Publications related to Fourier and wavelet transform analysis, a tool for visualising regular patterns in DNA

Correspondence principle between spherical and Euclidean wavelets

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the ...

2005

Generalized Biorthogonal Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9⁄7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by ...

SPIE2005

Stair climbing detection during daily physical activity using a miniature gyroscope

Kamiar Aminian, Anisoara Ionescu, Bijan Najafi, Brian Coley

A new method of monitoring physical activity that is able to detect walking upstairs using a miniature gyroscope attached to the shank is presented. Wavelet transformation, in conjunction with a simple kinematics model, was used to detect toe-off, heel-str ...

2005

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

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

Microscopy imaging often suffers from limited depth-of-focus. However, the specimen can be “optically sectioned” by moving the object along the optical axis; different areas appear in focus in different images. Extended depth-of-focus is a fusion algorithm ...

IEEE2004

Wavelets on the 2-Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We build wavelets on the 2-Hyperboloid. First, we define dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to

SO_0(1,2)

, we define a family of hyperbolic wavelets. The continuous wavelet transform (CW ...

2004

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

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

Microscopy imaging often suffers from limited depth-of-field. However, the specimen can be “optically sectioned” by moving the object along the optical axis. Then different areas appear in focus in different images. Extended depth-of-field is a fusion algo ...

Wiley-Liss2004

Wavelet and footprint sampling of signals with a finite rate of innovation

Martin Vetterli, Pier Luigi Dragotti

In this paper, we consider classes of not bandlimited signals, namely, streams of Diracs and piecewise polynomial signals, and show that these signals can be sampled and perfectly reconstructed using wavelets as sampling kernel. Due to the multiresolution ...

2004

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

Wavelet-based statistical analysis methods for fMRI are able to detect brain activity without smoothing the data. Typically, the statistical inference is performed in the wavelet domain by testing the t-values of each wavelet coefficient; subsequently, an ...

IEEE2004

Discrete Wavelet Frames on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this paper the Continuous Wavelet Transform on the sphere is exploited to build the asociated Discrete Wavelet Frames. First, the half-continuous frames, i.e. frames where the position remains a continuous variable, is presented and then the fully discr ...

EUSIPCO2004

Extended Depth-of-Field for Color Images in Light Microscopy: Image Fusion and 3D Visualization

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

Bright-field microscopy suffers from a relatively small depth-of-field. Typically, the specimen’s profile covers a range larger than the depth-of-field, and parts of the specimen that lie outside the object plane appear blurred. The specimen can be ‘scanne ...

2004

Fourier and wavelet transform analysis, a tool for visualising regular patterns in DNA

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Correspondence principle between spherical and Euclidean wavelets

Generalized Biorthogonal Daubechies Wavelets

Stair climbing detection during daily physical activity using a miniature gyroscope

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Wavelets on the 2-Hyperboloid

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

Wavelet and footprint sampling of signals with a finite rate of innovation

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

Discrete Wavelet Frames on the Sphere

Extended Depth-of-Field for Color Images in Light Microscopy: Image Fusion and 3D Visualization

Generalized Biorthogonal Daubechies Wavelets

Wavelet and footprint sampling of signals with a finite rate of innovation

Wavelets on the 2-Hyperboloid

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

Correspondence principle between spherical and Euclidean wavelets

Stair climbing detection during daily physical activity using a miniature gyroscope

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Discrete Wavelet Frames on the Sphere

Extended Depth-of-Field for Color Images in Light Microscopy: Image Fusion and 3D Visualization