A multiscale regularized restoration algorithm for XMM-Newton data

We introduce a new multiscale restoration algorithm for images with few photons counts and its use for denoising XMM data. We use a thresholding of the wavelet space so as to remove the noise contribution at each scale while preserving the multiscale information of the signal. Contrary to other algorithms the signal restoration process is the same whatever the signal to noise ratio is. Thresholds according to a Poisson noise process are indeed computed analytically at each scale thanks to the use of the unnormalized Haar wavelet transform. Promising preliminary results are obtained on X-ray data for Abell 2163 with the computation of a temperature map.Comment: To appear in the Proceedings of `Galaxy Clusters and the High Redshift Universe Observed in X-rays', XXIth Moriond Astrophysics Meeting (March 2001), Eds. Doris Neumann et a

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Wavelet-Neural Network Based Image Compression System for Colour Images

There are many images used by human being, such as medical, satellite, telescope, painting, and graphic or animation generated by computer images. In order to use these images practically, image compression method has an essential role for transmission and storage purposes. In this research, a wavelet based image compression technique is used. There are various wavelet filters available. The selection of filters has considerable impact on the compression performance. The filter which is suitable for one image may not be the best for another. The image characteristics are expected to be parameters that can be used to select the available wavelet filter. The main objective of this research is to develop an automatic wavelet-based colour image compression system using neural network. The system should select the appropriate wavelet for the image compression based on the image features. In order to reach the main goal, this study observes the cause-effect relation of image features on the wavelet codec (compression-decompression) performance. The images are compressed by applying different families of wavelets. Statistical hypothesis testing by non parametric test is used to establish the cause-effect relation between image features and the wavelet codec performance measurements. The image features used are image gradient, namely image activity measurement (IAM) and spatial frequency (SF) values of each colour component. This research is also carried out to select the most appropriate wavelet for colour image compression, based on certain image features using artificial neural network (ANN) as a tool. The IAM and SF values are used as the input; therefore, the wavelet filters are used as the output or target in the network training. This research has asserted that there are the cause-effect relations between image features and the wavelet codec performance measurements. Furthermore, the study reveals that the parameters in this investigation can be used for the selection of appropriate wavelet filters. An automatic wavelet-based colour image compression system using neural network is developed. The system can give considerably good results

Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra

We propose a non-parametric method to denoise 1D stellar spectra based on wavelet shrinkage followed by adaptive Kalman thresholding. Wavelet shrinkage denoising involves applying the discrete wavelet transform (DWT) to the input signal, 'shrinking' certain frequency components in the transform domain, and then applying inverse DWT to the reduced components. The performance of this procedure is influenced by the choice of base wavelet, the number of decomposition levels, and the thresholding function. Typically, these parameters are chosen by 'trial and error', which can be strongly dependent on the properties of the data being denoised. We here introduce an adaptive Kalman-filter-based thresholding method that eliminates the need for choosing the number of decomposition levels. We use the 'Haar' wavelet basis, which we found to provide excellent filtering for 1D stellar spectra, at a low computational cost. We introduce various levels of Poisson noise into synthetic PHOENIX spectra, and test the performance of several common denoising methods against our own. It proves superior in terms of noise suppression and peak shape preservation. We expect it may also be of use in automatically and accurately filtering low signal-to-noise galaxy and quasar spectra obtained from surveys such as SDSS, Gaia, LSST, PESSTO, VANDELS, LEGA-C, and DESI