Showing papers on "Multiresolution analysis published in 2022"

Laplacian Pyramid Dense Network for Hyperspectral Pansharpening

Abstract: Hyperspectral (HS) pansharpening aims to create a pansharpened image that integrates the spatial details of the panchromatic (PAN) image and the spectral content of the HS image. In this article, we present a deep convolutional network within the mature Gaussian–Laplacian pyramid for pansharpening (LPPNet). The overall structure of LPPNet is a cascade of the Laplacian pyramid dense network with a similar structure at each pyramid level. Following the general idea of multiresolution analysis (MRA), the subband residuals of the desired HS images are extracted from the PAN image and injected into the upsampled HS image to reconstruct the high-resolution HS images level by level. Applying the mature Laplace pyramid decomposition technique to the convolution neural network (CNN) can simplify the pansharpening problem into several pyramid-level learning problems so that the pansharpening problem can be solved with a shallow CNN with fewer parameters. Specifically, the Laplacian pyramid technology is used to decompose the image into different levels that can differentiate large- and small-scale details, and each level is handled by a spatial subnetwork in a divide-and-conquer way to make the network more efficient. Experimental results show that the proposed LPPNet method performs favorably against some state-of-the-art pansharpening methods in terms of objective indexes and subjective visual appearance.

Multiresolution Analysis Based on Dual-Scale Regression for Pansharpening

Abstract: Pansharpening technique is used to merge the original multispectral image (MS) with a high spatial resolution panchromatic image (PAN). Due to its robustness, the multiresolution analysis (MRA) is an important part of pansharpening. The scale regression model is effective for improving MRA. However, the existing MRA based on scale regression results into single-scale regression information, thus affecting the final pansharpening result. To address this problem, in this work, we propose a dual-scale regression-based MRA for pansharpening. First, we establish a scale regression-based model. Then, this model is improved using a high-pass modulation (HPM) injection scheme. Finally, the dual-scale information is added to the scale regression to construct the dual-scale regression for obtaining the final pansharpening result. We perform experiments using five datasets. The results show that the proposed method obtains a better pansharpening result as compared to various state-of-the-art MRA methods. In addition, the quantitative and qualitative analysis of the results shows that the proposed method achieves appropriate spatial and spectral resolution fusion. Therefore, it has a great potential in pansharpening technique.

Multiresolution wavelet analysis of noisy datasets with different measures for decomposition coefficients

Abstract: The possibility of distinguishing between different types of complex oscillations using datasets contaminated with measurement noise is studied based on multiresolution wavelet analysis (MWA). Unlike the conventional approach, which characterizes the differences in terms of standard deviations of detail wavelet coefficients at independent resolution levels, we consider ways to improve the separation between complex motions by applying several measures for the decomposition coefficients. We show that MWA’s capabilities in diagnosing dynamics can be expanded by applying detrended fluctuation analysis (DFA) to sets of detail wavelet coefficients or by computing the excess of the probability density function of these sets.

Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$

Abstract: A generalization of Mallat’s classical multiresolution analysis, based on the theory of spectral pairs, was considered in two articles by Gabardo and Nashed. In this setting, the associated translation set is no longer a discrete subgroup of \({\mathbb {R}}\) but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we continue the study based on this nonstandard setting and introduce fractional vector-valued nonuniform multiresolution analysis (Fr-VNUMRA) where the associated subspace of the function space has an orthonormal basis. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of fractional vector-valued nonuniform multiresolution analysis starting from a vector refinement mask with appropriate conditions. Nevertheless, to extend the scope of the present study, we worked to construct the associated wavelet packets for such an MRA and investigate their properties by means of fractional Fourier transform.

Gating-adapted Wavelet Multiresolution Analysis for Exposure Sequence Modeling in CTR Prediction

Abstract: The exposure sequence is being actively studied for user interest modeling in Click-Through Rate (CTR) prediction. However, the existing methods for exposure sequence modeling bring extensive computational burden and neglect noise problems, resulting in an excessively latency and the limited performance in online recommenders. In this paper, we propose to address the high latency and noise problems via Gating-adapted wavelet multiresolution analysis (Gama), which can effectively denoise the extremely long exposure sequence and adaptively capture the implied multi-dimension user interest with linear computational complexity. This is the first attempt to integrate non-parametric multiresolution analysis technique into deep neural network to model user exposure sequence. Extensive experiments on large scale benchmark dataset and real production dataset confirm the effectiveness of Gama for exposure sequence modeling, especially in cold-start scenarios. Benefited from its low latency and high effecitveness, Gama has been deployed in our real large-scale industrial recommender, successfully serving over hundreds of millions users.

Fusion of Evidences in Intensity Channels for Edge Detection in PolSAR Images

Abstract: Polarimetric synthetic aperture radar (PolSAR) sensors have reached an essential position in remote sensing. The images they provide have speckle noise, making their processing and analysis challenging tasks. We discuss an edge detection method based on the fusion of evidences obtained in the intensity channels hh, hv, and vv of PolSAR multilook images. The method consists of detecting transition points in the thinnest possible range of data that covers two regions using maximum likelihood under the Wishart distribution. The fusion methods used are: simple average, multiresolution discrete wavelet transform (MR-DWT), principal component analysis (PCA), receiver operating characteristic (ROC) statistics, multiresolution stationary wavelet transform (MR-SWT), and a multiresolution method based on singular value decomposition (MR-SVD). A quantitative analysis suggests that PCA and MR-SVD provide the best results.

Enhanced MultiResolution Analysis for MultiDimensional Data Utilizing Line Filtering Techniques

Abstract: In this article we introduce line Smoothness-Increasing Accuracy-Conserving Multi-Resolution Analysis. This is a procedure for exploiting convolution kernel post-processors for obtaining more accurate multidimensional multiresolution analysis in terms of error reduction. This filtering-projection tool allows for the transition of data between different resolutions while simultaneously decreasing errors in the fine grid approximation. It specifically allows for defining detail multiwavelet coefficients when translating coarse data onto finer meshes. These coefficients are usually not defined in such cases. We show how to analytically evaluate the resulting convolutions and express the filtered approximation in a new basis. This is done by combining the filtering procedure with projection operators that allow for computational implementation of this scale transition procedure. Further, this procedure can be applied to piecewise constant approximations to functions, as it provides error reduction. We demonstrate the effectiveness of this technique in two and three dimensions.

MRA of Fault-generated High-frequency Transient Signals using Mathematical Morphology. Comparison with Wavelet Transform

Abstract: Multiresolution analysis (MRA) is a sequence of decompositions of a signal to observe it at multiple resolutions. Therefore, it allows extracting signal features over a wide range of frequency spectrum. In this sense, high-frequency signals generated by electrical faults (short-circuits) in transmission lines can be characterized. The wavelet transform has become the most developed method by researchers for MRA, but this technique suffers from drawbacks that still makes it difficult to implement in real applications. However, a new method based on mathematical morphology has been proving useful in image processing, so this work proposes to develop the MRA of high-frequency signals by kilometer resolution based on fault location. In this regard, several simulations were performed on a power electrical system modeled in software ATP-Draw with a frequency-dependent transmission line model. These events were developed with high sampling frequencies and also consider the scenarios of different fault resistances and inception angles. Finally, the comparison with the wavelet transform is described.

A Multiresolution Analysis of Temporal Logic

Abstract: Is it possible to determine whether a signal violates a formula in Signal Temporal Logic (STL), if the monitor only has access to a low-resolution version of the signal? We answer this question affirmatively by demonstrating that temporal logic has a multiresolution structure, which parallels the multiresolution structure of signals. A formula in discrete-time Signal Temporal Logic (STL) is equivalently defined via the set of signals that satisfy it, known as its language. If a wavelet decomposition x = y + d is performed on each signal x in the language, we end up with two signal sets Y and D, where Y contains the low-resolution approximation signals y, and D contains the detail signals d needed to reconstruct the x’s. This paper provides a complete computational characterization of both Y and D using a novel constraint set encoding of STL, s.t. x satisfies a formula if and only if its decomposition signals satisfy their respective encoding constraints. Then a conservative logical approximation of Y is also provided: namely, we show that Y is over approximated by the language of a formula − 1. By iterating the decomposition, we obtain a sequence of lower-resolution formulas − 1, − 2, − 3,... which thus constitute a multiresolution analysis of. This work lays the foundation for multiresolution monitoring in distributed systems. One potential application of these results is a multiresolution monitor that can detect specification violation early by simply observing a low-resolution version of the signal to be monitored. 1

Multiresolution Neural Networks for Imaging

Abstract: We present MR-Net, a general architecture for multiresolution neural networks, and a framework for imaging applications based on this architecture. Our coordinate-based networks are continuous both in space and in scale as they are composed of multiple stages that progressively add finer details. Besides that, they are a compact and efficient representation. We show examples of multiresolution image representation and applications to texture magnification, minification, and antialiasing.

Estimation of Oceanic Surface Velocity Vector Fields Using Multiresolution.

Abstract: This dissertation presents a new method for the estimation of oceanic surface velocity vector fields using multiresolution. Multiresolution is the ability to analyze a signal at various levels of resolution. In this dissertation, wavelet analysis is used to obtain multiresolution. This method requires the use of two sea surface temperature (SST) images of the same region taken within a known time interval. Wavelet analysis is performed in both images to reveal their components at decreasing resolution levels. The comparison of these components at each level yields vector fields representing local displacements of features within the images. These vector fields are smoothed to eliminate noise and to produce coherent vector fields at each resolution level. Vector fields produced with images at levels with higher resolutions are used as refinements to vector fields found at lower resolution levels. Analysis of the operational parameters for the new method are presented in this dissertation. Artificial SST images and NOAA satellite SST images are used to test its accuracy. Comparison with drifter information is also performed. Extensions to the basic algorithm that improve the accuracy of estimations are also discussed. Finally, foreshadowing of the use of the new technique in GOES satellite images and hurricane imagery concludes this dissertation.

A new construction of shearlets

Abstract: In order to achieve optimally sparse approximations of signals exhibiting anisotropic singularities, the shearlet systems that are systems of functions generated by one generator with dilation, shear transformation and translation operators applied to it were introduced. In this paper, we will construct the shearlet systems that are not only Parseval frames for [Formula: see text] but they are also obtained from an [Formula: see text]-MRA associated with wavelet multiresolution, and by using this approach, we obtain the corresponding filters for these systems. For this purpose, the tensor product of the corresponding wavelet scaling function and a compact support bump function is used to construct the scaling function associated with the shearlet.

Analysis of EEG signals using multiresolution wavelet analysis and its extensions

Abstract: The paper deals with the problem of developing tools for studying complex signals recorded in various experimental research. Considering the non-stationary nature of many processes in nature, it is important to apply and improve methods for analyzing the structure of experimental processes in the dynamics of systems with time-varied characteristics. One of the most popular approaches is wavelet analysis and methods that use decomposition in the basis of wavelet functions as the main or intermediate stage of analysis. In this study, various versions of extended multiresolution wavelet analysis (MWA) were tested, aimed at improving the quality of diagnostics of complex oscillations and their changes when the operating conditions of the system change. The characterization of differences between various group using the kurtosis and skewness of the probability distribution of the wavelet coefficients of decompositions improves the diagnosis of age distinctions compared to the approach based on the standard deviations.

Balancing MultiWavelets (about balancing order and other discrete-time properties of multiwavelets)

Abstract: Multiwavelets are a generalization of wavelets where one allows the multiresolution analysis to be generated by a finite number of scaling functions instead of only one. This approach allows to overcome some limitations in the design of filter banks preventing the construction of non-trivial, orthonormal bases from compactly supported, symmetric wavelets.However, in order to obtain multifilter banks that are appropriate for processing scalar signals, new conditions, coined ''balancing'', have to be imposed in the design of multiwavelets. A thorough study of the discrete-time properties of multifilter banks shows that the balancing conditions are closely related to the important issue of the preservation of discrete-time polynomial signals. Balancing is then proved to be equivalent to a very natural factorization of the lowpass synthesis refinement mask and to some Strang-Fix conditions on a time-varying scalar subdivision operator. Connections are also made with the usual properties of the associated multiresolution analysis (approximation power, moments of the scaling functions, superfunction theory). MultiCoiflets, the natural generalization of Coiflets, come out as a special case of balanced multiwavelets.With the help of computational algebraic geometry, in particular Groebner bases methods, the design of several families of orthonormal balanced multiwavelets and multiCoiflets with compact support, symmetries and minimal-length multifilters is detailed. A new concept of discrete-time balanced smoothness is introduced to measure the influence of ergodic properties (zeros at preperiodic points of invariant cycles) on the smoothness of the iterated multifilter bank. Finally, the description of a significance tree image coder based on balanced multiwavelets concludes this thesis dissertation.

Volumetric Rendering on Wavelet-Based Adaptive Grid

Abstract: Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Multiresolution-analysis for stochastic hyperbolic conservation laws

Abstract: A multiresolution analysis (MRA) for solving stochastic conservation laws is proposed. Using a novel adaptation strategy and a higher-dimensional deterministic problem, a discontinuous Galerkin (DG) solver is derived. An MRA of the DG spaces for the proposed adaptation strategy is presented. Numerical results show that in the case of general stochastic distributions the performance of the DG solver is significantly improved by the novel adaptive strategy. The gain in efficiency is validated in computational experiments.