Objective: The present study introduces a fractional wavelet scattering network (FrScatNet), which is a generalized translation invariant version of the classical wavelet scattering network (ScatNet). Methods: In our approach, the FrScatNet is constructed based on the fractional wavelet transform (FRWT). The fractional scattering coefficients are iteratively computed using FRWTs and modulus operators. The feature vectors constructed by fractional scattering coefficients are usually used for signal classification. In this work, an application example of FrScatNet is provided in order to assess its performance on pathological images. Firstly, the FrScatNet extracts feature vectors from patches of the original histological images under different orders. Then we classify those patches into target (benign or malignant) and background groups. And the FrScatNet property is analyzed by comparing error rates computed from different fractional orders respectively. Based on the above pathological image classification, a gland segmentation algorithm is proposed by combining the boundary information and the gland location. Results: The error rates for different fractional orders of FrScatNet are examined and show that the classification accuracy is significantly improved in fractional scattering domain. We also compare the FrScatNet based gland segmentation method with those proposed in the 2015 MICCAI Gland Segmentation Challenge and our method achieves comparable results. Conclusion: The FrScatNet is shown to achieve accurate and robust results. More stable and discriminative fractional scattering coefficients are obtained by the FrScatNet in this work. Significance: The added fractional order parameter is able to analyze the image in the fractional scattering domain.
Southeast University（东南大学）；Université de Rennes 1（雷恩第一大学）；Centre de Recherche en Information Biomédicale Sino-français（中法生物医学信息研究中心）；Taiyuan University of Technology（太原理工大学）
One of the key challenges in the area of signal processing on graphs is to design transforms and dictionaries methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier transform (GFT) to graph fractional Fourier transform (GFRFT), which is then used to define a novel transform named spectral graph fractional wavelet transform (SGFRWT), which is a generalized and extended version of spectral graph wavelet transform (SGWT). A fast algorithm for SGFRWT is also derived and implemented based on Fourier series approximation. The potenti…
This report presents the results of a multi-scale wavelet based scheme for single image de-hazing and underwater image enhancement. The scheme is fast and highly localized in addition to global enhancement of hazy images. A PDE-based formulation enables additional versatility as the iterative nature allows more flexibility for various types of images. Visual and objective results from experiments indicate that the proposed approach competes favourably or surpasses most of the state-of-the-art approaches.
Southeast University（东南大学）；INSERM（法国国家健康与医学研究院）；Université de Rennes 1（雷恩第一大学）
Texture plays an important role in many image analysis applications. In this paper, we give a performance evaluation of color texture classification by performing wavelet scattering network in various color spaces. Experimental results on the KTH_TIPS_COL database show that opponent RGB based wavelet scattering network outperforms other color spaces. Therefore, when dealing with the problem of color texture classification, opponent RGB based wavelet scattering network is recommended.
We introduce a two-layer wavelet scattering network, for object classification. This scattering transform computes a spatial wavelet transform on the first layer and a new joint wavelet transform along spatial, angular and scale variables in the second layer. Numerical experiments demonstrate that this two layer convolution network, which involves no learning and no max pooling, performs efficiently on complex image data sets such as CalTech, with structural objects variability and clutter. It opens the possibility to simplify deep neural network learning by initializing the first layers with …
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…
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 Scatter…
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…
A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear modulus and averaging operators. The first network layer outputs SIFT-type descriptors whereas the next layers provide complementary invariant information which improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary …
This paper examines the possibility of, and the possible advantages to learning the filters of convolutional neural networks (CNNs) for image analysis in the wavelet domain. We are stimulated by both Mallat's scattering transform and the idea of filtering in the Fourier domain. It is important to explore new spaces in which to learn, as these may provide inherent advantages that are not available in the pixel space. However, the scattering transform is limited by its inability to learn in between scattering orders, and any Fourier domain filtering is limited by the large number of filter param…
Harvard University（哈佛大学）；Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）
Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in generalization, and provide dimension reduction. In this work, we introduce a fast-to-compute, translationally invariant and rotationally equivariant wavelet scattering network (EqWS) and filter bank of wavelets (triglets). We demonstrate the interpretability and quantify the invariance/equivariance of the coefficients, briefly commenting on difficulties with implement…
Southeast University（东南大学）；Université de Rennes（雷恩大学）；INSERM（法国国家健康与医学研究院）；Centre de Recherche en Information Biomédicale Sino-français (CRIBs)（中法生物医学信息研究中心）
Deep learning is a hot research topic in the field of machine learning methods and applications. Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but both of them are difficult to train since they need to train the generator (or encoder) and the discriminator (or decoder) simultaneously, which is easy to cause unstable training. In order to solve or alleviate the synchronous training difficult problems of GANs and VAEs, recently, researchers propose Generative Scattering Networks (GSNs), which use wavele…
The scattering transform network (STN), which has a similar structure as that of a popular convolutional neural network except its use of predefined convolution filters and a small number of layers, can generates a robust representation of an input signal relative to small deformations. We propose a novel Monogenic Wavelet Scattering Network (MWSN) for 2D texture image classification through a cascade of monogenic wavelet filtering with nonlinear modulus and averaging operators by replacing the 2D Morlet wavelet filtering in the standard STN. Our MWSN can extract useful hierarchical and direct…
Guizhou University（贵州大学）；Harbin Medical University Cancer Hospital（哈尔滨医科大学附属肿瘤医院）；Beijing Jiaotong University（北京交通大学）；Shanghai Jiao Tong University（上海交通大学）；University Lyon, INSA Lyon, CNRS, Inserm, IRP Metislab CREATIS UMR5220, U1206（里昂大学、里昂国立应用科学学院、法国国家科学研究中心、法国国家健康与医学研究院、IRP Metislab CREATIS UMR5220、U1206）
In vivo diffusion tensor imaging (DTI) is a promising technique to investigate noninvasively the fiber structures of the in vivo human heart. However, signal loss due to motions remains a persistent problem in in vivo cardiac DTI. We propose a novel motion-compensation method for investigating in vivo myocardium structures in DTI with free-breathing acquisitions. The method is based on an invertible Wavelet Scattering achieved by means of Convolutional Neural Network (WSCNN). It consists of first extracting translation-invariant wavelet scattering features from DW images acquired at different …
