Motion magnification in coronal seismology

We introduce a new method for the investigation of low-amplitude transverse oscillations of solar plasma non-uniformities, such as coronal loops, individual strands in coronal arcades, jets, prominence fibrils, polar plumes, and other contrast features, observed with imaging instruments. The method is based on the two-dimensional dual tree complex wavelet transform (DT$\mathbb{C}$WT). It allows us to magnify transverse, in the plane-of-the-sky, quasi-periodic motions of contrast features in image sequences. The tests performed on the artificial data cubes imitating exponentially decaying, multi-periodic and frequency-modulated kink oscillations of coronal loops showed the effectiveness, reliability and robustness of this technique. The algorithm was found to give linear scaling of the magnified amplitudes with the original amplitudes provided they are sufficiently small. Also, the magnification is independent of the oscillation period in a broad range of the periods. The application of this technique to SDO/AIA EUV data cubes of a non-flaring active region allowed for the improved detection of low-amplitude decay-less oscillations in the majority of loops.Comment: Accepted for publication in Solar Physic

各種の性質を改善した直交DTCWTの設計に関する研究

The Dual tree complex wavelet transforms (DTCWTs) have been found to be successful in many applications of signal and image processing. DTCWTs employ two real wavelet transforms, where one wavelet corresponds to the real part of complex wavelet and the other is the imaginary part. Two wavelet bases are required to be a Hilbert transform pair. Thus, DTCWTs are nearly shift invariant and have a good directional selectivity in two or higher dimensions with limited redundancies. In this dissertation, we propose two new classes of DTCWTs with improved properties. In Chapter 2, we review the Fourier transform at first and then introduce the fundamentals of dual tree complex wavelet transform. The wavelet transform has been proved to be a successful tool to express the signal in time and frequency domain simultaneously. To obtain the wavelet coefficients efficiently, the discrete wavelet transform has been introduced since it can be achieved by a tree of two-channel filter banks. Then, we discuss the design conditions of two-channel filter banks, i.e., the perfect reconstruction and orthonormality. Additionally, some properties of scaling and wavelet functions including orthonormality, symmetry and vanishing moments are also given. Moreover, the structure of DTCWT is introduced, where two wavelet bases are required to form a Hilbert transform pair. Thus, the corresponding scaling lowpass filters must satisfy the half-sample delay condition. Finally, the objective measures of quality are given to evaluate the performance of the complex wavelet. In Chapter 3, we propose a new class of DTCWTs with improved analyticity and frequency selectivity by using general IIR filters with numerator and denominator of different degree. In the common-factor technique proposed by Selesnick, the maximally at allpass filter was used to satisfy the halfsample delay condition, resulting in poor analyticity of complex wavelets. Thus, to improve the analyticity of complex wavelets, we present a method for designing allpass filters with the specified degree of flatness and equiripple phase response in the approximation band. Moreover, to improve the frequency selectivity of scaling lowpass filters, we locate the specified number of zeros at z = -1 and minimize the stopband error. The well-known Remez exchange algorithm has been applied to approximate the equiripple response. Therefore, a set of filter coefficients can be easily obtained by solving the eigenvalue problem. Furthermore, we investigate the performance on the proposed DTCWTs and dedicate how to choose the approximation band and stopband properly. It is shown that the conventional DTCWTs proposed by Selesnick are only the special cases of DTCWTs proposed in this dissertation. In Chapter 4, we propose another class of almost symmetric DTCWTs with arbitrary center of symmetry. We specify the degree of flatness of group delay, and the number of vanishing moments, then apply the Remez exchange algorithm to minimize the difference between two scaling lowpass filters in the frequency domain, in order to improve the analyticity of complex wavelets. Therefore, the equiripple behaviour of the error function can be obtained through a few iterations. Moreover, two scaling lowpass filters can be obtained simultaneously. As a result, the complex wavelets are orthogonal and almost symmetric, and have the improved analyticity. Since the group delay of scaling lowpass filters can be arbitrarily specified, the scaling functions have the arbitrary center of symmetry. Finally, several experiments of signal denoising are carried out to demonstrate the efficiency of the proposed DTCWTs. It is clear that the proposed DTCWTs can achieve better performance on noise reduction.電気通信大学201

Uses of Complex Wavelets in Deep Convolutional Neural Networks

Image understanding has long been a goal for computer vision. It has proved to be an exceptionally difficult task due to the large amounts of variability that are inherent to objects in a scene. Recent advances in supervised learning methods, particularly convolutional neural networks (CNNs), have pushed forth the frontier of what we have been able to train computers to do. Despite their successes, the mechanics of how these networks are able to recognize objects are little understood, and the networks themselves are often very difficult and time-consuming to train. It is very important that we improve our current approaches in every way possible. A CNN is built from connecting many learned convolutional layers in series. These convolutional layers are fairly crude in terms of signal processing - they are arbitrary taps of a finite impulse response filter, learned through stochastic gradient descent from random initial conditions. We believe that if we reformulate the problem, we may achieve many insights and benefits in training CNNs. Noting that modern CNNs are mostly viewed from and analyzed in the spatial domain, this thesis aims to view the convolutional layers in the frequency domain (viewing things in the frequency domain has proved useful in the past for denoising, filter design, compression and many other tasks). In particular, we use complex wavelets (rather than the Fourier transform or the discrete wavelet transform) as basis functions to reformulate image understanding with deep networks. In this thesis, we explore the most popular and well-developed form of using complex wavelets in deep learning, the ScatterNet from Stephane Mallat. We explore its current limitations by building a DeScatterNet and found that while it has many nice properties, it may not be sensitive to the most appropriate shapes for understanding natural images. We then develop a locally invariant convolutional layer, a combination of a complex wavelet transform, a modulus operation, and a learned mixing. To do this, we derive backpropagation equations and allow gradients to flow back through the (previously fixed) ScatterNet front end. Connecting several such locally invariant layers allows us to build learnable ScatterNet, a more flexible and general form of the ScatterNet (while still maintaining its desired properties). We show that the learnable ScatterNet can provide significant improvements over the regular ScatterNet when being used as a front end for a learning system. Additionally, we show that the locally invariant convolutional layer can directly replace convolutional layers in a deep CNN (and not just at the front-end). The locally invariant convolutional layers naturally downsample the input (because of the complex modulus) while increasing the channel dimension (because of the multiple wavelet orientations used). This is an operation that often happens in a CNN by a combination of a pooling and convolutional layer. It was at these locations in a CNN where the learnable ScatterNet performed best, implying it may be useful as learnable pooling layer. Finally, we develop a system to learn complex weights that act directly on the wavelet coefficients of signals, in place of a convolutional layer. We call this layer the wavelet gain layer and show it can be used alongside convolutional layers. The network designer may then choose to learn in the pixel or wavelet domains. This layer shows a lot of promise and affords more control over what regions of the frequency space we want our layer to learn from. Our experiments show that it can improve on learning in the pixel domain for early layers of a CNN

NOVEL OFDM SYSTEM BASED ON DUAL-TREE COMPLEX WAVELET TRANSFORM

The demand for higher and higher capacity in wireless networks, such as cellular, mobile and local area network etc, is driving the development of new signaling techniques with improved spectral and power efficiencies. At all stages of a transceiver, from the bandwidth efficiency of the modulation schemes through highly nonlinear power amplifier of the transmitters to the channel sharing between different users, the problems relating to power usage and spectrum are aplenty. In the coming future, orthogonal frequency division multiplexing (OFDM) technology promises to be a ready solution to achieving the high data capacity and better spectral efficiency in wireless communication systems by virtue of its well-known and desirable characteristics. Towards these ends, this dissertation investigates a novel OFDM system based on dual-tree complex wavelet transform (D

Assessment of Dual-Tree Complex Wavelet Transform to improve SNR in collaboration with Neuro-Fuzzy System for Heart Sound Identification

none6siThe research paper proposes a novel denoising method to improve the outcome of heartsound (HS)-based heart-condition identification by applying the dual-tree complex wavelet transform (DTCWT) together with the adaptive neuro-fuzzy inference System (ANFIS) classifier. The method consists of three steps: first, preprocessing to eliminate 50 Hz noise; second, applying four successive levels of DTCWT to denoise and reconstruct the time-domain HS signal; third, to evaluate ANFIS on a total of 2735 HS recordings from an international dataset (PhysioNet Challenge 2016). The results show that the signal-to-noise ratio (SNR) with DTCWT was significantly improved (p < 0.001) as compared to original HS recordings. Quantitatively, there was an 11% to many decibel (dB)-fold increase in SNR after DTCWT, representing a significant improvement in denoising HS. In addition, the ANFIS, using six time-domain features, resulted in 55–86% precision, 51–98% recall, 53–86% f-score, and 54–86% MAcc compared to other attempts on the same dataset. Therefore, DTCWT is a successful technique in removing noise from biosignals such as HS recordings. The adaptive property of ANFIS exhibited capability in classifying HS recordings.Special Issue “Biomedical Signal Processing”, Section BioelectronicsopenBassam Al-Naami, Hossam Fraihat, Jamal Al-Nabulsi, Nasr Y. Gharaibeh, Paolo Visconti, Abdel-Razzak Al-HinnawiAl-Naami, Bassam; Fraihat, Hossam; Al-Nabulsi, Jamal; Gharaibeh, Nasr Y.; Visconti, Paolo; Al-Hinnawi, Abdel-Razza

BEAT CLASSIFICATION USING HYBRID WAVELET TRANSFORM BASED FEATURES AND SUPERVISED LEARNING APPROACH

This paper describes an automatic heartbeat recognition based on QRS detection, feature extraction and classification. In this paper five different type of ECG beats of MIT BIH arrhythmia database are automatically classified. The proposed method involves QRS complex detection based on the differences and approximation derivation, inversion and threshold method. The computation of combined Discrete Wavelet Transform (DWT) and Dual Tree Complex Wavelet Transform (DTCWT) of hybrid features coefficients are obtained from the QRS segmented beat from ECG signal which are then used as a feature vector. Then the feature vectors are given to Extreme Learning Machine (ELM) and k- Nearest Neighbor (kNN) classifier for automatic classification of heartbeat. The performance of the proposed system is measured by sensitivity, specificity and accuracy measures

Fast fallback watermark detection using perceptual hashes

Forensic watermarking is often used to enable the tracing of digital pirates that leak copyright-protected videos. However, existing watermarking methods have a limited robustness and may be vulnerable to targeted attacks. Our previous work proposed a fallback detection method that uses secondary watermarks rather than the primary watermarks embedded by existing methods. However, the previously proposed fallback method is slow and requires access to all watermarked videos. This paper proposes to make the fallback watermark detection method faster using perceptual hashes instead of uncompressed secondary watermark signals. These perceptual hashes can be calculated prior to detection, such that the actual detection process is sped up with a factor of approximately 26,000 to 92,000. In this way, the proposed method tackles the main criticism about practical usability of the slow fallback method. The fast detection comes at the cost of a modest decrease in robustness, although the fast fallback detection method can still outperform the existing primary watermark method. In conclusion, the proposed method enables fast and more robust detection of watermarks that were embedded by existing watermarking methods