Multiresolution analysis

About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.

Selection of a suitable mother wavelet for analyzing power system fault transients

Abstract: In the literature, wavelet techniques are proposed for the analysis of power system transients. Many mother wavelets have been used for this analysis such as Haar, Daubechies (db), Symlets, and Coiflets. This paper describes a strategy to choose a suitable mother wavelet for this analysis. It also shows the deviation between Matlab and theoretical (mathematically calculated) db-wavelets when they are used for the analysis of power system transient. The simulation study is carried out using PSCAD simulation program and Matlab wavelet toolbox. The simulation results show that the theoretical db wavelet is more suitable for analyzing power system fault transients than the Matlab db wavelet.

iWave: CNN-Based Wavelet-Like Transform for Image Compression

Abstract: Wavelet transform is a powerful tool for multiresolution time-frequency analysis. It has been widely adopted in many image processing tasks, such as denoising, enhancement, fusion, and especially compression. Wavelets lead to the successful image coding standard JPEG-2000. Traditionally, wavelets were designed from the signal processing theory with certain assumption on the signal, but natural images are not as ideal as assumed by the theory. How to design content-adaptive wavelets for natural images remains a difficulty. Inspired by the recent progress of convolutional neural network (CNN), we propose iWave as a framework for deriving wavelet-like transform that is more suitable for natural image compression. iWave adopts an update-first lifting scheme, where the prediction filter is a trained CNN, to achieve wavelet-like transform. The CNN can be embedded into a deep network that is analogous to an auto-encoder, which is trained end-to-end. The trained wavelet-like transform still possesses the lifting structure, which ensures perfect reconstruction, supports multiresolution analysis, and is more interpretable than the deep networks trained as “black boxes.” We perform experiments to verify the generality as well as the speciality of iWave in comparison with JPEG-2000. When trained with a generic set of natural images and tested on the Kodak dataset, iWave achieves on average 4.4% and up to 14% BD-rate reductions. When trained and tested with a specific kind of textures, iWave provides as high as 27% BD-rate reduction.

Acuity-matching resolution degradation through wavelet coefficient scaling

Abstract: A wavelet-based multiresolution image representation method is developed matching human visual system (HVS) spatial acuity within multiple regions of interest (ROIs). ROIs are maintained at high (original) resolution while peripheral areas are gracefully degraded. Variable resolution images are generated by selectively scaling wavelet (detail) coefficients prior to reconstruction. The technique is equivalent to linear interpolation MIP-mapping which involves smooth subsampling (decomposition) prior to texture mapping (reconstruction). Multiple ROI degradation is achieved through wavelet coefficient scaling following Voronoi partitioning of the image plane.