International Journal of Wavelets, Multiresolution and Information Processing

This paper presents a novel approach to recognize images based on nonlinear wavelet approximation. The mathematical theory on nonlinear wavelet approximation is introduced, which shows that nonlinear approximation contains much more information of the original image than linear approximation. Based on this theory, a scheme to obtain the basic information of images with less data is provided. Experiments on face recognition produce effective matching rates.

This paper proposes a technique for indexing, clustering and retrieving images based on their edge features. In this technique, images are decomposed into several frequency bands using the Haar wavelet transform. From the one-level decomposition sub-bands an edge image is formed. Next, the higher order autocorrelation function is applied on the edge image to extract the edge features. These higher order autocorrelation features are normalized to generate a compact feature vector, which is invariant to shift, image size and gray level. Then, these feature vectors are clustered by a self-organizing map (SOM) based on their edge feature similarity. The performed experiments show the high precision of this technique in clustering and retrieving images in a large image database environment.

Recently, the wavelet transform has emerged as a cutting edge technology, within the field of image compression research. The basis functions of the wavelet transform are known as wavelets. There are a variety of different wavelet functions to suit the needs of different applications. Among the most popular wavelets are Haar, Daubechies, Coiflet and Biorthogonal, etc. The best wavelets (functions) for medical image compression are widely unknown. The purpose of this paper is to examine and compare the difference in impact and quality of a set of wavelet functions (wavelets) to image quality for implementation in a digitized still medical image compression with different modalities. We used two approaches to the measurement of medical image quality: objectively, using peak signal to noise ratio (PSNR) and subjectively, using perceived image quality. Finally, we defined an optimal wavelet filter for each modality of medical image.

Faces often produce inconsistent features under different lighting conditions. Classifying lighting effects within a face image is therefore the first crucial step of building a lighting invariant face recognition system. This paper presents a hybrid system to classify face images based on the lighting effects present in the image. The theories of multivariate discriminant analysis and wavelet packets transform are utilised to develop the proposed system. An extensive set of face images of different poses, illuminated from different angles, are used to train the system. The performance of the proposed system is evaluated by conducting experiments on different test sets and by comparing its results against those of some existing counterparts.

A wavelet-based forecasting method for time series is introduced. It is based on a multiple resolution decomposition of the signal, using the redundant "à trous" wavelet transform which has the advantage of being shift-invariant.

The result is a decomposition of the signal into a range of frequency scales. The prediction is based on a small number of coefficients on each of these scales. In its simplest form it is a linear prediction based on a wavelet transform of the signal. This method uses sparse modelling, but can be based on coefficients that are summaries or characteristics of large parts of the signal. The lower level of the decomposition can capture the long-range dependencies with only a few coefficients, while the higher levels capture the usual short-term dependencies.

We show the convergence of the method towards the optimal prediction in the autoregressive case. The method works well, as shown in simulation studies, and studies involving financial data.

It is well known that the Shannon Sampling Theorem allows us to fully recover a continuous-time bandlimited signal from its digital samples, as long as the sampling rate to be chosen is not smaller than the Nyquist frequency. This theory applies to all bandlimited signals, which may or may not occupy the entire frequency band. Hence, it is intuitively convincing that for continuous-time signals, such as those in speech, that do not fully utilize the entire frequency intervals, less digital samples are required for their full recovery. Current techniques in sub-band coding are used for achieving this goal. The objective of this paper is to present a wavelet theory for establishing the mathematical foundation of this sub-band coding approach. A wavelet packet decomposition of the signal provides the optimal sub-band coding bit-rate by using the Shannon wavelet library introduced in this paper.