We present a general framework for the design of a mother wavelet best adapted to a specific signal or to a class of signals. The filter’s coefficients are obtained via optimization of a smooth objective function. We develop an unconstrained gradient-based optimization algorithm for a discrete wavelet transform. The algorithm is extended to the joint optimization of the mother wavelet and of th...

An approach is presented for conducting multiscale statistical process control (MSSPC), based on a library of basis functions provided by wavelet packets. The proposed approach explores the improved ability of wavelet packets in extracting features with arbitrary locations, and having different localizations in the time-frequency domain, in order to improve the detection performances achieved w...

AVHRR is an imager flying on polar meteorological satellites that, due to its spatial resolution (about 1 km at Nadir view), produces a huge amount of data. A method based on the wavelet packet transform is devised to compress AVHRR images. The method is driven by the compression error (application dependent), so that different types of images have the same quality. The best basis wavelet packe...

The paper presents a new algorithm for the image inpainting problem. uses recently designed versatile library of quasi-analytic complex-valued wavelet packets (qWPs) which originate from polynomial splines arbitrary orders. Tensor products 1D qWPs provide diversity 2D oriented in multiple directions. For example, set fourth-level comprises 62 different properties these such as refined frequency...

The ancient documents present an important part of our individual and collective memory. In addition to their preservation, the digitization of these documents may offer users a great number of services like remote look-up and browsing rare documents. However, the documents, digitally formed, are likely to be modified or pirated. Therefore, we need to develop techniques of protecting images ste...

In this paper, we study the synthesis of Gegenbauer processes using the wavelet packets transform. In order to simulate a 1-factor Gegenbauer process, we introduce an original algorithm, inspired by the one proposed by Coifman and Wickerhauser [1], to adaptively search for the best-ortho-basis in the wavelet packet library where the covariance matrix of the transformed process is nearly diagona...

In this paper, we consider the problem of approximating a set of arbitrary, discrete-time, Gaussian random processes by a single, representative wavelet-based, Gaussian process. We measure the similarity between the original processes and the wavelet-based process with the Bhattacharyya coefficient. By manipulating the Bhattacharyya coefficient, we reduce the task of defining the representative...

Currently, the automatic wheezes detection methods are based on the identification of a particular shape of peaks in the respiratory power spectrum. These techniques present a high false detection rate, caused by the presence of peaks in normal sounds similar to those characterising wheezes. In this paper, a new method for automatic wheezes detection based on the wavelet packets was developed. ...

We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation of wavelet transforms on a quantum computer.