Dense pixelwise prediction such as semantic segmentation is an up-to-date challenge for deep convolutional neural networks (CNNs). Many state-of-the-art approaches either tackle the loss of high-resolution information due to pooling in the encoder stage, or use dilated convolutions or high-resolution lanes to maintain detailed feature maps and predictions. Motivated by the structural analogy between multi-resolution wavelet analysis and the pooling/unpooling layers of CNNs, we introduce discrete wavelet transform (DWT) into the CNN encoder-decoder architecture and propose WCNN. The high-frequency wavelet coefficients are computed at encoder, which are later used at the decoder to unpooled jointly with coarse-resolution feature maps through the inverse DWT. The DWT/iDWT is further used to develop two wavelet pyramids to capture the global context, where the multi-resolution DWT is applied to successively reduce the spatial resolution and increase the receptive field. Experiment with the Cityscape dataset, the proposed WCNNs are computationally efficient and yield improvements the accuracy for high-resolution dense pixelwise prediction.
German Aerospace Center (DLR)（德国航空航天中心（DLR））；Technical University of Munich（慕尼黑工业大学）
The knowledge about the placement and appearance of lane markings is a prerequisite for the creation of maps with high precision, necessary for autonomous driving, infrastructure monitoring, lane-wise traffic management, and urban planning. Lane markings are one of the important components of such maps. Lane markings convey the rules of roads to drivers. While these rules are learned by humans, an autonomous driving vehicle should be taught to learn them to localize itself. Therefore, accurate and reliable lane marking semantic segmentation in the imagery of roads and highways is needed to ach…
Graph Convolutional Networks (GCNs) are widely used in a variety of applications, and can be seen as an unstructured version of standard Convolutional Neural Networks (CNNs). As in CNNs, the computational cost of GCNs for large input graphs (such as large point clouds or meshes) can be high and inhibit the use of these networks, especially in environments with low computational resources. To ease these costs, quantization can be applied to GCNs. However, aggressive quantization of the feature maps can lead to a significant degradation in performance. On a different note, Haar wavelet transform…
Image-matched nonseparable wavelets can find potential use in many applications including image classification, segmen- tation, compressive sensing, etc. This paper proposes a novel design methodology that utilizes convolutional neural net- work (CNN) to design two-channel non-separable wavelet matched to a given image. The design is proposed on quin- cunx lattice. The loss function of the convolutional neural network is setup with total squared error between the given input image to CNN and the reconstructed image at the output of CNN, leading to perfect reconstruction at the end of train- in…
Convolutional neural networks are able to perform a hierarchical learning process starting with local features. However, a limited attention is paid to enhancing such elementary level features like edges. We propose and evaluate two wavelet-based edge feature enhancement methods to preprocess the input images to convolutional neural networks. The first method develops feature enhanced representations by decomposing the input images using wavelet transform and limited reconstructing subsequently. The second method develops such feature enhanced inputs to the network using local modulus maxima o…
We present a logarithmic-scale efficient convolutional neural network architecture for edge devices, named WaveletNet. Our model is based on the well-known depthwise convolution, and on two new layers, which we introduce in this work: a wavelet convolution and a depthwise fast wavelet transform. By breaking the symmetry in channel dimensions and applying a fast algorithm, WaveletNet shrinks the complexity of convolutional blocks by an O(logD/D) factor, where D is the number of channels. Experiments on CIFAR-10 and ImageNet classification show superior and comparable performances of WaveletNet …
The GHM multi-level discrete wavelet transform is proposed as preprocessing for image super resolution with convolutional neural networks. Previous works perform analysis with the Haar wavelet only. In this work, 37 single-level wavelets are experimentally analyzed from Haar, Daubechies, Biorthogonal, Reverse Biorthogonal, Coiflets, and Symlets wavelet families. All single-level wavelets report similar results indicating that the convolutional neural network is invariant to choice of wavelet in a single-level filter approach. However, the GHM multi-level wavelet achieves higher quality reconst…
Due to the potential risk of inducing cancers, radiation dose of X-ray CT should be reduced for routine patient scanning. However, in low-dose X-ray CT, severe artifacts usually occur due to photon starvation, beamhardening, etc, which decrease the reliability of diagnosis. Thus, high quality reconstruction from low-dose X-ray CT data has become one of the important research topics in CT community. Conventional model-based denoising approaches are, however, computationally very expensive, and image domain denoising approaches hardly deal with CT specific noise patterns. To address these issues…
Nanjing University of Science and Technology（南京理工大学）
The feature learning methods based on convolutional neural network (CNN) have successfully produced tremendous achievements in image classification tasks. However, the inherent noise and some other factors may weaken the effectiveness of the convolutional feature statistics. In this paper, we investigate Discrete Wavelet Transform (DWT) in the frequency domain and design a new Wavelet-Attention (WA) block to only implement attention in the high-frequency domain. Based on this, we propose a Wavelet-Attention convolutional neural network (WA-CNN) for image classification. Specifically, WA-CNN de…
Recently, the reference functions for the synthesis and analysis of the autostereoscopic multiview and integral images in three-dimensional displays we introduced. In the current paper, we propose the wavelets to analyze such images. The wavelets are built on the reference functions as on the scaling functions of the wavelet analysis. The continuous wavelet transform was successfully applied to the testing wireframe binary objects. The restored locations correspond to the structure of the testing wireframe binary objects.
Motivated with the concept of transform learning and the utility of rational wavelet transform in audio and speech processing, this paper proposes Rational Wavelet Transform Learning in Statistical sense (RWLS) for natural images. The proposed RWLS design is carried out via lifting framework and is shown to have a closed form solution. The efficacy of the learned transform is demonstrated in the application of compressed sensing (CS) based reconstruction. The learned RWLS is observed to perform better than the existing standard dyadic wavelet transforms.
The University of Tokyo（东京大学）；Digital Frontier Inc.（数字前沿株式会社）
Spatial and spectral approaches are two major approaches for image processing tasks such as image classification and object recognition. Among many such algorithms, convolutional neural networks (CNNs) have recently achieved significant performance improvement in many challenging tasks. Since CNNs process images directly in the spatial domain, they are essentially spatial approaches. Given that spatial and spectral approaches are known to have different characteristics, it will be interesting to incorporate a spectral approach into CNNs. We propose a novel CNN architecture, wavelet CNNs, which…
Indian Institute of Technology Madras (IITM)（印度理工学院马德拉斯分校）；Healthcare Technology Innovation Centre (HTIC), IITM（印度理工学院马德拉斯分校医疗技术创新中心）
Several variants of Convolutional Neural Networks (CNN) have been developed for Magnetic Resonance (MR) image reconstruction. Among them, U-Net has shown to be the baseline architecture for MR image reconstruction. However, sub-sampling is performed by its pooling layers, causing information loss which in turn leads to blur and missing fine details in the reconstructed image. We propose a modification to the U-Net architecture to recover fine structures. The proposed network is a wavelet packet transform based encoder-decoder CNN with residual learning called CNN. The proposed WCNN has discret…
We study image compression by a separable wavelet basis $\big\{ψ(2^{k_1}x-i)ψ(2^{k_2}y-j),$ $ϕ(x-i)ψ(2^{k_2}y-j),$ $ψ(2^{k_1}(x-i)ϕ(y-j),$ $ϕ(x-i)ϕ(y-i)\big\},$ where $k_1, k_2 \in \mathbb{Z}_+$; $i,j\in\mathbb{Z}$; and $ϕ,ψ$ are elements of a standard biorthogonal wavelet basis in $L_2(\mathbb{R})$. Because $k_1\ne k_2$, the supports of the basis elements are rectangles, and the corresponding transform is known as the {\em rectangular wavelet transform}. We prove that if one-dimensional wavelet basis has $M$ dual vanishing moments then the rate of approximation by $N$ coefficients of rectangu…
The University of Tokyo（东京大学）；Digital Frontier Inc.（数字前沿公司）
Texture classification is an important and challenging problem in many image processing applications. While convolutional neural networks (CNNs) achieved significant successes for image classification, texture classification remains a difficult problem since textures usually do not contain enough information regarding the shape of object. In image processing, texture classification has been traditionally studied well with spectral analyses which exploit repeated structures in many textures. Since CNNs process images as-is in the spatial domain whereas spectral analyses process images in the fr…
We propose a convolutional neural network (CNN) architecture for image classification based on subband decomposition of the image using wavelets. The proposed architecture decomposes the input image spectra into multiple critically sampled subbands, extracts features using a single CNN per subband, and finally, performs classification by combining the extracted features using a fully connected layer. Processing each of the subbands by an individual CNN, thereby limiting the learning scope of each CNN to a single subband, imposes a form of structural regularization. This provides better general…
Harbin Institute of Technology（哈尔滨工业大学）；Changzhi University（长治学院）
In computer vision, convolutional networks (CNNs) often adopts pooling to enlarge receptive field which has the advantage of low computational complexity. However, pooling can cause information loss and thus is detrimental to further operations such as features extraction and analysis. Recently, dilated filter has been proposed to trade off between receptive field size and efficiency. But the accompanying gridding effect can cause a sparse sampling of input images with checkerboard patterns. To address this problem, in this paper, we propose a novel multi-level wavelet CNN (MWCNN) model to ach…
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…
In this paper we present a comparative study on fusion of visual and thermal images using different wavelet transformations. Here, coefficients of discrete wavelet transforms from both visual and thermal images are computed separately and combined. Next, inverse discrete wavelet transformation is taken in order to obtain fused face image. Both Haar and Daubechies (db2) wavelet transforms have been used to compare recognition results. For experiments IRIS Thermal/Visual Face Database was used. Experimental results using Haar and Daubechies wavelets show that the performance of the approach pres…
This paper present a novel off-line signature recognition method based on multi scale Fourier Descriptor and wavelet transform . The main steps of constructing a signature recognition system are discussed and experiments on real data sets show that the average error rate can reach 1%. Finally we compare 8 distance measures between feature vectors with respect to the recognition performance. Key words: signature recognition; Fourier Descriptor; Wavelet transform; personal verification
The bilateral filter is a useful nonlinear filter which without smoothing edges, it does spatial averaging. In the literature, the effectiveness of this method for image denoising is shown. In this paper, an extension of this method is proposed which is based on complex wavelet transform. In fact, the bilateral filtering is applied to the low-frequency (approximation) subbands of the decomposed image using complex wavelet transform, while the thresholding approach is applied to the high frequency subbands. Using the bilateral filter in the complex wavelet domain forms a new image denoising fra…
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…
Stop-band Energy Constraint for Orthogonal Tunable Wavelet Units in Convolutional Neural Networks for Computer Vision problems
Jacobs School of Engineering, University of California San Diego（加州大学圣地亚哥分校 Jacobs 工程学院）；Department of Computer Engineering, Tech University of Korea（科技大学韩国分校 计算机工程系）
Center for Engineering and Technology of MIPT（莫斯科物理技术学院工程技术中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
Quite a few people in the world have to stay under permanent surveillance for health reasons; they include diabetic people or people with some other chronic conditions, the elderly and the disabled.These groups may face heightened risk of having life-threatening falls or of being struck by a syncope. Due to limited availability of resources a substantial part of people at risk can not receive necessary monitoring and thus are exposed to excessive danger. Nowadays, this problem is usually solved via applying Human Activity Recognition (HAR) methods. HAR is a perspective and fast-paced Data Scie…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；Seoul National University Bundang Hospital（首尔国立大学盆唐医院）
Model based iterative reconstruction (MBIR) algorithms for low-dose X-ray CT are computationally expensive. To address this problem, we recently proposed a deep convolutional neural network (CNN) for low-dose X-ray CT and won the second place in 2016 AAPM Low-Dose CT Grand Challenge. However, some of the texture were not fully recovered. To address this problem, here we propose a novel framelet-based denoising algorithm using wavelet residual network which synergistically combines the expressive power of deep learning and the performance guarantee from the framelet-based denoising algorithms. …
With the growing popularity of the Internet, digital images are used and transferred more frequently. Although this phenomenon facilitates easy access to information, it also creates security concerns and violates intellectual property rights by allowing illegal use, copying, and digital content theft. Using watermarks in digital images is one of the most common ways to maintain security. Watermarking is proving and declaring ownership of an image by adding a digital watermark to the original image. Watermarks can be either text or an image placed overtly or covertly in an image and are expect…
National Yang Ming Chiao Tung University（阳明交通大学）；University at Albany - SUNY（奥尔巴尼大学 - 纽约州立大学）；University at Buffalo（布法罗大学）
Pooling is a simple but essential layer in modern deep CNN architectures for feature aggregation and extraction. Typical CNN design focuses on the conv layers and activation functions, while leaving the pooling layers with fewer options. We introduce the Learning Discrete Wavelet Pooling (LDW-Pooling) that can be applied universally to replace standard pooling operations to better extract features with improved accuracy and efficiency. Motivated from the wavelet theory, we adopt the low-pass (L) and high-pass (H) filters horizontally and vertically for pooling on a 2D feature map. Feature sign…
State Key Laboratory of Information Engineering in Survey, Mapping and Remote Sensing（测绘遥感信息工程国家重点实验室）
Traffic forecasting is crucial for urban traffic management and guidance. However, existing methods rarely exploit the time-frequency properties of traffic speed observations, and often neglect the propagation of traffic flows from upstream to downstream road segments. In this paper, we propose a hybrid approach that learns the spatio-temporal dependency in traffic flows and predicts short-term traffic speeds on a road network. Specifically, we employ wavelet transform to decompose raw traffic data into several components with different frequency sub-bands. A Motif-based Graph Convolutional Re…
Biorthogonal Tunable Wavelet Unit with Lifting Scheme in Convolutional Neural Network
Electrical and Computer Engineering Department, University of California San Diego（加州大学圣地亚哥分校电气与计算机工程系）；Department of Computer Engineering, Tech University of Korea（韩国科技大学计算机工程系）
This article is about the architecture of a lossless wavelet filter bank with reprogrammable logic. It is based on second generation of wavelets with a reduced of number of operations. A new basic structure for parallel architecture and modules to forward and backward integer discrete wavelet transform is proposed.
École Polytechnique Federale de Lausanne（洛桑联邦理工学院）
A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again a wavelet. In particular, we provide sharp estimates of the localization, vanishing moments, and smoothness of the transformed wavelet. We work in the general setting of non-compactly supported wavelets. Our main result is that, in the presence of some minimal smoothness and decay, the Hilbert transform of a wavelet is again as smooth and oscillating as the original wavelet, whereas its localization is cont…
Tunable Wavelet Unit based Convolutional Neural Network in Optical Coherence Tomography Analysis Enhancement for Classifying Type of Epiretinal Membrane Surgery
University of California San Diego（加州大学圣迭戈分校）；Jacobs Retina Center（雅各布视网膜中心）
Aliraqia University（伊拉克大学）；University of Technology（科技大学）；Kyiv National University of Construction and Architecture（基辅国立建筑与建筑工程大学）；Al-Farahidi University（法拉希迪大学）
This work is unique in the use of discrete wavelets that were built from or derived from Chebyshev polynomials of the second and third kind, filter the Discrete Second Chebyshev Wavelets Transform (DSCWT), and derive two effective filters. The Filter Discrete Third Chebyshev Wavelets Transform (FDTCWT) is used in the process of analyzing color images and removing noise and impurities that accompany the image, as well as because of the large amount of data that makes up the image as it is taken. These data are massive, making it difficult to deal with each other during transmission. However to …
Public Safety Research Center, Konyang University（建阳大学公共安全研究中心）
We propose the multiview wavelets based on voxel patterns of autostereoscopic multiview displays. Direct and inverse continuous wavelet transforms of binary and gray-scale images were performed. The input to the inverse wavelet transform was the array of wavelet coefficients of the direct transform. A restored image reproduces the structure of the multiview image correctly. Also, we modified the dimension of the parallax and the depth of 3D images. The restored and modified images were displayed in 3D using lenticular plates. In each case, the visual 3D picture corresponds to the applied modif…
Convolutional neural network (CNN), with ability of feature learning and nonlinear mapping, has demonstrated its effectiveness in prognostics and health management (PHM). However, explanation on the physical meaning of a CNN architecture has rarely been studied. In this paper, a novel wavelet driven deep neural network termed as WaveletKernelNet (WKN) is presented, where a continuous wavelet convolutional (CWConv) layer is designed to replace the first convolutional layer of the standard CNN. This enables the first CWConv layer to discover more meaningful filters. Furthermore, only the scale p…
Both of Wavelet and Fast Fourier Transform are strong signal processing tools in the field of Data Analysis. In this paper fast fourier transform (FFT) and Wavelet Transform are employed to observe some important features of Solar image (December, 2004). We have tried to find out the periodicity and coherence of different sections of the solar image. We plotted the distribution of energy in solar surface by analyzing the solar image with scalograms and 3D-coefficient plots.
University of Science and Technology of China（中国科学技术大学）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）
Volumetric image compression has become an urgent task to effectively transmit and store images produced in biological research and clinical practice. At present, the most commonly used volumetric image compression methods are based on wavelet transform, such as JP3D. However, JP3D employs an ideal, separable, global, and fixed wavelet basis to convert input images from pixel domain to frequency domain, which seriously limits its performance. In this paper, we first design a 3-D trained wavelet-like transform to enable signal-dependent and non-separable transform. Then, an affine wavelet basis…
Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavel…
Velalar College of Engg.&Tech.（维拉拉尔工程技术学院）；PSG College of Technology（PSG理工学院）；Bannari Amman Institute of Technology（班纳里·阿曼理工学院）
A method for the design of Fast Haar wavelet for signal processing and image processing has been proposed. In the proposed work, the analysis bank and synthesis bank of Haar wavelet is modified by using polyphase structure. Finally, the Fast Haar wavelet was designed and it satisfies alias free and perfect reconstruction condition. Computational time and computational complexity is reduced in Fast Haar wavelet transform.
Human Activity Recognition (HAR) is an emerging technology with several applications in surveillance, security, and healthcare sectors. Noninvasive HAR systems based on Wi-Fi Channel State Information (CSI) signals can be developed leveraging the quick growth of ubiquitous Wi-Fi technologies, and the correlation between CSI dynamics and body motions. In this paper, we propose Principal Component-based Wavelet Convolutional Neural Network (or PCWCNN) -- a novel approach that offers robustness and efficiency for practical real-time applications. Our proposed method incorporates two efficient pre…
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…
In this paper we consider the problem of reconstructing an image that is downsampled in the space of its $SE(2)$ wavelet transform, which is motivated by classical models of simple cells receptive fields and feature preference maps in primary visual cortex. We prove that, whenever the problem is solvable, the reconstruction can be obtained by an elementary project and replace iterative scheme based on the reproducing kernel arising from the group structure, and show numerical results on real images.
