11,622 research outputs found
Learning Filters for the 2D Wavelet Transform
©2018 IEEEWe propose a new method for learning filters for the 2D discrete wavelet transform. We extend our previous work on the 1D wavelet transform in order to process images. We show that the 2D wavelet transform can be represented as a modified convolutional neural network (CNN). Doing so allows us to learn wavelet filters from data by gradient descent. Our learned wavelets are similar to traditional wavelets which are typically derived using Fourier methods. For filter comparison, we make use of a cosine measure under all filter rotations. The learned wavelets are able to capture the structure of the training data. Furthermore, we can generate images from our model in order to evaluate the filters. The main findings of this work is that wavelet functions can arise naturally from data, without the need for Fourier methods. Our model requires relatively few parameters compared to traditional CNNs, and is easily incorporated into neural network frameworks.Natural Sciences and Engineering Research Council of Canad
Kymatio: Scattering Transforms in Python
The wavelet scattering transform is an invariant signal representation
suitable for many signal processing and machine learning applications. We
present the Kymatio software package, an easy-to-use, high-performance Python
implementation of the scattering transform in 1D, 2D, and 3D that is compatible
with modern deep learning frameworks. All transforms may be executed on a GPU
(in addition to CPU), offering a considerable speed up over CPU
implementations. The package also has a small memory footprint, resulting
inefficient memory usage. The source code, documentation, and examples are
available undera BSD license at https://www.kymat.io
Cause Identification of Electromagnetic Transient Events using Spatiotemporal Feature Learning
This paper presents a spatiotemporal unsupervised feature learning method for
cause identification of electromagnetic transient events (EMTE) in power grids.
The proposed method is formulated based on the availability of
time-synchronized high-frequency measurement, and using the convolutional
neural network (CNN) as the spatiotemporal feature representation along with
softmax function. Despite the existing threshold-based, or energy-based events
analysis methods, such as support vector machine (SVM), autoencoder, and
tapered multi-layer perception (t-MLP) neural network, the proposed feature
learning is carried out with respect to both time and space. The effectiveness
of the proposed feature learning and the subsequent cause identification is
validated through the EMTP simulation of different events such as line
energization, capacitor bank energization, lightning, fault, and high-impedance
fault in the IEEE 30-bus, and the real-time digital simulation (RTDS) of the
WSCC 9-bus system.Comment: 9 pages, 7 figure
Wavelet Integrated CNNs for Noise-Robust Image Classification
Convolutional Neural Networks (CNNs) are generally prone to noise
interruptions, i.e., small image noise can cause drastic changes in the output.
To suppress the noise effect to the final predication, we enhance CNNs by
replacing max-pooling, strided-convolution, and average-pooling with Discrete
Wavelet Transform (DWT). We present general DWT and Inverse DWT (IDWT) layers
applicable to various wavelets like Haar, Daubechies, and Cohen, etc., and
design wavelet integrated CNNs (WaveCNets) using these layers for image
classification. In WaveCNets, feature maps are decomposed into the
low-frequency and high-frequency components during the down-sampling. The
low-frequency component stores main information including the basic object
structures, which is transmitted into the subsequent layers to extract robust
high-level features. The high-frequency components, containing most of the data
noise, are dropped during inference to improve the noise-robustness of the
WaveCNets. Our experimental results on ImageNet and ImageNet-C (the noisy
version of ImageNet) show that WaveCNets, the wavelet integrated versions of
VGG, ResNets, and DenseNet, achieve higher accuracy and better noise-robustness
than their vanilla versions.Comment: CVPR accepted pape
Deep Structured Features for Semantic Segmentation
We propose a highly structured neural network architecture for semantic
segmentation with an extremely small model size, suitable for low-power
embedded and mobile platforms. Specifically, our architecture combines i) a
Haar wavelet-based tree-like convolutional neural network (CNN), ii) a random
layer realizing a radial basis function kernel approximation, and iii) a linear
classifier. While stages i) and ii) are completely pre-specified, only the
linear classifier is learned from data. We apply the proposed architecture to
outdoor scene and aerial image semantic segmentation and show that the accuracy
of our architecture is competitive with conventional pixel classification CNNs.
Furthermore, we demonstrate that the proposed architecture is data efficient in
the sense of matching the accuracy of pixel classification CNNs when trained on
a much smaller data set.Comment: EUSIPCO 2017, 5 pages, 2 figure
A statistical multiresolution approach for face recognition using structural hidden Markov models
This paper introduces a novel methodology that combines the multiresolution feature of the discrete wavelet transform (DWT) with the local interactions of the facial structures expressed through the structural hidden Markov model (SHMM). A range of wavelet filters such as Haar, biorthogonal 9/7, and Coiflet, as well as Gabor, have been implemented in order to search for the best performance. SHMMs perform a thorough probabilistic analysis of any sequential pattern by revealing both its inner and outer structures simultaneously. Unlike traditional HMMs, the SHMMs do not perform the state conditional independence of the visible observation sequence assumption. This is achieved via the concept of local structures introduced by the SHMMs. Therefore, the long-range dependency problem inherent to traditional HMMs has been drastically reduced. SHMMs have not previously been applied to the problem of face identification. The results reported in this application have shown that SHMM outperforms the traditional hidden Markov model with a 73% increase in accuracy
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