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Wavelets: approximation and compression--a review

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Data compression on the sphere

Yves Wiaux, Jason Douglas McEwen

Large data-sets defined on the sphere arise in many fields. In particular, recent and forthcoming observations of the anisotropies of the cosmic microwave background (CMB) made on the celestial sphere contain approximately three and fifty mega-pixels respe ...

Indian Academy of Sciences2011

Sparse Image Representation by Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

Despite the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation are limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertic ...

Elsevier2010

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

Space-frequency quantization for image compression with directionlets

Martin Vetterli, Vladan Velisavljevic

The standard separable 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 efficiently capture 1-D discontinuities, like edges or contours. ...

2007

Image compression using an edge adapted redundant dictionary and wavelets

Pierre Vandergheynst, Lorenzo Granai, Lorenzo Peotta

Low bit rate image coding is an important problem regarding applications such as storage on low memory devices or streaming data on the internet. The state of the art in image compression is to use 2-D wavelets. The advantages of wavelet bases lie in their ...

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

Directionlets

Vladan Velisavljevic

Efficient representation of geometrical information in images is very important in many image processing areas, including compression, denoising and feature extraction. However, the design of transforms that can capture these geometrical features and repre ...

EPFL2005

Video Coding with Motion-Compensated Lifted Wavelet Transforms

This article explores the efficiency of motion-compensated three-dimensional transform coding, a compression scheme that employs a motion-compensated transform for a group of pictures. We investigate this coding scheme experimentally and theoretically. The ...

2004

Geometrical Image Denoising Using Quadtree Segmentation

Martin Vetterli, Rahul Shukla

We propose a quadtree segmentation based denoising algo- rithm, which attempts to capture the underlying geometrical structure hidden in real images corrupted by random noise. The algorithm is based on the quadtree coding scheme pro- posed in our earlier w ...

2004

Rate-distortion optimized geometrical image processing

Rahul Shukla

Since geometrical features, like edges, represent one of the most important perceptual information in an image, efficient exploitation of such geometrical information is a key ingredient of many image processing tasks, including compression, denoising and ...

EPFL2004