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.

Advantages of Laplacian pyramids over ''à trous'' wavelet transforms for pansharpening of multispectral images

Abstract: The advantages provided by the generalized Laplacian pyramid (GLP) over the widespread “`a trous” wavelet (ATW) transform for multispectral (MS) pansharpening based on multiresolution analysis (MRA) are investigated. The most notable difference depends on the way GLP and ATW deal with aliasing possibly occurring in the MS data, which is originated by insufficient sampling step size, or equivalently by a too high amplitude value of the modulation transfer function (MTF) at Nyquist frequency and may generate annoying jagged patterns that survive in the sharpened image. In this paper, it is proven that GLP is capable of compensating the aliasing of MS, unlike ATW, and analogously to component substitution (CS) fusion methods, thanks to the decimation and interpolation stages present in its flowchart. Experimental results will be presented in terms of quality/distortion global score indexes (SAM, ERGAS and Q4) for increasing amounts of aliasing, measured by the amplitude at Nyquist frequency of the Gaussian-like lowpass filter simulating the average MTF of the individual spectral channels of the instrument. GLP and ATW-based methods, both using the same MTF filters and the same global injection gain, will be compared to show the advantages of GLP over ATW in the presence of aliasing of the MS bands.

Nonlinear Smoothing and Multiresolution Analysis

Abstract: Operators on Sequences.- Basic Rank Selectors, Pulses and Impulses.- LULU-Smoothers, Signals and Ambiguity.- LULU-Intervals, Noise and Co-idempotence.- Smoothing and Approximation with Signals.- Variation Reduction and Shape Preservation.- Multiresolution Analysis of Sequences.- The Discrete Pulse Transform.- Fair Comparison with Linear Smoothers.- Interpretation and Future.

On the use of the Stockwell transform for image compression

Abstract: In this paper, we investigate the use of the Stockwell Transform for image compression. The proposed technique uses the Discrete Orthogonal Stockwell Transform (DOST), an orthogonal version of the Discrete Stockwell Transform (DST). These mathematical transforms provide a multiresolution spatial-frequency representation of a signal or image. First, we give a brief introduction for the Stockwell transform and the DOST. Then we outline a simplistic compression method based on setting the smallest coefficients to zero. In an experiment, we use this compression strategy on three different transforms: the Fast Fourier transform, the Daubechies wavelet transform and the DOST. The results show that the DOST outperforms the two other methods.

Close Accord on DWT Performance and Real-Time Implementation for Protection Applications

Abstract: In this paper, a simpler and faster algorithm of discrete wavelet transform (DWT) for a digital signal processing (DSP) implementation is proposed and intensively tested. Applicability of real-time implementation of this algorithm is verified. The computational frame in this algorithm is independent on the sampling rate, but it depends on the length of the mother wavelet filters. Therefore, signal with any sampling rate can be analyzed with the same computational effort. This implementation algorithm is exploited to investigate the DWT response experimentally. Impact of the mother wavelet, sampling frequency, fault inception angle and the signal transients on the resulted DWT levels is evaluated from the protection perspectives. Considering the DSP channel noise, these factors are strongly affect DWT response especially in high details spike, which the most of the protection applications depended on. Shortcomings of DWT application for protection relays are outlined and corrective recommendations are included.

Dynamic mode decomposition for multiscale nonlinear physics.

Abstract: We present a data-driven method for separating complex, multiscale systems into their constituent timescale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed subsets of the data, and dominant timescales are discovered using spectral clustering on their eigenvalues. This approach produces time series data for each identified component, which sum to a faithful reconstruction of the input signal. It differs from most other methods in the field of multiresolution analysis (MRA) in that it (1) accounts for spatial and temporal coherencies simultaneously, making it more robust to scale overlap between components, and (2) yields a closed-form expression for local dynamics at each scale, which can be used for short-term prediction of any or all components. Our technique is an extension of multi-resolution dynamic mode decomposition (mrDMD), generalized to treat a broader variety of multiscale systems and more faithfully reconstruct their isolated components. In this paper we present an overview of our algorithm and its results on two example physical systems, and briefly discuss some advantages and potential forecasting applications for the technique.