This paper introduces a Deep Scattering network that utilizes Dual-Tree complex wavelets to extract translation invariant representations from an input signal. The computationally efficient Dual-Tree wavelets decompose the input signal into densely spaced representations over scales. Translation invariance is introduced in the representations by applying a non-linearity over a region followed by averaging. The discriminatory information in the densely spaced, locally smooth, signal representations aids the learning of the classifier. The proposed network is shown to outperform Mallat's ScatterNet on four datasets with different modalities on classification accuracy.
We introduce a ScatterNet that uses a parametric log transformation with Dual-Tree complex wavelets to extract translation invariant representations from a multi-resolution image. The parametric transformation aids the OLS pruning algorithm by converting the skewed distributions into relatively mean-symmetric distributions while the Dual-Tree wavelets improve the computational efficiency of the network. The proposed network is shown to outperform Mallat's ScatterNet on two image datasets, both for classification accuracy and computational efficiency. The advantages of the proposed network over…
Technion – Israel Institute of Technology（以色列理工学院）
In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical tree, which is assumed to capture the geometry and structure of the input data. It is applied to the data using a modified version of the common one-dimensional (1D) wavelet filtering and decimation scheme, which can employ different wavelet filters. In each level of this wavelet decomposition scheme, a permutation derived from the tree is applied to the appro…
Matoshri College of Engineering and Research Centre（马托什里工程与研究中心学院）；University of Pune（浦那大学）
In Image Compression, the researchers' aim is to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular techniques for image compression. The wavelet transform is one of the major processing components of image compression. The result of the compression changes as per the basis and tap of the wavelet used. It is proposed that proper selection of mother wavelet on the basis of nature of images, improve the quality as well as compression ratio remarkably. We suggest …
The University of Nottingham（诺丁汉大学）；Edith Cowan University（埃迪斯科文大学）；Sunway University（双威大学）
The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between centre and surround classes. Discriminant power of features for the classification is measured as mutual information between distributions of image features and corresponding classes . As the estimated discrepancy very much depends on considered scale level, multi-scale structure and discriminant power are integrated by employing discrete wavelet features and Hidden Markov Tree (HMT). With wavelet coefficients and Hidden Markov Tree parameters, quad-tree like label s…
Jiangsu Key Lab of Spectral Imaging & Intelligence Sense, Nanjing University of Science and Technology（南京理工大学江苏省光谱成像与智能感知重点实验室）；Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology（南京理工大学高维信息智能感知与系统教育部重点实验室）
Photon counting 3D imaging allows to obtain 3D images with single-photon sensitivity and sub-ns temporal resolution. However, it is challenging to scale to high spatial resolution. In this work, we demonstrate a photon counting 3D imaging technique with short-pulsed structured illumination and a single-pixel photon counting detector. The proposed multi-resolution photon counting 3D imaging technique acquires a high-resolution 3D image from a coarse image and edges at successfully finer resolution sampled by Hadamard multiplexing along the wavelet trees. The detected power is significantly incr…
Sichuan University（四川大学）；UC San Diego（加利福尼亚大学圣地亚哥分校）
JPEG is one of the widely used lossy compression methods. JPEG-compressed images usually suffer from compression artifacts including blocking and blurring, especially at low bit-rates. Soft decoding is an effective solution to improve the quality of compressed images without changing codec or introducing extra coding bits. Inspired by the excellent performance of the deep convolutional neural networks (CNNs) on both low-level and high-level computer vision problems, we develop a dual pixel-wavelet domain deep CNNs-based soft decoding network for JPEG-compressed images, namely DPW-SDNet. The pi…
WaveGuard: Robust Deepfake Detection and Source Tracing via Dual-Tree Complex Wavelet and Graph Neural Networks
College of Computer Science and Technology, Xinjiang University（新疆大学计算机科学与技术学院）；Xinjiang Multimodal Intelligent Processing and Information Security Engineering Technology Research Center（新疆多模态智能处理与信息安全工程技术研究中心）；College of Computer Science and Electronic Engineering, Hunan University（湖南大学计算机科学与电子工程学院）；School of Computer Science, Hefei University of Technology（合肥工业大学计算机科学与技术学院）
University of Science and Technology of China（中国科学技术大学）；Huawei Technologies（华为技术有限公司）；Huawei Cloud BU（华为云业务单元）
When smartphone cameras are used to take photos of digital screens, usually moire patterns result, severely degrading photo quality. In this paper, we design a wavelet-based dual-branch network (WDNet) with a spatial attention mechanism for image demoireing. Existing image restoration methods working in the RGB domain have difficulty in distinguishing moire patterns from true scene texture. Unlike these methods, our network removes moire patterns in the wavelet domain to separate the frequencies of moire patterns from the image content. The network combines dense convolution modules and dilate…
Institut Gaspard Monge（加斯帕尔·蒙日研究所）；Université de Paris-Est Marne-la-Vallée（巴黎东马恩拉瓦莱大学）
Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is performed -- which occurs in particular when an additive noise is corrupting the signal to be analyzed -- it is useful to characterize the statistical properties of the dual-tree wavelet coefficients of this process. As dual-tree decompositions constitute overcomplete frame expansions, correlation structures are introduced among the coefficients, even when a whit…
WaveSFNet: A Wavelet-Based Codec and Spatial--Frequency Dual-Domain Gating Network for Spatiotemporal Prediction
College of Software Engineering, Sichuan University（四川大学软件工程学院）；College of Computer Science, Sichuan University（四川大学计算机科学学院）；Sichuan University National Key Laboratory of Fundamental Science on Synthetic Vision（四川大学合成视觉基础科学国家重点实验室）
Institut Gaspard Monge（加斯帕尔·蒙日研究所）；CNRS-UMR 8049（法国国家科学研究中心-混合研究单位8049）；Université de Marne la Vallée（马恩拉瓦莱大学）；Institut Français du Pétrole（法国石油研究院）
We propose a 2D generalization to the $M$-band case of the dual-tree decomposition structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address (\textit{i}) the construction of the dual basis and (\textit{ii}) the resulting directional analysis. We also revisit the necessary pre-processing stage in the $M$-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors…
École polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
The dual-tree complex wavelet transform (DT-CWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-CWT which, among other things, offers a direct explanation for the improvement in the shift-invariance. The representation is based on the shifting action of the group of fractional Hilbert transform (fHT) operators, which extends the notion of arbitrary phase-shifts from sinusoids to finite-energy signals (wavelets in particular). In particular, we characterize the shiftability of the DT-CWT in ter…
RVS College of Engineering and Technology（RVS工程技术学院）
In recent years, many research achievements are made in the medical image fusion field. Fusion is basically extraction of best of inputs and conveying it to the output. Medical Image fusion means that several of various modality image information is comprehended together to form one image to express its information. The aim of image fusion is to integrate complementary and redundant information. In this paper, a multimodal image fusion algorithm based on the dual-tree complex wavelet transform (DT-CWT) and adaptive particle swarm optimization (APSO) is proposed. Fusion is achieved through the …
We present a wavelet-based dual-stream network that addresses color cast and blurry details in underwater images. We handle these artifacts separately by decomposing an input image into multiple frequency bands using discrete wavelet transform, which generates the downsampled structure image and detail images. These sub-band images are used as input to our dual-stream network that incorporates two sub-networks: the multi-color space fusion network and the detail enhancement network. The multi-color space fusion network takes the decomposed structure image as input and estimates the color corre…
Georgia Institute of Technology（佐治亚理工学院）；The Ohio State University（俄亥俄州立大学）
We propose a novel algorithm for compressive imaging that exploits both the sparsity and persistence across scales found in the 2D wavelet transform coefficients of natural images. Like other recent works, we model wavelet structure using a hidden Markov tree (HMT) but, unlike other works, ours is based on loopy belief propagation (LBP). For LBP, we adopt a recently proposed "turbo" message passing schedule that alternates between exploitation of HMT structure and exploitation of compressive-measurement structure. For the latter, we leverage Donoho, Maleki, and Montanari's recently proposed ap…
GeoCueFormer: Geometry-Guided Wavelet Representation and Prediction-Cued Dual-Stage Decoder for Underwater Semantic Segmentation
Southwest University of Science and Technology（西南科技大学）；Columbia University（哥伦比亚大学）；Carnegie Mellon University（卡内基梅隆大学）；University of California, Berkeley（加州大学伯克利分校）
Wavelet-Guided Dual-Frequency Encoding for Remote Sensing Change Detection
School of Computer Science and Technology, Shandong Technology and Business University（山东科技职业大学计算机科学与技术学院）；College of Computer and Data Science, Fuzhou University（福州大学计算机与数据科学学院）；College of Computer Science and Technology, Qingdao University（青岛大学计算机科学与技术学院）；School of Computer Science and Engineering, South China University of Technology（华南理工大学计算机科学与工程学院）
Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-CWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the shifting action of the group of fractional Hilbert transforms (fHT) which allow us to extend the notion of arbitrary phase-shifts beyond pure sinusoids. We explicitly characterize this shifting action for a particular family of Gabor-like wavelets which, in effect, links the corresponding dual-tree transform with the framework of windowed-Fourier analysis. We…
Key Laboratory for Information Science of Electromagnetic Waves, Ministry of Education, Fudan University（复旦大学电磁波信息科学教育部重点实验室）；Discipline and Technology Center of Microwave Vision Intelligent Sensing, Fudan University（复旦大学微波视觉智能感知学科与技术中心）
With the heterogeneous nature of tissue texture, using a single resolution approach for optimum classification might not suffice. In contrast, a multiresolution wavelet packet analysis can decompose the input signal into a set of frequency subbands giving the opportunity to characterise the texture at the appropriate frequency channel. An adaptive best bases algorithm for optimal bases selection for meningioma histopathological images is proposed, via applying the fractal dimension (FD) as the bases selection criterion in a tree-structured manner. Thereby, the most significant subband that bet…
Rutgers University（罗格斯大学）；Twitter Inc.（推特公司）；North Carolina Museum of Art（北卡罗来纳艺术博物馆）；Duke University（杜克大学）
In this paper, computer-based techniques for stylistic analysis of paintings are applied to the five panels of the 14th century Peruzzi Altarpiece by Giotto di Bondone. Features are extracted by combining a dual-tree complex wavelet transform with a hidden Markov tree (HMT) model. Hierarchical clustering is used to identify stylistic keywords in image patches, and keyword frequencies are calculated for sub-images that each contains many patches. A generative hierarchical Bayesian model learns stylistic patterns of keywords; these patterns are then used to characterize the styles of the sub-ima…
Unsupervised deep learning has recently demonstrated the promise of producing high-quality samples. While it has tremendous potential to promote the image colorization task, the performance is limited owing to the high-dimension of data manifold and model capability. This study presents a novel scheme that exploits the score-based generative model in wavelet domain to address the issues. By taking advantage of the multi-scale and multi-channel representation via wavelet transform, the proposed model learns the richer priors from stacked coarse and detailed wavelet coefficient components jointl…
Dual-domain Modulation Network for Lightweight Image Super-Resolution
Pattern Recognition and Intelligent System Laboratory, School of Artificial Intelligence, Beijing University of Posts and Telecommunications（模式识别与智能系统实验室，人工智能学院，北京邮电大学）；School of Microelectronics, Tianjin University（微电子学院，天津大学）；Institute of Advanced Technology, Nanjing University of Posts and Telecommunications（先进技术研究院，南京邮电大学）
GDSR: Global-Detail Integration through Dual-Branch Network with Wavelet Losses for Remote Sensing Image Super-Resolution
School of Computer Technology and Application, Qinghai University（青海大学计算机技术与应用学院）；Qinghai Provincial Laboratory for Intelligent Computing and Application, Qinghai University（青海省智能计算与应用实验室）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）；School of Computer and Information Science, Qinghai Institute of Technology（青海理工大学计算机与信息科学学院）；College of Agriculture and Animal Husbandry, Qinghai University（青海大学农业与动物科学学院）
Neural radiance fields (NeRF) have demonstrated the potential of coordinate-based neural representation (neural fields or implicit neural representation) in neural rendering. However, using a multi-layer perceptron (MLP) to represent a 3D scene or object requires enormous computational resources and time. There have been recent studies on how to reduce these computational inefficiencies by using additional data structures, such as grids or trees. Despite the promising performance, the explicit data structure necessitates a substantial amount of memory. In this work, we present a method to redu…
We propose a novel framework for real-time black-box universal attacks which disrupts activations of early convolutional layers in deep learning models. Our hypothesis is that perturbations produced in the wavelet space disrupt early convolutional layers more effectively than perturbations performed in the time domain. The main challenge in adversarial attacks is to preserve low frequency image content while minimally changing the most meaningful high frequency content. To address this, we formulate an optimization problem using time-scale (wavelet) representations as a dual space in three ste…
Functional MRI Time Series Generation via Wavelet-Based Image Transform and Spectral Flow Matching for Brain Disorder Identification
School of Information Technology, Monash University Malaysia（墨尔本大学马来西亚分校信息科技学院）；School of Engineering, Monash University Malaysia（墨尔本大学马来西亚分校工程学院）；Statistics Program, King Abdullah University of Science and Technology（国王阿卜杜勒·阿齐兹大学科学与技术学院统计学项目）
