Multiresolution Analysis Framework Research Articles

Multi-resolution analysis enables fidelity-ensured deconvolution for fluorescence microscopy

Fluorescence microscopic imaging is essentially a convolution process distorted by random noise, limiting critical parameters such as imaging speed, duration, and resolution. Though algorithmic compensation has shown great potential to enhance these pivotal aspects, its fidelity remains questioned. Here we develop a physics-rooted computational resolution extension and denoising method with ensured fidelity. Our approach employs a multi-resolution analysis (MRA) framework to extract the two main characteristics of fluorescence images against noise: across-edge contrast, and along-edge continuity. By constraining the two features in a model-solution framework using framelet and curvelet, we develop MRA deconvolution algorithms, which improve the signal-to-noise ratio (SNR) up to 10 dB higher than spatial derivative based penalties, and can provide up to two-fold fidelity-ensured resolution improvement rather than the artifact-prone Richardson-Lucy inference. We demonstrate our methods can improve the performance of various diffraction-limited and super-resolution microscopies with ensured fidelity, enabling accomplishments of more challenging imaging tasks.

Scalar Relativistic Effects with Multiwavelets: Implementation and Benchmark.

The importance of relativistic effects in quantum chemistry is widely recognized, not only for heavier elements but throughout the periodic table. At the same time, relativistic effects are strongest in the nuclear region, where the description of electrons through a linear combination of atomic orbitals becomes more challenging. Furthermore, the choice of basis sets for heavier elements is limited compared with lighter elements where precise basis sets are available. Thanks to the framework of multiresolution analysis, multiwavelets provide an appealing alternative to overcoming this challenge: they lead to robust error control and adaptive algorithms that automatically refine the basis set description until the desired precision is reached. This allows one to achieve a proper description of the nuclear region. In this work, we extended the multiwavelet-based code MRChem to the scalar zero-order regular approximation framework. We validated our implementation by comparing the total energies for a small set of elements and molecules. To confirm the validity of our implementation, we compared both against a radial numerical code for atoms and the plane-wave-based code EXCITING.

A High-Confidence Intelligent Measurement Method for Aero-Engine Oil Debris Based on Improved Variational Mode Decomposition Denoising

This paper presents an effective method for measuring oil debris with high confidence to ensure the wear monitoring of aero-engines, which suffers from severe noise interference, weak signal characteristics, and false detection. First, an improved variational mode decomposition algorithm is proposed, which combines wavelet transform and interval threshold processing to suppress the complex noise interference on the signal. Then, a long-short-term memory neural network with deep scattering spectrum preprocessing is used to identify the signal characteristics under the multi-resolution analysis framework. The optimal hyperparameters are automatically configured using Bayesian optimization to solve the problem of weak, distorted, and hard-to-extract signal characteristics. Finally, a detection algorithm based on multi-window fusion judgment is applied to improve the confidence of the detection process, reduce the false detection and false alarm rate, and calculate the debris size information according to the sensor principle. The experimental results show that the proposed method can extract debris signals from noise with a signal-to-noise ratio improvement of more than 9 dB, achieve a high recognition accuracy of 99.76% with a missed detection rate of 0.24%, and output size information of debris to meet the need for aero-engine oil debris measurement.

Ear recognition based on discriminant multi-resolution image representation

The multi-resolution analysis is more appropriate for extracting information from measured data, because it is generally multi-scale in nature. This paper proposes a new approach for ear representation, based on multi-resolution analysis framework. Such representation relies on significantly Gabor wavelet, local phase quantisation (LPQ) descriptor and spatial pyramid histogram (SPH) method. First, to capture the local structure in ear image, the Gabor wavelet function with two scales and four orientations is used. Second, to fully explore the blur invariant property and the texture information in different scales and directions spaces, the LPQ operator is applied on the image responses of Gabor filter to get label LPQ images. Third, the SPH of horizontal decomposition is applied for each of them, to obtain local ear feature descriptors. Next, the obtained histograms are normalised. Then, the global representation of ear image is obtained by concatenating all the local feature descriptors. After that, a discriminant representation of ear image is constructed using whitened linear discriminant analysis. Finally, the K-nearest neighbour classifier is used for identification. Experiments conducted on two ear databases (IIT Delhi-1 and IIT Delhi-2); show that the proposed approach provides a significant accuracy improvement compared to the state-of-the-art methods.

Ear recognition based on discriminant multi-resolution image representation

The multi-resolution analysis is more appropriate for extracting information from measured data, because it is generally multi-scale in nature. This paper proposes a new approach for ear representation, based on multi-resolution analysis framework. Such representation relies on significantly Gabor wavelet, local phase quantisation (LPQ) descriptor and spatial pyramid histogram (SPH) method. First, to capture the local structure in ear image, the Gabor wavelet function with two scales and four orientations is used. Second, to fully explore the blur invariant property and the texture information in different scales and directions spaces, the LPQ operator is applied on the image responses of Gabor filter to get label LPQ images. Third, the SPH of horizontal decomposition is applied for each of them, to obtain local ear feature descriptors. Next, the obtained histograms are normalised. Then, the global representation of ear image is obtained by concatenating all the local feature descriptors. After that, a discriminant representation of ear image is constructed using whitened linear discriminant analysis. Finally, the K-nearest neighbour classifier is used for identification. Experiments conducted on two ear databases (IIT Delhi-1 and IIT Delhi-2); show that the proposed approach provides a significant accuracy improvement compared to the state-of-the-art methods.

A multiresolution triangular plate-bending element method

A triangular plate-bending element with a new multi-resolution analysis (MRA) is proposed and a novel multiresolution triangular element method is hence presented. The MRA framework is formulated out of a displacement subspace sequence whose basis functions are built out of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by means of extending the shape function triangle domain for a split node at the zero coordinates to the hexagon area enclosing the zero coordinates. As a result, a new split-full node notion is presented and a novel rational MRA concept together with the resolution level (RL) is constituted for the element. Via practical examples, it is found that the traditional triangular plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated. The continuous full node shape function unveils secrets behind assembling artificially of node-related items in global matrix formation by the conventional FEM.

Common idiosyncratic volatility and returns: From an investment horizon perspective

Abstract“Idiosyncratic risk–return puzzle” is conflicting and confusing. It becomes more complex by the introduction of the common idiosyncratic volatility (CIV). We shed new light on the issue from the perspective of heterogeneity of investors with different investment horizons. We study the “CIV puzzle” with Chinese A‐Share market evidence and further contribute by employing the wavelet multiresolution analysis framework to decompose the overall CIV into timescales that refer to risks in different terms. We apply these timescales in Fama–Macbeth regressions to investigate their pricing effects. The results suggest that the “CIV puzzle” is an investment horizon specification problem. The relationship between returns and common idiosyncratic risk is negative in the short run, positive in the intermediate run, and then negative again in the longer run. We also contribute to the international empirical evidence with an in‐depth analysis of the Chinese stock market over the period 1999–2016. The results are robust across different specifications of the CIV. Our findings have important implications for portfolio and risk management.

Wavelet-Galerkin method for reconstruction of structural dynamic responses

In this article, the wavelet-Galerkin method is adopted for calculating structural dynamic responses under the framework of multiresolution analysis. At first, the second-order differential equation of motion is transformed into wavelet domain through function expansion with scaling function at the chosen resolution level. The number of basis function is uniquely determined, and the corresponding coefficients are approximated by numerical quadrature method. And then the two-term connection coefficients are derived and computed at various scales. After this, the dynamic responses of the system with single degree of freedom subjected to sinusoidal excitation are obtained and validated. Subsequently, the proposed method is extended to multidegree-of-freedom systems based on mode-superposition method. Finally, the parametric study is performed, and the simulation results show that the identified dynamic responses match the true responses very well with appropriate choice of the resolution level and the wavelet order.

Integration of wavelet transform, Local Binary Patterns and moments for content-based image retrieval

The proliferation of large number of images has made it necessary to develop systems for indexing and organizing images for easy access. This has made Content-Based Image Retrieval (CBIR) an important area of research in Computer Vision. This paper proposes a combination of features in multiresolution analysis framework for image retrieval. In this work, the concept of multiresolution analysis has been exploited through the use of wavelet transform. This paper combines Local Binary Pattern (LBP) with Legendre Moments at multiple resolutions of wavelet decomposition of image. First, LBP codes of Discrete Wavelet Transform (DWT) coefficients of images are computed to extract texture feature from image. The Legendre Moments of these LBP codes are then computed to extract shape feature from texture feature for constructing feature vectors. These feature vectors are used to search and retrieve visually similar images from large database. The proposed method has been tested on five benchmark datasets, namely, Corel-1K, Olivia-2688, Corel-5K, Corel-10K, and GHIM-10K, and performance of the proposed method has been measured in terms of precision and recall. The experimental results demonstrate that the proposed method outperforms some of the other state-of-the-art methods in terms of precision and recall.

Isotropic and Steerable Wavelets in N Dimensions. A multiresolution analysis framework.

This document describes the implementation of the external module ITKIsotropicWavelets, a multiresolution (MRA) analysis framework using isotropic and steerable wavelets in the frequency domain. This framework provides the backbone for state of the art filters for denoising, feature detection or phase analysis in N-dimensions. It focus on reusability, and highly decoupled modules for easy extension and implementation of new filters, and it contains a filter for multiresolution phase analysis,The backbone of the multi-scale analysis is provided by an isotropic band-limited wavelet pyramid, and the detection of directional features is provided by coupling the pyramid with a generalized Riesz transform. The generalized Riesz transform of order N behaves like a smoothed version of the Nth order derivatives of the signal. Also, it is steerable: its components impulse responses can be rotated to any spatial orientation, reducing computation time when detecting directional features.This paper is accompanied with the source code, input data, parameters and output data that the author used for validating the algorithm described in this paper. This adheres to the fundamental principle that scientific publications must facilitate reproducibility of the reported results.

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

A Multifractal-Based Wavefront Phase Estimation Technique for Ground-Based Astronomical Observations

Turbulence in the Earth's atmosphere interferes with the propagation of planar wavefronts from outer space, resulting in a phase-distorted nonplanar wavefront. This phase distortion is responsible for the refractive blurring of images accounting to the loss in spatial resolution power of ground-based telescopes. The technology widely used to remove this phase distortion is adaptive optics (AO). In AO, an estimate of the distorted phase is provided by a wavefront sensor (WFS) in the form of low-resolution slope measurements of the wavefront. The estimate is then used to create a corrected wavefront that (approximately) removes the phase distortion from the incoming wavefronts. Phase reconstruction from WFS measurements is done by solving large linear systems, followed by interpolating the low-resolution phase to its desired high resolution. In this paper, we propose an alternate technique to wavefront phase reconstruction using concepts derived from the microcanonical multiscale formalism, which is a specific approach to multifractality. We take into account an a priori information of the wavefront phase, provided by the multifractal exponents. Then, through the framework of multiresolution analysis and wavelet transform, we address the problem of phase reconstruction from low-resolution WFS measurements. Comparison, in terms of reconstruction quality, with classical techniques in AO proves the superiority of our approach.

A multi-resolution analysis based finite element model updating method for damage identification

A novel finite element (FE) model updating method based on multi-resolution analysis (MRA) is proposed. The true stiffness of the FE model is considered as the superposition of two pieces of stiffness information of different resolutions: the pre-defined stiffness information and updating stiffness information. While the resolution of former is solely decided by the meshing density of the FE model, the resolution of latter is decided by the limited information obtained from the experiment. The latter resolution is considerably lower than the former. Second generation wavelet is adopted to describe the updating stiffness information in the framework of MRA. This updating stiffness in MRA is realized at low level of resolution, therefore, needs less number of updating parameters. The efficiency of the optimization process is thus enhanced. The proposed method is suitable for the identification of multiple irregular cracks and performs well in capturing the global features of the structural damage. After the global features are identified, a refinement process proposed in the paper can be carried out to improve the performance of the MRA of the updating information. The effectiveness of the method is verified by numerical simulations of a box girder and the experiment of a three-span continues pre-stressed concrete bridge. It is shown that the proposed method corresponds well to the global features of the structural damage and is stable against the perturbation of modal parameters and small variations of the damage.

A Comparative Study of the Dwt and Wpt for Electrochemical Information Extraction of a LiCoO2 Cell

In general, an experimental discharging/charging terminal voltage is highly dependent to the pulse current. According to the pulse currents including different magnitude, time interval, and type (discharging/charging), it is possible to get various terminal voltages with non-stationary and transient phenomena. In this work, for elaborate information extraction of electrochemical characteristics from a LiCoO2 cell, the wavelet transform (WT) can be properly considered as a significant role. The WT is a state-of-the-art mathematical approach that decomposes a time domain signal into different frequency groups and provides an effective solution for analyzing the non-stationary signals. Specifically, this work introduces a comparative study of the discrete wavelet transform (DWT) and wavelet packet transform (WPT) for electrochemical feature extraction of a LiCoO2 cell. Both of DWT and WPT have the framework of multi-resolution analysis (MRA) with a vigorous function of both time and frequency localization. Through MRA requiring filtering and down-sampling, the information on the electrochemical characteristics of a LiCoO2 cell can be extracted from the discharging/charging voltage signal (DCVS) over a wide frequency range. Namely, the structure of the WPT is similar with that of the DWT. The main difference in the two techniques is the decomposition ability of high frequency band. In the DWT-based MRA, only the low frequency band is decomposed giving a right recursive binary tree structure, whereas in the WPT-based MRA, the low, as well as the high frequency bands are decomposed giving a balanced binary tree structure. Thus, the WPT can be defined as extension of the DWT. According to the DCVS with and without frequent discharging/charging, one of the two techniques will be finally selected as the optimum solution of electrochemical characteristics analysis. Extracted information can be usefully applied to cell’s discrimination for stable pack configuration, model-based state-of-charge (SOC) and state-of-health (SOH) estimations, etc.

A rectangular shell element formulation with a new multi-resolution analysis

A multi-resolution rectangular shell element with membrane-bending based on the Kirchhoff-Love theory is proposed. The multi-resolution analysis (MRA) framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape functions. The basic node shape functions are constructed from shifting to other three quadrants around a specific node of a basic element in one quadrant and joining the corresponding node shape functions of four elements at the specific node. The MRA endows the proposed element with the resolution level (RL) to adjust the element node number, thus modulating structural analysis accuracy accordingly. The node shape functions of Kronecker delta property make the treatment of element boundary condition quite convenient and enable the stiffness matrix and the loading column vectors of the proposed element to be automatically acquired through quadraturing around nodes in RL adjusting. As a result, the traditional 4-node rectangular shell element is a mono-resolution one and also a special case of the proposed element. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The simplicity and clarity of node shape function formulation with the Kronecker delta property, and the rational MRA enable the proposed element method to be implemented more rationally, easily and efficiently than the conventional mono-resolution rectangular shell element method or other corresponding MRA methods.

Regularizing the molecular potential in electronic structure calculations. I. SCF methods.

We present a method to remove the singular nuclear potential in a molecule and replace it with a regularized potential that is more amenable to be represented numerically. The singular nuclear potential is canceled by the similarity-transformed kinetic energy operator giving rise to an effective nuclear potential that contains derivative operators acting on the wave function. The method is fully equivalent to the non-similarity-transformed version. We give numerical examples within the framework of multi-resolution analysis for medium-sized molecules.

A multiresolution finite element method based on a new quadrilateral plate element

A new multiresolution quadrilateral plate element is proposed and a multiresolution finite element method is hence presented. The multiresolution analysis (MRA) framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape function. The basic node shape function is constructed by extending shape function around a specific node. The MRA endows the proposed element with the resolution level (RL) to adjust the element node number, thus modulating structural analysis accuracy accordingly. As a result, the traditional 4-node quadrilateral plate element and method is a monoresolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The rational MRA enable the implementation of the multiresolution element method to be more rational and efficient than that of the conventional monoresolution plate element method or other corresponding MRA methods such as the wavelet finite element method, the meshfree method, and the natural element method etc.

A hexahedron element formulation with a new multi-resolution analysis

A multiresolution hexahedron element is presented with a new multiresolution analysis (MRA) framework. The MRA framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on element domain of a basic node shape function. The basic node shape function is constructed from shifting to other seven quadrants around a specific node of a basic isoparametric element in one quadrant and joining the corresponding node shape functions of eight elements at the specific node. The MRA endows the proposed element with the resolution level (RL) to adjust structural analysis accuracy. As a result, the traditional 8-node hexahedron element is a monoresolution one and also a special case of the proposed element. The meshing for the monoresolution finite element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the solid mathematical basis. The simplicity and clarity of shape function construction with the Kronecker delta property and the rational MRA enable the proposed element method to be more rational, easier and efficient in its implementation than the conventional mono-resolution solid element method or other MRA methods. The multiresolution hexahedron element method is more adapted to dealing with the accurate computation of structural problems.

Forecasting Crude Oil Price with Multiscale Denoising Ensemble Model

Crude oil price becomes more volatile and sensitive to increasingly diversified influencing factors with higher level of deregulations worldwide. Current methodologies are being challenged as they have been constrained by traditional approaches assuming homogeneous time horizons and investment strategies. Approximations they provided over the long term time horizon no longer satisfy the accuracy requirement at shorter term and more microlevels. This paper proposes a novel crude oil price forecasting model based on the wavelet denoising ARMA models ensemble by least square support vector regression with the reduced forecasting matrix dimensions by independent component analysis. The proposed methodology combines the multi resolution analysis and nonlinear ensemble framework. The wavelet denoising based algorithm is introduced to separate and extract the underlying data components with distinct features, corresponding to investors with different investment scales, which are modeled with time series models of different specifications and parameters. Then least square support vector regression is introduced to nonlinearly ensemble results based on different wavelet families to further reduce the estimation biases and improve the forecasting generalizability. Empirical studies show the significant performance improvement when the proposed model is tested against the bench-mark models.

Computer Aided Diagnosis of Diabetic Retinopathy Using Multi-Resolution Analysis and Feature Ranking Frame Work

Computer Aided Diagnosis of Diabetic Retinopathy Using Multi-Resolution Analysis and Feature Ranking Frame Work