Analysis and interpretation of medical images are of clinical importance for medical diagnosis and treatment while they also have technical implications for computer vision and pattern recognition. In this context, one of the most fundamental issues is the detection of object boundaries, which is often useful for further processes such as organ/tissue recognition, image registration, motion analysis, measurement of anatomical and physiological parameters, etc. Although one of the best methods of edge detection is based on WAVELET TRANSFORM, the standard WAVELET TRANSFORM has its own shortcomings such as lack of shift invariant and lack of directional selectivity in sub-bands in multidimensional applications. The DISCRETE complex WAVELET TRANSFORM, which is based on complex mother WAVELET, not only overcomes these shortcomings but has acceptable redundancy and complexity as well. It is especially useful for multidimensional situations and for high accuracy applications such as medical image processing. In this paper, the shortcomings of ordinary WAVELET TRANSFORM are initially investigated and comparisons are made between the standard WAVELET and the complex WAVELET. Then, the DISCRETE complex WAVELET domain is applied for image enhancement and edge detection of noisy images. The simulation results show that our method exhibits a better performance, especially in noisy cases, as compared with the standard WAVELET and spatial methods.

This paper deals with the one-dimensional DISCRETE WAVELET TRANSFORM (1D DWT) of four scaling coefficients are computed numerically by designing a convolutive operator. The near-zone contribution of the integral is calculated through WAVELET TRANSFORM and for the far-zone contribution the classic expansion of the spherical harmonics applied. Finally the geoidal heights are determined over a territory in Canada.

The derivation of the static reference corrections was generally based on a fairly simple geological model close to the surface. The lack of detailed information near the surface leads to inaccuracies in this model and, therefore, in static corrections. Residual static corrections are designed to correct small inaccuracies in the near-surface model. Their application should lead to an improvement of the final section treated compared to that in which only static corrections is applied. For example, if the final stacked section is to be inverted to produce an acoustic impedance section, it is important that the variations in amplitude along the section represent the changes in the reflection coefficient as close as possible. This is unlikely to be the case if small residual static errors are present. In addition, static reference corrections are not a unique set of values because a change in reference results in a different set of corrections. Due to variation in the Earth's surface, velocities, and thicknesses of near-surface layers, the shape of the travel time hyperbola changes. These deviations, called static, result in misalignments and events lost in the CMP, so they must be corrected during the processing. After correcting the statics of long wavelengths, there are still some short-wavelength anomalies. These “residual” statics are due to variations not counted in the low-velocity layer. The estimation of the residual static in complex areas is one of the main problems posed by the processing of seismic data, and the results from this processing step affect the quality of the final reconstructed image and the results of the interpretation. Residual static can be estimated by different methods such as travel time inversion, power stacking, and sparsity maximization, which are based on a coherent surface assumption. An effective method must be able to denoise the seismic signal without losing useful data and have to function properly in the presence of random noise. In the frequency domain, it is possible to separate the noise from the main data, so denoising in the frequency domain can be useful. Besides, the TRANSFORMation areas are data-driven and require no information below the surface. The methods in the frequency domain generally use the Fourier TRANSFORM, which takes time and has certain limits. WAVELET TRANSFORMation methods always provide a faster procedure than Fourier TRANSFORMation. We have found that this type of WAVELET TRANSFORM could provide a data-oriented method for analyzing and synthesizing data according to the oscillation behavior of the signal. Tune able Q Factor DISCRETE WAVELET TRANSFORM (TQWT) is a new method that provides a reliable framework for the residual static correction. In this TRANSFORMation, the quality factor (Q), which relates to the particular oscillatory behavior of the data, could be adjusted in the signal by the user, and this characteristic leads to a good correspondence with the seismic signal. The Q factor of an oscillatory pulse is the ratio of its center frequency to its bandwidth. TQWT is developed by a tow channel filter bank. The use of a low-pass filter eliminates high-frequency data,these high-frequency components are the effect of residual static. After filtering, the data will be smoother,this amount of correction gives the time offset for the residual static correction. This time difference must apply to all traces. Applying this method to synthetic and real data shows a good correction of the residual static.

The stochastic computing (SC) method is a low-cost alternative to conventional binary computing that processes digital data in the form of pseudo-random bit-streams in which bit-flip errors have a trivial effect on the signal final value because of the highly redundant encoding format of this method. As a result, this computational method is used for fault-tolerant digital applications. In this paper, stochastic computing has been chosen to implement 2-dimensional DISCRETE WAVELET TRANSFORM (2-D DWT) as a case study. The performance of the circuit is analyzed through two different faulty experiments. The results show that stochastic 2-D DWT outperforms binary implementation. Although SC provides inherent fault tolerance, we have proposed four structures based on dual modular redundancy to improve SC reliability. Improving the reliability of the stochastic circuits with the least area overhead is considered the main objective in these structures. The proposed methods are applied to improve the reliability of stochastic WAVELET TRANSFORM circuits. Experimental results show that all proposed structures improve the reliability of stochastic circuits, especially in extremely noisy conditions where fault tolerance of SC is reduced.

The two-Dimensional DISCRETE WAVELET TRANSFORM (2D-DWT) is widely used in various applications for multimedia data processing, including image and video compression standards. However, this TRANSFORM is computational intensive than conventional conversions, such as the DISCRETE cosine TRANSFORM. In this paper, in order to improve the performance of 2D-DWT, we use Single Instruction, Multiple Data (SIMD) set instructions including Advanced Vector Extensions (AVX), Fused Multiply-Add (FMA), and AVX2 supported by most General-Purpose Processors (GPP). These technologies capable to process 256-bit data located in SIMD registers. The AVX technology can process eight 32-bit floating point numbers, while AVX2 processes sixteen 16-bit fixed-point numbers. In other words, it is possible to exploit 8-and 16-way data-level parallelism. In addition, two different way of parallelism, Row Column WAVELET TRANSFORM (RCWT) which processes rows and columns separately and Line-Based WAVELET TRANSFORM (LBWT) that processes both rows and columns in a single loop are used. Experimental results of different WAVELET TRANSFORM with different image sizes on a GPP show that the speedups of up to 28. 8x yield. Furthermore, LBWT approach improves performance more than RCWT. This is because it uses memory hierarchy structure more efficiently than RCWT approach.

Period and trend are two main effective and important factors in hydro-climatological time series and because of this importance, different methods have been introduced and applied to study of them, until now. Most of these methods are statistical basis and they are classified in the non-parametric tests. WAVELET TRANSFORM is a mathematical based powerful method which has been widely used in signal processing and time series analysis in recent years. In this research, trend and main periodic patterns similarity in temperature and vaporpressure has been studied in Babolsar, Tehran and Shahroud synoptic stations during 55 years period (from 1956to 2010), using WAVELET method and the sequential Mann-Kendall trend test. The results show that long term fluctuation patterns in temperature and vapor pressure have more correlations in the arid and semi-arid climates, as well as short term oscillation patterns in temperature and vapor pressure in the humid climates, and thesedominant periods increase with the aridity of region.

This research is an attempt to introduce a desirable model for modeling and forecasting the fluctuations of financial processes. For modelling the fluctuations of financial processes, we have used the combination of the GARCH model and the DISCRETE WAVELET TRANSFORM. In this thesis, we are presented a model for forecasting fluctuations of returns of exchange price index. Stock price index data has been reviewed. The data was collected from the site https: //databank. mefa. ir/data from 1/1/1390 to 29/12/1396. Due to the importance of return on financial data, the returns series is calculated and applied for modeling. After preparing data, the two combination models namely ARMAARCH and DWT-GARCH are fitted to the data series. The results show that the DWT-GARCH model has better performance than the ARMA-ARCH model. The DWT-GARCH model can significantly improve prediction outcomes and reduce the conditional variance by overcoming the defects of the GARCH family models that can not model the partial features of a process and maintain the benefits of using models The GARCH family describes the fluctuations.

Epilepsy is a neurological disorder occurs at the central nervous system, Electroencephalography (EEG) is the reliable tool for analysing the human brain activity with the help of the signals, moreover, it plays a significant role in the detection of epileptic seizures. The abnormal electrical discharge leads to loss of memory; from the recent survey over five crore people are affected by epilepsy. An effective detection system is a vital solution for detecting the epileptic disease in the initial stage. In this paper, an improved epilepsy seizure detecting system is developed with a better accuracy; the EEG signal in both time and frequency domain with the use of DISCRETE Stationary WAVELET-based Stockwell TRANSFORM (DSWST) is proposed. The feature extraction is processed by a temporal feature, spectral feature and Amplitude Distribution Estimation (ADE) from EEG signals in which the normal EEG signals will have various spectral and temporal centroids. Also, a modified filter bank based particle swarm optimization (MF-PSO) helps for the feature selection; it significantly improves the classifier accuracy. Finally, a Hybrid K nearest support vector machine (Kn-SVM) is employed for classification to investigate the performance of feature to classify the brain signals into three groups of normal (healthy), seizure free (inter-ictal) and during a seizure (ictal) groups.