Publications related to Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

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

Fast directional correlation on the sphere with steerable filters

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L stands for the ...

2006

Directionlets: Anisotropic Multidirectional representation with separable filtering

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensio ...

2006

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

From Differential Equations to the Construction of New Wavelet-Like Bases

Michaël Unser, Ildar Khalidov

In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the ...

IEEE2006

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

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

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

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Pierre Vandergheynst, Oscar Divorra Escoda

In this work, we study the effect of inserting spatially local temporal adaptivity to motion compensated frame adaptive transforms for video coding. Motion compensation aligns the temporal wavelet decomposition along motion trajectories. However, valid tra ...

2004

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

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

Fast directional correlation on the sphere with steerable filters

Directionlets: Anisotropic Multidirectional representation with separable filtering

Low-Rate Reduced Complexity Image Compression using Directionlets

From Differential Equations to the Construction of New Wavelet-Like Bases

Exponential-Spline Wavelet Bases

Generalized L-Spline Wavelet Bases

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

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

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Directionlets: Anisotropic Multidirectional representation with separable filtering

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

From Differential Equations to the Construction of New Wavelet-Like Bases

Fast directional correlation on the sphere with steerable filters

Low-Rate Reduced Complexity Image Compression using Directionlets

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

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

Exponential-Spline Wavelet Bases

Generalized L-Spline Wavelet Bases

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding