Image registration using the Walsh transform.

This paper presents a new algorithm which can be used to register images of the same or different modalities, e.g., images with multiple channels, such as X-rays, temperature or elevation, or simply images of different spectral bands. In particular, a correlation-based scheme is used, but instead of gray values, it correlates numbers formulated by different combinations of the extracted local Walsh coefficients of the images. Each image patch is expanded in terms of Walsh basis functions. Each Walsh basis function can be thought of as measuring a different aspect of local structure, e.g., horizontal edge, corner, etc. The coefficients of the expansion, therefore, can be thought of as dense local features, estimating at each point the degree of presence of, for example, a horizontal edge, a corner with contrast of a certain type, etc. These coefficients are normalized and used as digits in a chosen number system which allows one to create a unique number for each type of local structure. The choice of the basis of the number system allows one to give different emphasis to different types of local feature (e.g., corners versus edges), and, thus, the method we present forms a unified framework in terms of which several feature matching methods may be interpreted. The algorithm is compared with wavelet and contour based approaches, using simulated and real images. The two images are assumed to differ from each other by a rotation and a translation only.     

Fast computation of zoom-DFT via the Walsh transform

A method is introduced to compute zoom-DFT of a time aeries via its Walsh transform, which can be useful in applications where both discrete Fourier and discrete Walsh transforms of a sampled data function are required to be computed simultaneously with high resolution.     

Walsh transform applied to digital filtering

The filtering process can also be implemented by other transformations than the well-known Fourier transformation. The paper is devoted to the one-dimensional (1-D) and two-dimensional (2-D) digital filtering process by the use of 1-D and 2-D discrete Walsh transforms (DWTs). Particularly, the optimum Walsh filter problem with one- and two-dimensional discrete data with emphasis on reduction of the computational requirements is considered. The optimum Walsh filters which are determined are based upon some modified minimum-mean-square-error criterion. Two basic classes of signals, which are to be filtered, have been taken into account: periodic signals and stationary random processes. Two computational examples are given.     

Performance analysis of a wireless multirate direct-sequence CDMAusing fast Walsh transform and decorrelating detection

We analyze the performance of a flexible multirate scheme for direct-sequence code division multiple-access (CDMA) mobile radio systems. The proposed scheme uses a variable processing gain serial pseudonoise modulation as a multirate strategy. To reduce the interference effects, the CDMA system utilizes the coherent fast Walsh transform transmission technique. The proposed scheme can be used in the reverse link (mobile-to-base station) of the upcoming third-generation wide-band CDMA system (has the feature of coherent reverse link). We analyze the system performance with and without using a decorrelating multiuser detector. The uncoded bit-error probability (BEP) with and without decorrelating detection on a multipath fading channel is derived analytically. In addition, the validity of the analysis results is demonstrated by computer simulations using the IMT-2000 vehicular multipath channel model. In order to make sure that the proposed processing techniques do not distort the soft values at the demodulator output, the proposed multirate scheme is also simulated in case of using turbo codes. The turbo-coded BEP is calculated for different user data rates and different number of decoding iterations     

Spike detection using the continuous wavelet transform

This paper combines wavelet transforms with basic detection theory to develop a new unsupervised method for robustly detecting and localizing spikes in noisy neural recordings. The method does not require the construction of templates, or the supervised setting of thresholds. We present extensive Monte Carlo simulations, based on actual extracellular recordings, to show that this technique surpasses other commonly used methods in a wide variety of recording conditions. We further demonstrate that falsely detected spikes corresponding to our method resemble actual spikes more than the false positives of other techniques such as amplitude thresholding. Moreover, the simplicity of the method allows for nearly real-time execution.     

Fast computation of discrete Hartley transform via Walsh?Hadamard transform

A new fast algorithm is proposed to compute the discrete Hartley transform (DHT) via the Walsh?Hadamard transform (WHT). The processing is carried out on an interframe basis in (N × N) data blocks, where N is an integer power of two. The WHT coefficients are obtained directly, and then used to obtain the DHT coefficients. This is achieved by a transform matrix, the H-transform matrix, which is ortho-normal and has a block-diagonal structure. A complete derivation of the block-diagonal structure for the H-transform matrix is given.     

LFM signal detection using LPP-Hough transform

This paper presents a new method to detect linear frequency modulated (LFM) signals by jointly using the local polynomial periodogram (LPP) and the Hough transform. Theoretical comparison is made on the 3 dB signal-to-noise ratios (SNRs), achieved by the pseudo-Wigner-Ville distribution (PWVD) and the LPP, to show that the latter is important to achieve significant increase of noise margins in the Hough transform domain. The results of computer simulations are presented for the detection of mono- and multi-component LFM signals corrupted by additive white Gaussian noise and impulsive noise. It is also found that by using the time-frequency filtering, the computational complexity of the detection can be substantially reduced. Both the theoretical analysis and the simulation results show that the proposed method achieves significant performance improvement on detecting the LFM signals in very low signal-to-noise ratio environments.     

EEG信号中癫痫棘波的小波变换检测

基于小波变换良好的时频局部化特性,研究了一种利用连续小波变换提取脑电信号中的癫痫棘波的方法,实验结果表明这种方法能够方便而有效地对脑电信号中的癫痫棘波进行检测。     

Algorithm for identifying skew symmetries through Walsh transform

An algorithm for the identification of skew equivalent and skew non-equivalent symmetries in Boolean functions through Walsh spectral coefficients is presented. Experimental results on a large number of functions show that the approach is very efficient     

A simple analogue approach to fast Walsh transform

A version of a fast Walsh transform algorithm is derived by setting an analogy with a programme chart of a sports tournament.     

A note on the finite Walsh transform (Corresp.)

The theory of the finite Walsh transform is presented as a background to current interest in the fast Walsh transform algorithm.     

Multiscale corner detection by using wavelet transform

A multiscale corner detection algorithm based on the wavelet transform of contour orientation is proposed. It can utilize both the information of the local extrema and modulus of transform results to detect corners and arcs effectively. The ramp-width of contour orientation profile, which can be computed using the transformed modulus of two scales, reveals the difference between corner and arc and is utilized in the determination of corner points. The experimental results have shown that the detector is more effective than both the single- and multiple-scale detectors. They also demonstrate that the detector is insensitive to boundary noise. In addition, the proposed method is more efficient than the other multiscale corner detector because it operates on fewer number of scales, which can be implemented by a fast transform algorithm.     

Characterisation of threshold functions under the Walsh transform and linear translation

Some new results showing the classification of Boolean functions of order n, n ? 5, under the Rademacher?Walsh transform, together with the operation of spectral translation, are examined. It is found that there are 48 prototype functions, of which 21 are threshold functions. Examination of the canonic spectral forms of these threshold functions shows that a threshold function may be identified uniquely for n ? 5, under a sum-of-squares criterion.     

An anomaly intrusion detection method using fourier transform

A set of discrete points obtained from audit records on a behavior session is processed with Fourier transform. The criterion of selecting Fourier transform coefficients is introduced, and is used to find a unified value from the set of coefficients. This unified value is compared with a threshold to determine whether the session is abnormal. Finally simple test results are reported.     

Four-dimensional matrix Walsh transform for lossless compression of color video

This article presents a coding method for the lossless compression of color video.In the proposed method,four-dimensional matrix Walsh transform(4D-M-Walsh-T)is used for color video coding.The whole n frames of a color video sequence are divided into '3D-blocks' which are image width(row component),image height(column component),image width(vertical component)in a color video sequence,and adjacency(depth component)of n frames(Y,U or V)of the video sequence.Similar to the method of 2D-Walsh transform,4D-M-Walsh-T is 4D sub-matrices,and the size of each sub-matrix is n.The method can fully utilize correlations to encode for lossless compression and reduce the redundancy of color video,such as adjacent pixels in one frame or different frames of a video at the same time.Experimental results show that the proposed method can achieve higher lossless compression ratio(CR)for the color video sequence.     

Embolic Doppler ultrasound signal detection using discrete wavelet transform

Asymptomatic circulating emboli can be detected by Doppler ultrasound. Embolic Doppler ultrasound signals are short duration transient like signals. The wavelet transform is an ideal method for analysis and detection of such signals by optimizing time-frequency resolution. We propose a detection system based on the discrete wavelet transform (DWT) and study some parameters, which might be useful for describing embolic signals (ES). We used a fast DWT algorithm based on the Daubechies eighth-order wavelet filters with eight scales. In order to evaluate feasibility of the DWT of ES, two independent data sets, each comprising of short segments containing an ES (N=100), artifact (N=100) or Doppler speckle (DS) (N=100), were used. After applying the DWT to the data, several parameters were evaluated. The threshold values used for both data sets were optimized using the first data set. While the DWT coefficients resulting from artifacts dominantly appear at the higher scales (five, six, seven, and eight), the DWT coefficients at the lower scales (one, two, three, and four) are mainly dominated by ES and DS. The DWT is able to filter out most of the artifacts inherently during the transform process. For the first data set, 98 out of 100 ES were detected as ES. For the second data set, 95 out of 100 ES were detected as ES when the same threshold values were used. The algorithm was also tested with a third data set comprising 202 normal ES; 198 signals were detected as ES.     

Colour image detection and matching using modified generalisedHough transform

A new approach to 2-dimensional (2D) colour-image detection and matching using a modified version of the generalised Hough transform (GHT) is proposed. In the conventional GHT, the useful colour information existing in the input image and the relationship between each pixel and its neighbourhood are not used. Furthermore, lighting changes in the image are not usually considered. Therefore, the conventional GHT is seldom applied to colour images. In the proposed approach, lighting are removed using normalised colour values. Next, certain critical pixels of an input colour image whose neighbourhoods have larger variances of normalised colour values are extracted. For each critical pixel, a feature vector, which includes the normalised colour values of the pixel as well as those of the pixel's neighbours, is then constructed. A modified voting rule for the GHT is therefore proposed which is based on a similarity-measure function of the feature vectors. High maximum peaks in the cell array are searched finally as the result. The proposed method is robust for colour-image detection and matching in noisy, occlusive, and lighting-change environments, as demonstrated by experimental results     

Electronic implementation of the discrete Walsh transform with a variable number of data

We present an electronic system that calculates the discrete Walsh transform of a function of which any number of samples has been previously taken. In previous publications, one finds systems designed for a fixed number of samples, normally a power of two. This restriction is too great bearing in mind that no physical function is really periodical, especially in the field of biophysics, where -many important applications of this type of device are found. This makes it impossible to obtain a preset number of samples and makes the selection of sampling frequency difficult.     

Efficient technique for circle detection using hypothesis filteringand Hough transform

A fast circle detection method using a variant of Hough-like technique is reported. The proposed technique is simple in implementation, efficient in computation and robust to noise. In general, to evaluate circle parameters for all possible point triplets in an edge image containing n points, _nC₃ enumerations of the points have to be examined. However, if specific relations of the circle points are sought, the required number of enumerations can be reduced. The authors propose one such scheme of detection with point triplets possessing right angle property and the required enumerations can be reduced to _nC₂. Moreover, a novel processing strategy known as hypothesis filtering is introduced. The strategy includes two hypothesis constraints termed consistency checking with gradient angles and neighbouring points validation. Experimental results are demonstrated to reveal the performance of the method in detecting circles in both synthetic and real images. Since the proposed method adopts a right angle criterion for hypothesis, circles occluded or broken by more than one half may not be detected. Test results show that the limitation of the proposed method appears to be acceptable. When compared with established Hough transform techniques, the main strengths of the proposed detection method are its attractively computational and memory complexities and good accuracy of detection     

Noise-robust pitch detection method using wavelet transform with aliasing compensation

An improved wavelet-based method is developed for extracting pitch information from noisy speech. It uses a modified spatial correlation function which is originally applied to wavelet-based signal denoising to improve the performance of pitch detection in a noisy environment. The modified spatial correlation function needed in the proposed pitch detection method makes use of an aliasing compensation algorithm to eliminate the aliasing distortion that arises from the downsampling and upsampling operations of the wavelet transform. As a consequence, this allows one to further increase the accuracy of pitch detection. It is shown in various experimental results that this new method gives a considerable performance improvement when compared with other conventional and wavelet-based methods.