Enhanced image denoising with MWRDCNN using residual dense blocks.
problem Image denoising with improved performance and robustness.
method Multi-wavelet residual dense convolutional neural network (MWRDCNN) with residual dense blocks (RDBs).
result Significantly improved performance in image denoising compared to existing techniques.
Improves CNN stability by translating classical signal denoising methods.
problem Stability of CNNs is poorly understood.
method Interprets classical signal denoising methods as ResNet architectures.
result Translates diffusivities, shrinkage functions, and regularizers into CNN activation functions.
Improved low-dose CT images with deep learning and framelet denoising.
problem Low-dose X-ray CT images often lack texture and detail.
method Proposed a wavelet residual network combining deep learning and framelet denoising.
result Significantly improved performance in preserving image detail.
Dual model predicts electricity spot prices using neural networks and wavelets.
problem Forecasting hourly electricity spot prices.
method Dual generalized long memory modelling with k-factor GARMA and G-GARCH models, using LLWNN and PSO for variance prediction.
result The hybrid k-factor GARMA-LLWNN model outperforms other methods in forecasting accuracy.
Proposes mWDN for interpreting time series analysis.
problem Lack of effective modeling for frequency information in time series analysis.
method Wavelet-based multilevel neural network structure (mWDN).
result Demonstrates excellent performance and interpretability of mWDN models.
Wavelets help compress neural networks efficiently.
problem Efficiently compressing linear layers in neural networks.
method Learnable wavelet transforms to compress RNNs.
result Wavelet compressed RNNs have fewer parameters and perform competitively.
Proposes a neural network method to learn wavelet filters from data.
problem Learning structured wavelet filters from raw data.
method Formulates discrete wavelet transform as a neural network, trains with gradient descent.
result Trained model produces wavelets similar to traditional Fourier-derived ones.
Improved wavelet filters enhance neural network performance.
problem Enhancing wavelet transform for better neural network representations.
method Extending gradient-based filter learning to dual-tree wavelet transform.
result Directional filters improve dual-tree wavelet transform performance.
Wavelet Networks learn from raw time-series data, outperforming conventional CNNs.
problem Learning from raw time-series data efficiently and effectively.
method Constructing scale-translation equivariant neural networks based on wavelet symmetries.
result Wavelet Networks outperform conventional CNNs on raw waveforms and spectrograms.
VDWs enhance graph neural networks for analyzing complex data.
problem Analyzing data on non-Euclidean geometries.
method Incorporating vector diffusion wavelets into geometric graph neural networks.
result VDW-GNNs effectively analyze synthetic and real-world data.
This paper investigates the hedging effectiveness of a dynamic moving window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dy…
Paper introduces rational Gaussian wavelets for efficient signal approximation.
problem Efficiently approximating complex signals with few coefficients.
method Continuous wavelet transform using rational Gaussian wavelets with adjustable parameters.
result Proposed rational Gaussian wavelets provide accurate signal approximations.
GWNN uses graph wavelets for efficient graph CNNs.
problem Spectral graph CNNs' high computational cost and lack of interpretability.
method Graph wavelet transform for efficient graph convolution.
result GWNN significantly outperforms spectral graph CNNs.
Wavelet Kolmogorov-Arnold Networks improve federated learning performance.
problem Improving performance in federated learning with heterogeneous data.
method Implemented Wav-KAN with CWT and DWT for multiresolution capability, integrating wavelet-based activation functions.
result Significant improvements in computational efficiency, robustness, and accuracy in federated learning.
Express Wavenet reduces neural network parameters to 1% of standard networks.
problem Optical neural networks with high parameter count.
method Wavelet modulation, random shift wavelets, expressway structure.
result Express Wavenet achieves high accuracy with significantly fewer parameters.
Paper introduces a neural framework for accurate energy forecasting.
problem Challenges of forecasting energy demand and supply due to variability of renewable sources and dynamic consumption patterns.
method Integrates Neural ODEs, graph attention, multi-resolution wavelet transformations, and adaptive learning of frequencies.
result Consistently outperforms state-of-the-art baselines in various forecasting metrics across diverse datasets.
AWD distills neural network info into interpretable wavelets.
problem Imbalanced interpretability and efficiency in deep learning models.
method Adaptive wavelet distillation (AWD) penalizes neural network attributions in wavelet domain.
result AWD yields a concise, efficient, and interpretable model.
Wav-KAN improves neural network interpretability and performance.
problem Challenges in interpretability, training speed, robustness, and performance of traditional neural networks.
method Integrates wavelet functions into the Kolmogorov-Arnold network structure for efficient data representation.
result Enhanced accuracy, faster training speeds, and increased robustness compared to existing methods.
Develops wavelet-based neural network approximation theory.
problem Analyzing neural network approximation capabilities over various activation functions.
method Wavelet frame theory on spaces of homogeneous type, sufficient conditions for approximation, error estimates.
result Derives sufficient conditions for neural networks to approximate any functions in a given space, including non-smooth activations.
MODWST improves classification tasks with wavelet scattering.
problem Signal classification challenges.
method Combines MODWT and WST for feature extraction.
result MODWST outperforms CNNs in limited data scenarios.
Improved texture synthesis using wavelet-based statistics with rectifier non-linearity.
problem Improving texture synthesis quality using wavelet representations.
method Proposes a family of statistics based on non-linear wavelet representations with a generalized rectifier non-linearity.
result Significantly improves visual quality of texture synthesis compared to classical wavelet-based models.
A new WNN framework selects wavelet bases for efficient learning.
problem Challenges in constructing accurate wavelet bases and high computational costs in WNN.
method Introduces a constructive WNN that selects initial bases and trains functions by introducing new bases for predefined accuracy while reducing computational costs.
result Significantly improves computational efficiency through a frequency estimator and wavelet-basis increase mechanism.
WCAM assesses neural network reliability by attributing decisions to wavelet scales.
problem Challenges in evaluating neural network reliability and feature robustness.
method Introduces WCAM, a wavelet-based attribution method to assess decision reliability.
result WCAM reveals where and on what scales a model focuses, enabling reliable decision assessment.
Enhances DSN with multi-family wavelet transforms and sparsity.
problem Improving interpretability and expressive power of DSN.
method Multi-family wavelet transforms and optimal thresholding.
result Enhanced robustness and diversity of scattering coefficients.
Geometric wavelet scattering on manifolds improves neural network understanding.
problem Improving neural network understanding on manifold and graph domains.
method Defining a geometric scattering transform based on wavelet filters and nonlinearities.
result Generalizes deformation stability and local translation invariance to manifolds.
PDE-Net learns PDEs from data using neural networks.
problem Learning PDEs from complex system dynamics.
method Proposes PDE-Net, a feed-forward deep network to learn differential operators and nonlinear responses.
result PDE-Net can accurately predict dynamics and uncover hidden PDE models.
WaveletGAN improves GANs by homogenizing noise through multi-channel wavelet filtering.
problem Current noise generation models in GANs struggle with homogenizing noise, leading to low-fidelity samples.
method Proposes a multi-channel wavelet-based filtering method to homogenize noise in GANs.
result WaveletGAN generates high-fidelity samples with the smallest FIDs on Fashion-MNIST, KMNIST, and SVHN datasets.
Improved KELM for multiclass classification with wavelet kernel.
problem Low test accuracy in multiclass classification problems.
method Mexican Hat wavelet kernel ELM.
result Significantly improved performance compared to other classifiers.
Cake wavelets minimize orientation score uncertainty.
problem Minimizing uncertainty in orientation scores.
method Axiomatically derived wavelets for orientation score lifting.
result Uncertainty gap of cake wavelets is less than 1.1.
A new GNN module learns geometric scattering features for better graph classification and feature exploration.
problem Learning long-range graph relations and extracting meaningful features from graphs.
method Proposes a learnable geometric scattering (LEGS) module in graph neural networks (GNNs), incorporating wavelet filters.
result LEGS-based GNNs outperform existing methods in graph classification and feature extraction tasks.
Study proposes a new method for MRI image reconstruction using denoising autoencoders and undecimated wavelet transforms.
problem Efficient MRI image reconstruction using under-sampled data.
method Undecimated wavelet transform, denoising autoencoder, proximal gradient algorithm.
result The proposed method enhances MRI image reconstruction efficiency and robustness.
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on identical semi-discrete wavelet frames in each network layer…
CGNNs use wavelets for continuous function generation in infinite-dimensional spaces.
problem Generating continuous functions in infinite-dimensional spaces for applications like inverse problems.
method Inspired by DCGAN, CGNNs use wavelet multiresolution analysis with convolutional and nonlinear layers.
result CGNNs can be injective under certain conditions on filters and nonlinearity, leading to Lipschitz stability estimates.
WavPool improves deep neural networks with wavelet-based pooling.
problem Improving efficiency and performance of deep neural networks.
method Introducing WavPool, a wavelet-transform-based pooling layer.
result WavPool outperforms existing network architectures by 10% on CIFAR-10.
New CycleGAN uses invertible generator for faster, less resource-intensive CT denoising.
problem Efficient unsupervised CT denoising without paired data.
method Single generator with wavelet residual domain, no discriminators, cycle consistency via invertible generator.
result Significantly improved denoising performance with faster training and less parameters.
RP-WNO extends WNO with uncertainty quantification, useful for scientists and engineers.
problem Uncertainty in predictions of deep learning models.
method Randomized Prior Wavelet Neural Operator (RP-WNO) with uncertainty quantification module.
result RP-WNO effectively estimates uncertainty in predictions.
Paper defends iris recognition from adversarial examples using wavelet decomposition.
problem Adversarial examples threaten deep neural networks in biometric applications.
method Wavelet domain denoising of input examples to detect and mitigate adversarial attacks.
result Proposed defense strategies improve recognition accuracy against adversarial attacks.
Generative models are created by inverting a wavelet Scattering transform.
problem Understanding and simplifying the mathematics behind generative models.
method Inverts a fixed embedding operator using a wavelet Scattering transform.
result Scattering generators produce similar results to GANs and VAEs without optimization.
Logistic regression with wavelets achieves bacterial infection detection accuracy.
problem Interpreting complex biomedical signal models for high-stakes decisions.
method Wavelet features and knockoff variables for feature selection.
result Logistic regression outperforms neural networks in bacterial infection detection.
We discuss approximation of functions using deep neural nets. Given a function f on a d-dimensional manifold Γ⊂Rm, we construct a sparsely-connected depth-4 neural network and bound its error in approximating f. The size of the network depends on dimension and curvature of the manifold Γ, the…
Wavelet and LSTM models improve stock price forecasting.
problem Predicting non-stationary stock prices.
method Wavelet Transform for denoising, SVR and LSTM for prediction.
result Improved accuracy in stock price predictions.
Graph scattering transforms are stable to metric perturbations of network topology.
problem Stability of graph data representations under metric perturbations.
method Extending scattering transforms to network data using multiresolution graph wavelets and graph convolutions.
result Graph scattering transforms are stable to metric perturbations of the underlying network topology.
MathNet uses wavelets for graph representation and learning.
problem Graph Neural Networks (GNNs) for graph classification and regression.
method Multiresolution Haar-like wavelets, graph convolution, and pooling.
result MathNet achieves notable accuracy gains on graph classification and regression tasks.
Deep decoder generates images with few parameters, comparable to wavelets.
problem Representing and generating natural images efficiently.
method Untrained deep neural network with simple architecture (no convolutions).
result Deep decoder compresses images into concise weights, comparable to wavelet thresholding.
A method uses image processing and deep learning for financial market state prediction.
problem Low signal-to-noise ratio in financial time series data.
method Wavelet transform for denoising, convolutional neural network for pattern extraction.
result Competitive prediction accuracy of market states 'Up' and 'Down' on S&P 500 data.
We develop a neural network model to classify liver cancer patients into high-risk and low-risk groups using genomic data. Our approach provides a novel technique to classify big data sets using neural network models. We preprocess the data before training the neural network models. We first expand the data using wavel…
Unified graph scattering transforms improve theoretical properties of graph neural networks.
problem Improving theoretical guarantees for graph neural networks.
method Introducing windowed and non-windowed geometric scattering transforms for graphs.
result Unified family of graph scattering transforms with provable stability and invariance.
A cost-effective method to generate high-resolution images using wavelet-based super-resolution.
problem High compute resources required for training state-of-the-art image generation models.
method Wavelet-based two-step training framework: low-frequency sampling followed by super-resolution.
result Achieves FID of 10.59 on ImageNet 512x512 with half the compute of BigGAN.