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.

An intuitive guide to wavelets for economists

Abstract: Wavelet analysis, although used extensively in disciplines such as signal processing, engineering, medical sciences, physics and astronomy, has not yet fully entered the economics discipline. In this discussion paper, wavelet analysis is introduced in an intuitive manner, and the existing economics and finance literature that utilises wavelets is explored. Extensive examples of exploratory wavelet analysis are given, many using Canadian, US and Finnish industrial production data. Finally, potential future applications for wavelet analysis in economics are also discussed and explored.

Analysing time-varying power system harmonics using wavelet transform

Abstract: This paper presents the possibilities offered by the dyadic-orthonormal wavelet transform used in the multiresolution analysis of voltage- and current-signals. This transform proves to have some advantages over the classical FFT-based algorithms, when used in electric power quality assessment and the analysis of waveforms. Practical examples using waveforms generated by energy saving lighting equipment, remote-control signals and an adjustable speed drive, are presented.

New prospects for time domain analysis

Abstract: The method of moments with scaling functions is applied directly to Maxwell's equations. As a result, we obtain a new three-dimensional time domain scheme with highly linear dispersion characteristics that allows one to incorporate the advantages of multiresolution analysis. First examples suggest significant reductions with respect to computer resources. >

Adaptive Inpainting Algorithm Based on DCT Induced Wavelet Regularization

Abstract: In this paper, we propose an image inpainting optimization model whose objective function is a smoothed l1 norm of the weighted nondecimated discrete cosine transform (DCT) coefficients of the underlying image. By identifying the objective function of the proposed model as a sum of a differentiable term and a nondifferentiable term, we present a basic algorithm inspired by Beck and Teboulle's recent work on the model. Based on this basic algorithm, we propose an automatic way to determine the weights involved in the model and update them in each iteration. The DCT as an orthogonal transform is used in various applications. We view the rows of a DCT matrix as the filters associated with a multiresolution analysis. Nondecimated wavelet transforms with these filters are explored in order to analyze the images to be inpainted. Our numerical experiments verify that under the proposed framework, the filters from a DCT matrix demonstrate promise for the task of image inpainting.

Wavelet-regularized reconstruction for rapid MRI

Abstract: We propose a reconstruction scheme adapted to MRI that takes advantage of a sparsity constraint in the wavelet domain. We show that artifacts are significantly reduced compared to conventional reconstruction methods. Our approach is also competitive with Total Variation regularization both in terms of MSE and computation time. We show that l1 regularization allows partial recovery of the missing k-space regions. We also present a multi-level version that significantly reduces the computational cost.