A Study on Some Aspects of Wavelet Fractal Compression

Based on explanation of wavelet fractal compression method, the significance of introducing wavelet decomposition into conventional fractal compression method is deeply investigated from the point of theoretical and practical view. The result of study can be regarded as valuable guidelines for taking advantages of wavelet transform to develop more effective image compression algorithm.

Efficient Quadtree based Fractal Image Coding Scheme in Wavelet Transform Domain *

This paper presents an efficient quadtree based fractal image coding scheme in wavelet transform domain based on the wavelet based theory of fractal image compression introduced by Davis. In the scheme, zerotrees of wavelet coefficients are used to reduce the number of domain blocks, which leads to lower bit cost required to represent the location information of fractal coding, and overall entropy constrained optimization is performed for the decision trees as well as for the sets of scalar quantizers and self quantizers of wavelet subtrees. Experiment results show that at the low bit rates, the proposed scheme gives about 1 dB improvement in PSNR over the reported results.

Gravity compression forward modeling and multiscale inversion based on wavelet transform

The main problems in three-dimensional gravity inversion are the non-uniqueness of the solutions and the high computational cost of large data sets. To minimize the high computational cost, we propose a new sorting method to reduce fluctuations and the high frequency of the sensitivity matrix prior to applying the wavelet transform. Consequently, the sparsity and compression ratio of the sensitivity matrix are improved as well as the accuracy of the forward modeling. Furthermore, memory storage requirements are reduced and the forward modeling is accelerated compared with uncompressed forward modeling. The forward modeling results suggest that the compression ratio of the sensitivity matrix can be more than 300. Furthermore, multiscale inversion based on the wavelet transform is applied to gravity inversion. By decomposing the gravity inversion into subproblems of different scales, the non-uniqueness and stability of the gravity inversion are improved as multiscale data are considered. Finally, we applied conventional focusing inversion and multiscale inversion on simulated and measured data to demonstrate the effectiveness of the proposed gravity inversion method.

DEM Compression Based on Integer Wavelet Transform

DEM data is an important component of spatial database in GIS. The data volume is so huge that compression is necessary. Wavelet transform has many advantages and has become a trend in data compression. Considering the simplicity and high efficiency of the compression system, integer wavelet transform is applied to DEM and a simple coding algorithm with high efficiency is introduced. Experiments on a variety of DEM are carried out and some useful rules are presented at the end of this paper.

Seismic data compression based on integer wavelet transform

Due to the particularity of the seismic data, they must be treated by lossless compression algorithm in some cases. In the paper, based on the integer wavelet transform, the lossless compression algorithm is studied. Comparing with the traditional algorithm, it can better improve the compression rate. CDF (2, n) biorthogonal wavelet family can lead to better compression ratio than other CDF family, SWE and CRF, which is owe to its capability in can- celing data redundancies and focusing data characteristics. CDF (2, n) family is suitable as the wavelet function of the lossless compression seismic data.

An Approach to Integer Wavelet Transform for Medical Image Compression in PACS

We study an approach to integer wavelet transform for lossless compression of medical image in medical picture archiving and communication system (PACS). By lifting scheme a reversible integer wavelet transform is generated, which has the similar features with the corresponding biorthogonal wavelet transform. Experimental results of the method based on integer wavelet transform are given to show better performance and great applicable potentiality in medical image compression.

WAVELET TRANSFORM IN FRACTAL IMAGE ENCODING

This paper presents some results of the relation between wavelet transform and fractal transform. The wavelet transform of the attractor of fractal transform posseses translational and scale invariance. So we speed the fractal image encoding by testing the invariance of the wavelet transform appropriate for image encoding. The classfication scheme of range blocks by wavelet transform is given in this paper.

Quantization-Based Robust Image Watermarking Using the Dual Tree Complex Wavelet Transform

Conventional quantization index modulation (QIM) watermarking uses the fixed quantization step size for the host signal.This scheme is not robust against geometric distortions and may lead to poor fidelity in some areas of content.Thus,we proposed a quantization-based image watermarking in the dual tree complex wavelet domain.We took advantages of the dual tree complex wavelets (perfect reconstruction,approximate shift invariance,and directional selectivity).For the case of watermark detecting,the probability of false alarm and probability of false negative were exploited and verified by simulation.Experimental results demonstrate that the proposed method is robust against JPEG compression,additive white Gaussian noise (AWGN),and some kinds of geometric attacks such as scaling,rotation,etc.

Wavelet Transform-Based Distributed Compressed Sensing in Wireless Sensor Networks

Wireless Sensor Networks(WSN) are mainly characterized by a potentially large number of distributed sensor nodes which collectively transmit information about sensed events to the sink.In this paper,we present a Distributed Wavelet Basis Generation(DWBG) algorithm performing at the sink to obtain the distributed wavelet basis in WSN.And on this basis,a Wavelet Transform-based Distributed Compressed Sensing(WTDCS) algorithm is proposed to compress and reconstruct the sensed data with spatial correlation.Finally,we make a detailed analysis of relationship between reconstruction performance and WTDCS algorithm parameters such as the compression ratio,the channel Signal-to-Noise Ratio(SNR),the observation noise power and the correlation decay parameter by simulation.The simulation results show that WTDCS can achieve high performance in terms of energy and reconstruction accuracy,as compared to the conventional distributed wavelet transform algorithm.

An Improved Singularity Computing Algorithm Based on Wavelet Transform Modulus Maxima Method

In order to reduce the hidden danger of noise which can be charactered by singularity spectrum, a new algorithm based on wavelet transform modulus maxima method was proposed. Singularity analysis is one of the most promising new approaches for extracting noise hidden information from noisy time series . Because of singularity strength is hard to calculate accurately, a wavelet transform modulus maxima method was used to get singularity spectrum. The singularity spectrum of white noise and aluminium interconnection electromigration noise was calculated and analyzed. The experimental results show that the new algorithm is more accurate than tradition estimating algorithm. The proposed method is feasible and efficient.

3-D Wavelet Transform for Very Low Bit-Rate Video Coding

A new improved Goh's 3 D wavelet transform(WT) coding scheme is presented in this paper. The new scheme has great advantages including a simple code structure, low computation cost and good performance in PSNR, compression ratios and visual quality of reconstructions, when compared to the other existing 3 D WT coding methods and the 2 D WT based coding methods. The new 3 D WT coding scheme is suitable for very low bit rate video coding.

Entropy of images after wavelet transform

We studied the variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layers, and the effect of wavelet bases and image frequency components on entropy. Numerous experiments were done on typical images to calculate (using Matlab) the entropy before and after wavelet transform. It was verified that, to obtain minimal entropy, a three-layer decomposition should be adopted rather than higher orders. The result achieved by using biorthogonal wavelet decomposition is better than that of the orthogonal wavelet decomposition. The results are not directly proportional to the vanishing moment, however.

Compressed Sensing Based on the Single Layer Wavelet Transform for Image Fusion

In this paper, a new method of combination single layer wavelet transform and compressive sensing is proposed for image fusion. In which only measured the high-pass wavelet coefficients of the image but preserved the low-pass wavelet coefficient. Then, fuse the low-pass wavelet coefficients and the measurements of high-pass wavelet coefficient with different schemes. For the reconstruction, by using the minimization of total variation algorithm (TV), high-pass wavelet coefficients could be recovered by the fused measurements. Finally, the fused image could be reconstructed by the inverse wavelet transform. The experiments show the proposed method provides promising fusion performance with a low computational complexity.

Image interpolation based on Wavelet Transform

Image interpolation is widely studied and used in digital image processing. In this paper, a method of image magnification according to the properties of fi＇actal interpolation and wavelet transformation are presented. We focus the development of edge forming methods to be applied as a post process of standard image zooming methods for grayscale images, with the hope of retaining edges. Experiments make sure it valid.

Authentication Method Using a Discrete Wavelet Transform for a Digital Moving Image

Recently, several digital watermarking techniques have been proposed for hiding data in the frequency domain of moving image files to protect their copyrights. However, in order to detect the water marking sufficiently after heavy compression, it is necessary to insert the watermarking with strong intensity into a moving image, and this results in visible deterioration of the moving image. We previously proposed an authentication method using a discrete wavelet transform for a digital static image file. In contrast to digital watermarking, no additional information is inserted into the original static image in the previously proposed method, and the image is authenticated by features extracted by the wavelet transform and characteristic coding. In the present study, we developed an authentication method for a moving image by using the previously proposed method for astatic image and a newly proposed method for selecting several frames in the moving image. No additional information is inserted into the original moving image by the newly proposed method or into the original static image by the previously proposed method. The experimental results show that the proposed method has a high tolerance of authentication to both compressions and vicious attacks.

On Wavelet Transform General Modulus Maxima Metric for Singularity Classification in Mammograms

Continuous wavelet transform is employed to detect singularities in 2-D signals by tracking modulus maxima along maxima lines and particularly applied to microcalcification detection in mammograms. The microcalcifications are modeled as smoothed positive impulse functions. Other target property detection can be performed by adjusting its mathematical model. In this application, the general modulus maximum and its scale of each singular point are detected and statistically analyzed locally in its neighborhood. The diagnosed microcalcification cluster results are compared with health tissue results, showing that general modulus maxima can serve as a suspicious spot detection tool with the detection performance no significantly sensitive to the breast tissue background properties. Performed fractal analysis of selected singularities supports the statistical findings. It is important to select the suitable computation parameters-thresholds of magnitude, argument and frequency range-in accordance to mathematical description of the target property as well as spatial and numerical resolution of the analyzed signal. The tests are performed on a set of images with empirically selected parameters for 200 μm/pixel spatial and 8 bits/pixel numerical resolution, appropriate for detection of the suspicious spots in a mammogram. The results show that the magnitude of a singularity general maximum can play a significant role in the detection of microcalcification, while zooming into a cluster in image finer spatial resolution both magnitude of general maximum and the spatial distribution of the selected set of singularities may lead to the breast abnormality characterization.

An Authentication Method for Digital Audio Using a Discrete Wavelet Transform

Recently, several digital watermarking techniques have been proposed for hiding data in the frequency domain of audio files in order to protect their copyrights. In general, there is a tradeoff between the quality of watermarked audio and the tolerance of watermarks to signal processing methods, such as compression. In previous research, we simultaneously improved the performance of both by developing a multipurpose optimization problem for deciding the positions of watermarks in the frequency domain of audio data and obtaining a near-optimum solution to the problem. This solution was obtained using a wavelet transform and a genetic algorithm. However, obtaining the near-optimum solution was very time consuming. To overcome this issue essentially, we have developed an authentication method for digital audio using a discrete wavelet transform. In contrast to digital watermarking, no additional information is inserted into the original audio by the proposed method, and the audio is authenticated using features extracted by the wavelet transform and characteristic coding in the proposed method. Accordingly, one can always use copyright-protected original audio. The experimental results show that the method has high tolerance of authentication to all types of MP3, AAC, and WMA compression. In addition, the processing time of the method is acceptable for every-day use.

A hyperspectral image compression algorithm based on wavelet transformation and fractal composition (AWFC)

Starting with a fractal-based image-compression algorithm based on wavelet transformation for hyperspectral images, the authors were able to obtain more spectral bands with the help of of hyperspectral remote sensing. Because large amounts of data and limited bandwidth complicate the storage and transmission of data measured by TB-level bits, it is important to compress image data acquired by hyperspectral sensors such as MODIS, PHI, and OMIS; otherwise, conventional lossless compression algorithms cannot reach adequate compression ratios. Other loss-compression methods can reach high compression ratios but lack good image fidelity, especially for hyperspectral image data. Among the third generation of image compression algorithms, fractal image compression based on wavelet transformation is superior to traditional compression methods,because it has high compression ratios and good image fidelity, and requires less computing time. To keep the spectral dimension invariable, the authors compared the results of two compression algorithms based on the storage-file structures of BSQ and of BIP, and improved the HV and Quadtree partitioning and domain-range matching algorithms in order to accelerate their encode/decode efficiency. The authors' Hyperspectral Image Process and Analysis System (HIPAS) software used a VC++6.0 integrated development environment (IDE), with which good experimental results were obtained. Possible modifications of the algorithm and limitations of the method are also discussed.

A Novel Fractal Wavelet Image Compression Approach

By investigating the limitation of existing wavelet tree based image compression methods, we propose a novel wavelet fractal image compression method in this paper. Briefly, the initial errors are appointed given the different levels of importance accorded the frequency sublevel band wavelet coefficients. Higher frequency sublevel bands would lead to larger initial errors. As a result, the sizes of sublevel blocks and super blocks would be changed according to the initial errors. The matching sizes between sublevel blocks and super blocks would be changed according to the permitted errors and compression rates. Systematic analyses are performed and the experimental results demonstrate that the proposed method provides a satisfactory performance with a clearly increasing rate of compression and speed of encoding without reducing SNR and the quality of decoded images. Simulation results show that our method is superior to the traditional wavelet tree based methods of fractal image compression.

Speech compression scheme based on wavelet transform and vector quantization

A coding method of speech compression, which is based on Wavlet Transform and Vector Quantization (VQ), is developed and studied. The Wavlet Thansform or Wavlet Packet Thansform is used to process the speech signal, then VQ is used to compress the coefficients of Wavlet Thansform, and the entropy coding is used to decrease the bit rate. The experimental results show that the speech signal, sampled by 8 kHz sampling rate and 8 bit quatisation,i.e., 64 kbit/s bit rate, can be compressed to 6 - 8 kbit/s, and still have high speech quality,and the low-delay, only 8 ms.