Adaptive lifting schemes with perfect reconstruction

In this paper, we propose a framework for constructing adaptive wavelet decompositions using the lifting scheme. A major requirement is that perfect reconstruction is possible without any overhead cost. In this paper we restrict ourselves to the update lifting stage. It is assumed that the update filter utilises local gradient information to adapt itself to the signal in the sense that smaller gradients `evoke' stronger update filters. As a result, sharp transitions in a signal will not be smoothed to the same extent as regions which are more homogeneous. The approach taken in this paper differs from other adaptive schemes found in the literature in the sense that that no bookkeeping is required in order to have perfect reconstruction

Building nonredundant adaptive wavelets by update lifting

Adaptive wavelet decompositions appear useful in various applications in image and video processing, such as image analysis, compression, feature extraction, denoising and deconvolution, or optic flow estimation. For such tasks it may be important that the multiresolution representations take into account the characteristics of the underlying signal and do leave intact important signal characteristics such as sharp transitions, edges, singularities or other regions of interest. In this paper, we propose a technique for building adaptive wavelets by means of an extension of the lifting scheme. The classical lifting scheme provides a simple yet flexible method for building new, possibly nonlinear, wavelets from existing ones. It comprises a given wavelet transform, followed by a prediction and an update step. The update step in such a scheme computes a modification of the approximation signal, using information in the detail band. It is obvious that such an operation can be inverted, and therefore the perfect reconstruction property is guaranteed. In this paper we propose a lifting scheme including an adaptive update lifting and a fixed prediction lifting step

A matlab toolbox for image fusion (MATIFUS).

The MATIFUS toolbox is presented. It is a collection of functions and furnished with a graphical user interface that supports a range of image fusion operations. Almost all of the toolbox functions are written in the MATLAB language. Implementations of multiresolution schemes are used that are either publicly available or can be purchased as licensed software. MATIFUS can be downloaded from a website and is available under the conditions of an agreement with the Dutch Technology Foundation ST

Adaptive wavelets for image compression using update lifting: quantisation and error analysis

Classical linear wavelet representations of images have the drawback that they are not optimally suited to represent edge information. To overcome this problem, nonlinear multiresolution decompositions have been designed that can take into account the characteristics of the input signal/image. In our previous work [20,22] we have introduced an adaptive lifting framework, that does not require bookkeeping but has the property that it processes edges and homogeneous image regions in a different fashion. The current paper discusses the effects of quantisation in such an adaptive wavelet decomposition, as such an analysis is essential for the application of these adaptive decompositions in image compression. We provide conditions for recovering the original decisions at the synthesis and show how to estimate the reconstructions error in terms of the quantisation error