Discrete Walsh-Hadamard Transform Research Articles

A New Pointwise Convolution in Deep Neural Networks Through Extremely Fast and Non Parametric Transforms

Some conventional transforms such as Discrete Walsh-Hadamard Transform (DWHT) and Discrete Cosine Transform (DCT) have been widely used as feature extractors in image processing but rarely applied in neural networks. However, we found that these conventional transforms can serve as a powerful feature extractor in channel dimension without any learnable parameters in deep neural networks. This paper firstly proposes to apply conventional transforms on pointwise convolution, showing that such transforms can significantly reduce the computational complexity of neural networks without accuracy degradation on various classification tasks and even on face detection task. Our comprehensive experiments show that the proposed DWHT-based model gained 1.49% accuracy increase with 79.4% reduced parameters and 49.4% reduced FLOPs compared with its baseline model on the CIFAR 100 dataset while achieving comparable accuracy under the condition that 81.4% of parameters and 49.4% of FLOPs reduced on SVHN dataset. Additionally, our DWHT-based model showed comparable accuracy with 89.2% reduced parameters and 26.5% reduced FLOPs compared to the baseline models on WIDER FACE and FDDB datasets.

Multi-Focus Image Fusion Based on Discrete Walsh-Hadamard Transform and Guided Filtering

Multi-Focus Image Fusion Based on Discrete Walsh-Hadamard Transform and Guided Filtering

Protection technique for series capacitor compensated three phase transmission line connected with distributed generation using discrete Walsh Hadamard transform

This study proposes a discrete Walsh Hadamard transform (DWHT) based protection technique for the detection of fault and identification of faulty phase in series capacitor compensated three phase transmission line connected with distributed generation (DG). DWHT has been used for processing of the three phase current signals. To recognize the reliability of the proposed protection technique, it is tested for variation in fault type, fault location, fault resistance, ground resistance and fault inception time. Simulation results of DWHT-based proposed technique exemplify that the proposed technique correctly detects the faults and identifies the faulty phase accurately.Keywords: Discrete Walsh Hadamard transform, distributed generation connected series capacitor compensated three phase transmission line, fault detection, faulty phase identification

Comparative Analysis of Various Transformation Techniques for Voiceless Consonants Modeling

In this paper, a comparison of various transformation techniques, namely Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT) and Discrete Walsh Hadamard Transform (DWHT) is performed in the context of their application to voiceless consonant modeling. Speech features based on these transformation techniques are extracted. These features are mean and derivative values of cepstrum coefficients, derived from each transformation. Fea-ture extraction is performed on the speech signal divided into short-time seg-ments. The kNN and Naive Bayes methods are used for phoneme classification. Experiments show that DFT and DCT give better classification accuracy than DWHT. The result of DFT was not significantly different from DCT, but it was for DWHT. The same tendency was revealed for DCT. It was checked with the usage of the ANOVA test that the difference between results obtained by DCT and DWHT is significant.

Iterative Receiver with Low Complexity for Downlink Multicarrier Communications over Rapidly Time‐Varying Channels

This study proposes an iterative, joint channel estimation, equalization, and data detection method in the presence of high mobility for a multicarrier downlink system that communicates over rapidly time‐varying channels. The proposed method uses a basis expansion method (BEM) which has low computational complexity and helps to reduce the number of coefficients needed to represent a time‐varying channel and therefore is extremely easy to implement practically. Unlike the current literature, which is almost entirely focused on the uplink communication systems due to their computational costs, this method prioritizes the goal of being feasible in a downlink system with a reasonable performance. The proposed suboptimal algorithm is based on the space‐alternating generalized expectation‐maximization (SAGE) algorithm and the time‐varying channel is represented by orthogonal basis functions obtained by means of discrete Walsh‐Hadamard transform (DWHT). The resulting receiver iterates between maximum a posteriori (MAP) based channel estimation in the subspace spanned by the orthogonal basis functions and successive interference cancellation. Numerical examples show that the proposed algorithm has a satisfactory symbol error rate with low computational complexity and also has a reasonable peak‐to‐average power ratio (PAPR) reduction effect.

Real-time estimation and detection of non-linearity in bio-signals using wireless brain-computer interface

In this paper, the work is mainly concentrated on removing non-linear parameters to make the physiological signals more linear and reducing the complexity of the signals. This paper discusses three different types of techniques that can be successfully utilised to remove non-linear parameters in EEG and ECG. (i) Transformation technique using Discrete Walsh-Hadamard Transform (DWHT); (ii) application of fuzzy logic control and (iii) building the Adaptive Neuro-Fuzzy Inference System (ANFIS) model for fuzzy. This work has been inspired by the need to arrive at an efficient, simple, accurate and quicker method for analysis of bio-signal.

Algorithm of Walsh-Hadamard Transform with Optical Approach

In this paper, the fast algorithm to Walsh-Hadamard transform (WHT) is studied from the point of view of the optical computation. Firstly, MSD addition and butterfly calculation in discrete WHT are presented in detail. Then the design and implementation scheme of fast algorithm of WHT is proposed and the software simulations to fast WHT are carried out optically. Meanwhile, the computational complexity of the algorithms in time and space are analyzed. The analysis shows that the problem of WHT with large-scale data can be solved in a few of clock cycles with optical computational method. The scheme also provides a good way for the design of fast optical Walsh-Hadamard transformer and an application in ternary optical computer.

Speech Compression Based on Discrete Walsh Hadamard Transform

This paper presents a new lossy compression algorithm for stationary signal based on Discrete Walsh Hadamard Transform (DWHT). The principle of compression algorithm consists in framing the original speech signal into stationary frames and applying the DWHT. Then, the obtained coefficients are thresholded in order to truncate all coefficients below a given thresholds values. Compression is achieved by efficient encoding of the string values of zeros. A comparative study of performance between the algorithms based on DWHT and Discrete Wavelet Transform (DWT) is performed in terms of some objective criteria: compression ratio (CR), signal to noise ratio, peak signal to noise ratio (SNR), normalized root mean square error (NRMSE) and CPU time. The simulation results show that the algorithm based on DWHT is characterized by a very low complexity implementation and improved CR, SNR, PSNR and NRMSE compared to the DWT algorithm and this for stationary frame.

SIMPLE STRUCTURES FOR UNIMODULAR FILTER BANKS WITH REGULARITY

In this paper we propose two new parameterizations for unimodular filter banks (UMFBs) by exploiting the canonical forms of the nilpotent matrix present in the factorization of UMFBs. A judicious choice of the canonical structure leads to simple implementation. The use of Discrete Walsh Hadamard Transform (DWHT) saves a major amount of multiplication. The presence of the nilpotent matrix also facilitates the design of filter banks with unequal length analysis and synthesis filters. The structures ensure perfect reconstruction (PR) with minimal delay in the McMillan sense. The free parameters can be obtained through unconstrained optimization, which is hardly possible with the existing design methods. Design examples are presented based on the proposed structures. Although there is a significant reduction in the number of free parameters, the performances of these structures are found to be comparable with and better than the existing design techniques for UMFBs. The design of a class of decomposable higher order UMFBs with unequal lengths of analysis and synthesis filters is done. Also, the design of a one-regular filter bank based on the simplest structure proposed is presented.

A new class of fast shape-adaptive orthogonal transforms and their application to region-based image compression

Region-based approaches to image and video compression have been very actively explored in the last few years. It is widely expected that they will result in rate/quality gains and expanded functionalities. In such approaches, one of the essential problems is the representation of luminance and color in arbitrarily shaped regions. For rectangular blocks extracted from natural images, the discrete cosine transform (DCT) has been found to perform close to the eigentransform. Although for arbitrarily shaped regions orthogonalization-based procedures have been shown to perform very well, their computational complexity and memory requirements are prohibitive for today's technology. Therefore, other approaches are presently investigated, and particular attention is paid to low implementation complexity. In this paper, we propose a new class of orthogonal transforms that self-adapt to arbitrary shapes. The new algorithms are derived from flow graphs of standard fast transform algorithms by a suitable modification of certain butterfly operators. First, we show how to derive a shape-adaptive transform from the discrete Walsh-Hadamard transform (DWHT) flow graph. Then, we discuss modifications needed to arrive at a DCT-based shape adaptive transform. We give implementation details of this transform, and compare its computational complexity with several well-known approaches. We also evaluate the energy compaction performance of the new transform for both synthetic and natural data. We conclude that the proposed DCT-based shape-adaptive transform gives a very beneficial compaction/complexity ratio compared to other well-known approaches. The complexity of the new method does not exceed the complexity of two nonadaptive DCT's on a circumscribing rectangle, and therefore, unlike other tested methods with comparable energy compaction, it is suitable for large regions. This property should prove very valuable in the future when true region-based image/video compression methods are developed.

A new approach to reduce the 'blocking effect' of transform coding (image coding)

A combined-transform coding (CTC) scheme to reduce the blocking effect of conventional block transform coding and hence to improve the subjective performance is presented. The scheme is described, and its information-theoretic properties are discussed. Computer simulation results for a chest X-ray image are presented. The CTC scheme, the JPEG baseline scheme, and the conventional discrete Walsh-Hadamard transform (DWHT) are compared to demonstrate the performance improvement for the CTC scheme. The advantages of the CTC scheme include no ringing effect as there is no error propagation across the boundary, no additional computation, and distortion always held within a certain level.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A combined-transform coding (CTC) scheme for medical images

A combined-transform coding (CTC) scheme is proposed to reduce the blocking artifact of conventional block transform coding and hence to improve the subjective performance. The proposed CTC scheme is described and its information-theoretic properties are investigated. Computer simulation results for a class of chest X-ray images are presented. A comparison between the CTC scheme and the conventional discrete cosine transform (DCT) and discrete Walsh-Hadamard transform (DWHT) demonstrates the performance improvement of the proposed scheme. In addition, combined coding can also be used in noiseless coding, yielding a slight improvement in the compression performance if it is used properly.

A combined-transform coding (CTC) scheme for image data compression

The authors propose a combined-transform-coding (CTC) scheme to reduce the blocking effect due to division of subblocks and to achieve better subjective performance. The proposed CTC scheme is described, and its information-theoretic properties are investigated. A comparison between the CTC scheme and conventional discrete cosine transform (DCT) and discrete Walsh-Hadamard transform (DWHT) schemes was made to demonstrate the performance improvement of the proposed scheme. The advantages of the CTC scheme also include (1) no ringing effect due to the absence of error propagation across block boundaries, (2) no additional computation, and (3) the ability to hold distortion below a certain threshold. In addition, it was found that the idea of combined coding can also be used in noiseless coding.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>