Wavelet Packet Transform

Wavelet transform (WT) is a mathematical function that multiplies the signal during all its length, with elongated and compressed versions of a wavelet. A signal is decomposed into a low frequency component (called approximation) and a high-frequency component (called detail). The approximation in is then decomposed into a second level of approximation and detail, and this process is repeated. WT can extract signal information in the time domain at different frequency bands and provides flexible time-frequency resolution properties. However, WT has one drawback that the frequency resolution is rather poor in the High frequency region. Thus, it faces difficulties indiscriminating between signals having close high frequency components. To overcome the drawback of Wavelet transform, wavelet packet transform is used as one of the most generalized signal decomposition methods. Wavelet packets are alternative wavelet bases formed by taking linear combination of the usual wavelet functions.

Abstract: The high security necessities in work and management motivated prospering of biometric technologies. Currently iris recognition is largely endorsed system. An expanding biometric identification technique which offers distinct verification based on distinguishing feature or characteristic possessed by the individual. Here, a fast methodology for classification and identification is suggested. The proposed system advances the effectiveness of iris recognition system. A joint tactic of SVM-Distance matching along with HAAR wavelet packet transform for feature extraction is used. For iris detection, Hough transform and Doughman's rubber sheet model for normalization is used. As in multi-faceted iris pattern, most of the information lies within zigzag collarette area, it is chosen for feature extraction. The proposed method shows a trade-off between two approaches SVM-HD and SVM-MD in terms of recognition accuracy and execution time. Maximum accuracy rate of 99.72% is achieved on CASIAV1.0 database.

In communication systems and other speech related systems, background noise is a severe problem. The speech signal gets polluted by the noises that are from transmission medium and surroundings. Noise degrades the quality and the intelligibility of the speech signals. Addition of noise is by various factors like heavy machines, pumps, vehicles, using radio communication device or over noisy telephone channel. The basic idea behind the project work is to denoise the noisy telephonic speech signal. This work is based on studying and implementing wavelets as denoising algorithm. The Wavelet Transform (WT) and Wavelet Packet Transform (WPT) implemented for the work is Discrete. Haar, Daubechies, Symlet and Coiflet wavelets are implemented for denoising of telephonic speech signal. Performance of telephonic speech signal is evaluated on the basis of SNR (signal to noise ratio) and RMSE (root mean square error). SNR and RMSE are calculated for both Soft Thresholding and Hard Thresholding.

Abstract: Now the world became more digitalized and the digital communication over the internet increases day by day. At present days the digital data is widely transfer over the internet and the whole information of living being has been uploaded on the server. With the increase of internet use, the misuse of private data also increases. There exist are many hackers and they may easily hack our private data too. So now a days security of private data has become major part of concern. For the prospective of security, cryptography and steganography of secret data can be used. In cryptography the original secret message is converted into ciphertext that is understood. While in steganography technique the secret data is hiding in cover media. Cover media may be multimedia file such as data, images, audios and videos. In this paper we are introducing video steganography technique using discrete wavelet packet transform (DWPT). Additional security can be achieved by using combined cryptography and steganography for better security of secret information. Result shows that the video steganography using discrete wavelet transform provide better performance parameter as compare to other technique of steganography.

Multiple Input Multiple output (MIMO) antennas can be combined with orthogonal frequency division multiplexing (OFDM) to ensure spatial diversity gain and/or to increase spectral efficiency. MIMO communication system with Alamouti methods can improve the bit error rate (BER) and signal to noise ratio (SNR) thus distortions are reduced for higher data rate. Conventionally OFDM is Fast Fourier Transform (FFT) based system, it uses IFFT (Inverse FFT) blocks in the transmitter and FFT blocks in the receiver. Replacing the FFT with Discrete Wavelet Packet Transform (DWPT) makes the system’s performance further improved. This leads to a new scenario of DWPT based MIMO OFDM system. In this work, the STBC-MIMO-OFDM under the scenario of having multiple antennas system, with QAM in Rayleigh fading channel for different values of Quadrature Amplitude Modulation (QAM) points (8, 32 and 64) are implemented. By evaluating the BER performance and the transmission capacity, it turns out that the DWPT based MIMO-OFDM system is superior compared with the FFT-MIMO-OFDM system. BER performance of the system is analyzed under different channel environments to assess the WPT based MIMO-OFDM performance in order to compare it with FFT based MIMO-OFDM system. In this paper the numerical results of the simulation consist a new contribution and are obtained using MATLAB. The simulation of DWPT-OFDM was accomplished with Haar mother based multicarrier. Whereas for both the latter and the conventional FFT-OFDM were subjected to the same conditions, for the multi-antenna system channel capacity and QAM modulation (8, 32, and 64) points in flat fading channels with AWGN and selective fading channel with AWGN. Computer simulation results demonstrate that the proposed wavelet based MIMO-OFDM system outperforms in Alamouti (two transmit antenna and two receive antenna) due to the overlapping nature of DWPT dispensing the addition of cyclic prefix and less hardware complexity as in FFT based MIMO-OFDM.

A blind digital image watermarking scheme, which embeds watermark in the wavelet domain of an image by using the discrete wavelet packet transform (DWPT) and quantization of the selected dominant coefficients, was proposed in this paper. In addition to this, blind detection of the watermark is applied in this method. It saves the time and space for transferring the original image and saving the original image, respectively. The results of experiments show that the proposed method is very robust against JPEG compression and Gaussian noise. The algorithm is user-defined. It needs a large number of experiments to decide a proper value. Moreover, the capacity, which is an important part of digital watermarking, will also be developed in our future work.

The signal is decomposed in to original signal (A) and noise signal (D) using a wavelet packet transform, the reconstruction of the signal will determine the magnitude of the presence of original signal (AAD) and or noise signal (ADD).The spectral density frequency of the original signal is relatively low and that of noisy signal is relatively high as shown in Fig. 3.

value. The extension of discrete wavelet transform is discrete wavelet packet transform in which we split both low pass and high pass filters at all scales in filter bank implementation to obtain flexible and detail analysis transform for denoising the sound signals [8]. In [9], wavelet packet approach which deals with heterogeneous noise for preprocessing of mass spectrometry data is discussed which incorporate a variance change point de- tection method in thresholding. Wavelet packet method has been used to reduce the Additive White Gaussian Noise from the speech signal which shows significant SNR improvement [10]. The rest of the article is organ- ized as follows: In Section 2, brief theory of discrete wavelet packet transform (DWPT) is given. Wavelet packet adaptive block denoising scheme is discussed in Section 3, which is preceded by block denoising algo- rithm based on DWPT in Section 4. The various experi- mental results are discussed in Section 5. Section 6 gives the concluding remarks based on the experimental re- sults.

The wavelet packet transform is the extensively utilized technique amid numerous signal dispensation ap- proaches that were used for fault analysis. A windowing technique with inconstant size area is supported to ac- complish the signal examination.WPT is used to examine the high frequency and also the low frequency data. The personal computer can be used to detect and recognize the sternness of the fault.

In this thesis, we present a technique that we call the Adaptive Discriminant Wavelet Packet Transform (ADWPT). ADWPT transforms an input signal, in the case of this thesis, histological images of Meningioma samples into a mul- tiresolution representation that decomposes the image in to various spatial and frequency resolutions. This decomposition represents the edges and other textu- ral information in the image at multiple resolutions. The ADWPT finds the best spatial-frequency resolutions to describe the signal so that the most discriminant features that differentiate between the various meningioma subtypes are selected. These spatial-frequency subbands are used to extract Gray Level Co-occurrence Matrix (GLCM) based statistical features. These features are used to describe the texture and to perform classification using various pattern classifiers. The technique aims to mimic the HVS as it acquires a textural representation with edge and non-edge information in different subbands and subsequently uses the statistical features extracted (as per the statistical approach), for texture descrip- tion and classification.

By making additional assumptions on the source signals, several time-frequency (TF) algorithms are proposed to solve the SCA problems [12-14]. In [13] ， it divides the TF methods into three sets. And all the approaches presented in the papers which involve in [8] use the same TF transforms i.e. the Short-Time Fourier Transform (STFT). However, the STFT includes the choice of the window functions and overlap length. In order to overcome these restrictions, wavelet packet transform has been proposed for BSS to instead of STFT, which allows isolation of the fine details within each decomposition level and enables adaptive subband decomposition [14]. In [14], it acquires the mixed matrix by searching the independent sub-components based on approximation of the mutual information (MI) with the assumption of wide-band source signals are dependent and some of their sub-components are independent. This assumption may help to solve some practical BSS problems, but it does not necessarily hold. In this paper, we assume that the mixing model is expressed as model (1) in which the number of sources is equal to or larger than the number of observations (i.e. m ≤ n ), in addition, all of the source signals are sparse in at least one frequency sub-band. Without loss of generality, it is further assumed that the columns of A are normalized [3- 4], i.e. 2

Abstract: Image enhancement is the process of sharpening image feature so that it is more suitable for some specific applications where the quality of the image is important for human perception. Here a multi-image enhancement technique which is based on wavelet packet transform is presented for the images distorted by atmospheric turbulence, where multiple low resolution images are processed to form a single high quality enhanced image. In wavelet packet transform both the approximation coefficients, which is the low frequency portion, and detailed coefficients, which is the high frequency portion of the previous levels, are used for processing in the next level. So without losing any part, the image can be represented with time-frequency information. This finds application in feature extraction and object recognition. Here first step is aligning the Region of Interest (ROI) from all input images using phase correlation method. Then it is combined in transform domain with the help of wavelet packet transform. Performance comparison parameters are calculated for the output image and it is compared with the parameters obtained from other techniques.

Feature selection performs compression of feature space to preserve maximum discriminative power of features for classification. We use this analogy to do compression of document feature space using Wavelet Packet Transform. Vector format(e.g. dictionary en- coded vector) representation of a document is equiv- alent to a digital representation. This vector format can then be processed using wavelet transform to get a compressed representation of the document in terms of wavelet coefficients. Document features are trans- formed into wavelet coefficients. Wavelet coefficients are ranked and selected based on their discrimination power between classes. Classification model is trained on these highly informative coefficients. Results show a considerable improvement in model accuracy using our dimensionality reduction technique.

Abstract—A new digital watermarking algorithm for color images based on Integer Wavelet Packet Transform and Feed Forward RBF (Radial Basis Function) Neural Network was proposed in this paper. Currently, there are some shortcomings such as weak resistance on the intentional attacks of geometric distortion and noise in some digital watermarking algorithm. Now we are introducing an approach using IWPT, as it yields a representation which is lossless, as it maps an integer-valued sequence onto integer- valued coefficients in the transformed domain. . Finally, the RBF (Radial Basis Function) neural network is used for memorizing the original image and watermark and then the trained neural network is used to extract the watermarked image. A scheme for detect and recovering intentional attacks is applied before watermark detection. Experimental results show that proposed algorithm increases robustness of watermarked images under attacks like cropping, shearing, noise etc. as compared to DWT.

From the above study, it can be concluded Wavelet Packet Transform-based MCS using Daubechies 8 filters can give the best BER vs. SNR performance using two elements which can reduce the overall system cost, Increase the coverage and reliability of the system, Power burden is all on the transmitter so the receivers can save power. Processing time is slightly increased when WPM is employed but 3 dB to 4 dB is sufficient gain with one less element at the transmitter for this system to be acceptable. An addition of an extra element with DWT-based system will also increase the processing time and the hardware cost. It is also concluded from the results above that for the communication system orthogonal wavelets of Daubechies family show the best overall performance and orthogonal wavelets perform alike in terms of BER but differ in processing time. From the results it is also evident that even though 2x1 transmitters are employed they perform just like a SISO system because of the independent channels and the sudden changes are due to the small symbol length while when the CSI is known and the signal adds constructively at the receiver the error is minimized.

An investigation into the wavelet packet transform (WPT) modulation scheme for Multiple Input Multiple Output (MIMO) band-limited systems is presented. The implementation involves using the WPT as the base multiplexing technology at baseband, instead of the traditional Fast Fourier Transform (FFT) common in Orthogonal Frequency Division Multiplexing (OFDM) systems. An investigation for a WPT-MIMO multicarrier system, using the Alamouti diversity technique, is presented. Results are consistent with those in the original Alamouti work. The scheme is then implemented for WPT-MIMO and FFT- MIMO cases with extended receiver diversity, namely 2 ×Nr MIMO systems, where Nr is the number of receiver elements. It is found that the diversity gain decreases with increasing receiver diversity and that WPT-MIMO systems can be more advantageous than FFT-based MIMO-OFDM systems.

preprocessed spectra with different methods. The classification results demonstrate that 2D wavelet packet transform, as a preprocessing method, was more effective in spectral data compression and extracting useful features. Based on the results of PLS-DA classification, it can also be concluded that the selection of appropriate preprocessing methods and decomposition levels are crucial for data analysis of NIR spectra. Different from 1D wavelet packet transform, the 2D wavelet packet transform can generate a quadtree with more than two forks in the process of decomposition, so the data compression is more effective. The results suggest that 2D wavelet packet transform is feasible as a data preprocess method for the development of a diagnostic approach of early stage endometrial cancer based on the NIR spectra of endometrial tissues.

Abstract — For image compression, it is very necessary that the selection of transform should reduce the size of the resultant data as compared to the original data set. For continuous and discrete time cases, wavelet transform and wavelet packet transform has emerged as popular techniques. While integer wavelet using the lifting scheme significantly reduces the computation time, a completely new approach for further speeding up the computation. First, wavelet packet transforms (WPT) and lifting scheme (LS) are used. Then an application of the LS to WPT is presented which leads to the generation of integer wavelet packet transform (IWPT).another technique is used for image compression is fractal image compression (FIC) is based on the partitioned iterated function system (PIFS) which utilizes the self-similarity property in the image to achieve the purpose of compression., the linear regression technique from robust statistics is embedded into the encoding procedure of the fractal image compression. Another drawback of FIC is the poor retrieved image qualities when compressing corrupted images, the fractal image compression scheme should be insensitive to those noises presented in the corrupted image. This leads to a new concept of robust fractal image compression.Another technique for image compression is new multi-layered representation technique for image compression, which combine Curvelet transform and local DCT in order to benefit from the advantages of each. Curvelet transform is one of the recently developed multiscale transform, which possess directional features and provides optimally sparse representation of objects with edges, but not for the textured feature. We exploit morphological component analysis (MCA) method to separate the image into two layers: piecewise smooth layer and textured structure layer, respectively associated to curvelet transform and local DCT. Each layer is encoded independently with a different transform at a different bit rate.

In this paper, FFT and wavelet packet transform combined, the characteristics of the transformer vibration signal extraction, Firstly, the signal is analyzed by FFT, and the main frequency components of the signal are obtained. Then according to these frequency components, the wavelet packet decomposition level is adaptively selected, and the frequency band is decomposed and reconstructed. In this method, based on the spectrum obtained by FFT, the wavelet packet decomposition level can be adaptively selected and the frequency band can be selectively analyzed for high resolution. It improves the accuracy of wavelet packet analysis; meanwhile, it also reduces the computational complexity and improves the real-time performance of feature information extraction.

Pattern recognition in histopathological image analysis requires new techniques and methods. Various techniques have been presented and some state of the art techniques have been applied to complex textural data in histological images. In this paper, we compare the novel Adaptive Discriminant Wavelet Packet Transform (ADWPT) with a few prominent techniques in texture analysis namely Local Binary Patterns (LBP), Grey Level Co-occurrence Matrices (GLCMs) and Gabor Transforms. We show that ADWPT is a better technique for Meningioma subtype classification and produces classification accuracies of as high as 90%.