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.

Method and apparatus for performing non-dyadic wavelet transforms

Abstract: A technique for compressing data using non-dyadic wavelet transforms. The non-dyadic wavelet transforms may be derived from a generalized model or specific non-dyadic wavelet transforms may be constructed as needed to enhance the desired image qualities in a compressed image. The non-dyadic wavelet transforms may be differentially applied to different data dimensions to accommodate non-square transformations. In addition, the non-dyadic wavelet transforms can be cascaded to achieve novel image resolutions in the compressed images.

Implementation of the discrete wavelet transform and multiresolution analysis in the encrypted domain

Abstract: Signal processing in the encrypted domain is a new technology for protecting valuable signals from insecure signal processing. Although there has been some research in the area, this field of research is still in its infancy. In this paper, we propose a scheme for implementing discrete wavelet transform (DWT) and multi-resolution analysis (MRA) in a homomorphic encrypted domain. We first suggest a framework for performing DWT and inverse discrete wavelet transform (IDWT) in the encrypted domain and then conduct an analysis of data expansion and quantization errors on the framework. In order to solve the problem of data expansion, which is very important in practical applications, we then present a novel method for reducing data expansion in the case that both DWT and IDWT are performed. With the proposed method, multi-level DWT/IDWT can be performed with less data expansion in a homomorphic encrypted domain. We address the case of a two-dimensional Haar wavelet transform and give some experiments to demonstrate the advantages of our improved method. To the best of our knowledge, this is the first paper on the implementation of DWT and MRA in the encrypted domain.

Multiresolution Analysis and Supercompact Multiwavelets

Abstract: The Haar wavelets can represent exactly any piecewise constant function. The motivation for the present development is Alpert's family of compact orthogonal multiwavelets that can represent exactly any piecewise polynomial function. We choose to derive the algorithm in the style and notation of Harten's multiresolution analysis as extended to multiwavelets by the authors. We begin with a description of the nested grid hierarchy. Next comes the decomposition, which is the heart of the algorithm, and finally the reconstruction. The basis functions (which are nonfractal) retain the spatial compactness of the Haar basis functions, which enhances the algorithm application to nonperiodic and piecewise continuous data.

A multiresolution technique for video indexing and retrieval

Abstract: This paper presents a novel approach to multiresolution analysis and scalability in video indexing and retrieval. A scalable algorithm for video parsing and key-frame extraction is introduced. The technique is based on real-time analysis of MPEG motion variables and scalable metrics simplification by discrete contour evolution. Furthermore, a hierarchical key-frame retrieval method using scalable colour histogram analysis is presented. It offers customisable levels of detail in the descriptor space, where the relevance order is determined by degradation of the image, and not by degradation of the image histogram. To assess the performance of the approach, several experiments have been conducted. Selected results are reported.