Traditional Multiscale Methods Research Articles

DehazeModel: Enhancing Image Clarity with an Encoder-Decoder CNN Approach

We introduce DehazeModel, a Convolutional Neural Network (CNN) tailored for the purpose of enhancing single images by removing haze. DehazeModel comprises several components, including pre-processing, image dehazing, and post-processing modules. The pre-processing module, which is trainable, generates enhanced inputs featuring a wider array of characteristics compared to manually chosen pre-processing methods. The Image Dehazing module employs a novel encoder-decoder framework, overcoming common issues found in traditional multi-scale methods. Moreover, the post-processing module aids in minimizing artifacts in the resultant output. Experimental findings indicate that DehazeModel surpasses existing state-of-the-art techniques on the RESIDE dataset. Our experiments, conducted on both indoor and outdoor images, illustrate the robustness of our approach across various scenarios, independent of atmospheric scattering effects.

Wide-Band Butterfly Network: Stable and Efficient Inversion Via Multi-Frequency Neural Networks

We introduce an end-to-end deep learning architecture called the wide-band butterfly network (WideBNet) for approximating the inverse scattering map from wide-band scattering data. This architecture incorporates tools from computational harmonic analysis, such as the butterfly factorization, and traditional multi-scale methods, such as the Cooley–Tukey FFT algorithm, to drastically reduce the number of trainable parameters to match the inherent complexity of the problem. As a result, WideBNet is efficient: it requires fewer training points than off-the-shelf architectures and has stable training dynamics which are compatible with standard weight initialization strategies. The architecture automatically adapts to the dimensions of the data with only a few hyper-parameters that the user must specify. WideBNet is able to produce images that are competitive with optimization-based approaches, but at a fraction of the cost, and we also demonstrate numerically that it learns to super-resolve scatterers with a full aperture configuration.

Deep learning-based on-line image analysis for continuous industrial crystallization processes

In situ microscopic imaging is a useful tool in monitoring crystallization processes, including crystal nucleation, growth, aggregation and breakage, as well as possible polymorphic transition. To convert the qualitative information to be quantitative for the purpose of process optimization and control, accurate analysis of crystal images is essential. However, the accuracy of image segmentation with traditional methods is largely affected by many factors, including solid concentration and image quality. In this study, the deep learning technique using mask region-based convolutional neural network (Mask R-CNN) is investigated for the analysis of on-line images from an industrial crystallizer of 10 m3 operated in continuous mode with high solid concentration and overlapped particles. With detailed label points for each crystal and transfer learning technique, two models trained with 70,908 and 7,709 crystals respectively are compared for the effect of training data amount. The former model effectively segments the aggregated and overlapped crystals even at high solid concentrations. Moreover, it performs much better than the latter one and traditional multi-scale method both in terms of precision and recall, revealing the importance of large number of crystals in deep learning. Some geometrical characteristics of segmented crystals are also analyzed, involving equivalent diameter, circularity, and aspect ratio.

Approximate analytical solution in slow-fast system based on modified multi-scale method

A simple, yet accurate modified multi-scale method (MMSM) for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed. This method depends on the classical multi-scale method (MSM) and the method of variation of parameters. Assuming that the forced excitation is a constant, one could easily obtain the approximate analytical solution of the simplified system based on the traditional MSM. Then, this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant excitation. To certify the correctness and precision of the proposed analytical method, the van der Pol system with two scales subject to slowly periodic excitation is investigated; this system presents rich dynamical phenomena such as spiking (SP), spiking-quiescence (SP-QS), and quiescence (QS) responses. The approximate analytical expressions of the three types of responses are given by the MMSM, and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method (HBM). The results obtained by the present method are considerably better than those obtained by traditional methods, quantitatively and qualitatively, particularly when the excitation frequency is far less than the natural frequency of the system.

Convolutional Neural Networks With Class-Driven Loss for Multiscale VHR Remote Sensing Image Classification

Because land covers always have different scales, multiscale methods are widely used in very-high-resolution (VHR) remote sensing image classification. Traditional multiscale methods usually capture multiscale information by using rectangular windows of different sizes. Each scale contains the same number of training samples and is independently trained. Hence, the training process is time-consuming. In this article, a novel convolutional neural network with a class-driven loss (CNNs-CDL) model is proposed for multiscale VHR remote sensing image classification. First, a multiscale sample construction method is proposed to select a training sample and capture the relationships among different scale samples. The lowest-scale samples are selected on the lowest-resolution image and are mapped to the higher-resolution image without additional label information. Then, a CNN with class-driven loss is trained with the lowest-scale training samples. Class-driven loss can effectively learn the spatial dependence between the nonadjacent samples to promote classification accuracy. Finally, the CNN model is fine-tuned with the higher-scale samples. Although the number of higher-scale training samples increases, the fine-tuning process requires only a small number of iterations to converge. Hence, the proposed model can effectively reduce the training time. The experimental results for three VHR remote sensing images show that the proposed method performs better than several recently proposed methods.

CT and MRI image fusion based on multiscale decomposition method and hybrid approach

In the fusion process of medical computed tomography (CT) and magnetic resonance image (MRI), traditional multiscale methods often reduce the contrast of fused images. Although sparse representation (SR) methods overcome this shortcoming, they are often too smooth along the strong edges of the fusion image. To overcome these shortcomings, CT and MRI image fusion based on multiscale decomposition method and hybrid approach is proposed. There are three main steps. First, the cartoon parts and texture parts of CT and MRI are obtained by the improved image decomposition method using global sparse gradients. Second, the large structure cartoon parts are fused using the specific cartoon dictionary and the `L1-max norm' principle. The textured parts are fused using non-subsampled contourlet transformation (NSCT) and the maximum energy rule. Finally, the final result is obtained by superimposing the fused cartoon part and the fused texture part. The experimental results demonstrate that the proposed method outperforms the state-of-the-art method SR and NSCT in terms of visual effect and objective quality.

Self-Learning Multiscale Simulation

Molecular dynamics (MD) simulation plays more and more crucial roles in understanding the underlying molecular mechanisms of many biological processes. Unfortunately, due to the large number of degrees of freedom involved and inherently rugged energy surface, the time scale currently reachable by accurate all-atom (AA) simulation is far below typical biologically relevant time scale. Coarse graining the molecular representation can accelerate sampling, but the coarse grained (CG) simulation is unavoidably less accurate in energy estimate. To surmount these problems, a number of strategies have been proposed to integrate the AA and CG simulations, which is often called multiscale simulations. However, traditional multiscale methods heavily rely on the accuracy of the CG model. If the CG potential has its major basins different from those of AA potential, the multiscale simulation is not efficient and sometimes even bias the sampling. Here, we propose a new multiscale simulation method, self-learning multiscale molecular dynamics (SLMS-MD), which can achieve high accuracy and high sampling efficiency simultaneously. Based on the resolution exchange MD between atomistic and CG replicas, a self-learning strategy is introduced to progressively improve the initial CG potential by an iterative way based on the previously sampled CG conformations and their corresponding AA energies. The CG simulation ensures the efficient and broad sampling, and simultaneously the AA energies shape up the accuracy of the CG potential. Testing results show that the SLMS-MD can optimally combine the advantages of the AA and CG simulations, and achieve accurate and efficient multiscale simulations even when the initial CG potential is very poor. The resulting free energy converged to the exact result much faster than that by the replica exchange method. This method is generic and can be applied to many biological as well as non-biological problems.

Representation of Fourier Integral Operators Using Shearlets

Traditional methods of time-frequency and multiscale analysis, such as wavelets and Gabor frames, have been successfully employed for representing most classes of pseudodifferential operators. However, these methods are not equally effective in dealing with Fourier Integral Operators in general. In this article, we show that the shearlets, recently introduced by the authors and their collaborators, provide very efficient representations for a large class of Fourier Integral Operators. The shearlets are an affine-like system of well-localized waveforms at various scales, locations and orientations, which are particularly efficient in representing anisotropic functions. Using this approach, we prove that the matrix representation of a Fourier Integral Operator with respect to a Parseval frame of shearlets is sparse and well-organized. This fact recovers a similar result recently obtained by Candes and Demanet using curvelets, which illustrates the benefits of directional multiscale representations (such as curvelets and shearlets) in the study of those functions and operators where traditional multiscale methods are unable to provide the appropriate geometric analysis in the phase space.