Publications related to Generalized Biorthogonal Daubechies Wavelets

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007

Low-Rate Reduced Complexity Image Compression using Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) disco ...

2006

Wavelets on non-Euclidean manifolds

Iva Bogdanova Vandergheynst

This dissertation investigates wavelets as a multiscale tool on non-Euclidean manifolds. The growing importance of using non-Euclidean manifolds as a geometric model for data comes from the diversity of the data collected. In this work we mostly deal with ...

EPFL2006

Image Coding of 3D Volume Using Wavelet Transform for Fast Retrieval of 2D Images

Vijayaraghavan Thirumalai

An encoder/decoder system for 3D volumetric medical data is proposed. The system allows fast access to any 2D image by decoding only the relevant information from each subband image and thus provides minimum decoding time. This will be of immense use for t ...

2006

Exponential-Spline Wavelet Bases

Michaël Unser, Ildar Khalidov

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of

L _{ 2 }

, wit ...

IEEE2005

Generalized L-Spline Wavelet Bases

Michaël Unser, Thierry Blu, Ildar Khalidov

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

SPIE2005

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

Michaël Unser, Theo Lasser

The combination of wavelength multiplexing and spectral interferometry allows for the encoding of multidimensional information and its transmission over a mono-dimensional channel; for example, measurements of a surface's topography acquired through a mono ...

SPIE2005

Generalized Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the Daubechies wavelet family. The context is that of a non-stationary multiresolution analysis—i.e., a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. ...

IEEE2005

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

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

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

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

Generalized Biorthogonal Daubechies Wavelets

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A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Low-Rate Reduced Complexity Image Compression using Directionlets

Wavelets on non-Euclidean manifolds

Image Coding of 3D Volume Using Wavelet Transform for Fast Retrieval of 2D Images

Exponential-Spline Wavelet Bases

Generalized L-Spline Wavelet Bases

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

Generalized Daubechies Wavelets

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

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

Wavelets on non-Euclidean manifolds

Exponential-Spline Wavelet Bases

Image Coding of 3D Volume Using Wavelet Transform for Fast Retrieval of 2D Images

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

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

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Low-Rate Reduced Complexity Image Compression using Directionlets

Generalized L-Spline Wavelet Bases

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Generalized Daubechies Wavelets