, Dimitri Nestor Alice Van De Ville

Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-ba ...

SPIE2009

Fractional Laplacian Pyramids

Michaël Unser, Ricard Delgado Gonzalo, Pouya Dehghani Tafti

We provide an extension of the L-2-spline pyramid (Unser et al., 1993) using polyharmonic splines. We analytically prove that the corresponding error pyramid behaves exactly as a multi-scale Laplace operator. We use the multiresolution properties of polyha ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

Robust single-view geometry and motion reconstruction

Mark Pauly, Hao Li

We present a framework and algorithms for robust geometry and motion reconstruction of complex deforming shapes. Our method makes use of a smooth template that provides a crude approximation of the scanned object and serves as a geometric and topological p ...

2009

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gr ...

Institute of Electrical and Electronics Engineers2008

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

Michaël Unser, Dimitri Nestor Alice Van De Ville, Ildar Khalidov

Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an

\ell_{ 1 }

-regularization constraint, which favors sparse solutions in the wavelet dom ...

Institute of Electrical and Electronics Engineers2008

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Michaël Unser, Dimitri Nestor Alice Van De Ville

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

Institute of Electrical and Electronics Engineers2008

Discrete-Time Wavelet Extrema Representation - Design and Consistent Reconstruction

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Sensing and Recovery under Sparsity Constraints

A Time-Domain Wavelet-Based Approach for Fluorescence Diffuse Optical Tomography

Wavelet Steerability and the Higher-Order Riesz Transform

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Fractional Laplacian Pyramids

Robust single-view geometry and motion reconstruction

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

A Time-Domain Wavelet-Based Approach for Fluorescence Diffuse Optical Tomography

Wavelet Steerability and the Higher-Order Riesz Transform

Robust single-view geometry and motion reconstruction

Sensing and Recovery under Sparsity Constraints

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Fractional Laplacian Pyramids

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression