Comments on "Frequency decomposition and computing of ultrasound medical images with wavelet packets"

In this paper, errors and discrepancies in the subject paper [Cincotti et al., (2002)] are highlighted. A comment, concerning the axial resolution associated to the adopted processing procedure is also reported.     

Despeckling of medical ultrasound images using Daubechies complex wavelet transform

The paper presents a novel despeckling method, based on Daubechies complex wavelet transform, for medical ultrasound images. Daubechies complex wavelet transform is used due to its approximate shift invariance property and extra information in imaginary plane of complex wavelet domain when compared to real wavelet domain. A wavelet shrinkage factor has been derived to estimate the noise-free wavelet coefficients. The proposed method firstly detects strong edges using imaginary component of complex scaling coefficients and then applies shrinkage on magnitude of complex wavelet coefficients in the wavelet domain at non-edge points. The proposed shrinkage depends on the statistical parameters of complex wavelet coefficients of noisy image which makes it adaptive in nature. Effectiveness of the proposed method is compared on the basis of signal to mean square error (SMSE) and signal to noise ratio (SNR). The experimental results demonstrate that the proposed method outperforms other conventional despeckling methods as well as wavelet based log transformed and non-log transformed methods on test images. Application of the proposed method on real diagnostic ultrasound images has shown a clear improvement over other methods.     

A binary wavelet decomposition of binary images

We construct a theory of binary wavelet decompositions of finite binary images. The new binary wavelet transform uses simple module-2 operations. It shares many of the important characteristics of the real wavelet transform. In particular, it yields an output similar to the thresholded output of a real wavelet transform operating on the underlying binary image. We begin by introducing a new binary field transform to use as an alternative to the discrete Fourier transform over GF(2). The corresponding concept of sequence spectra over GF(2) is defined. Using this transform, a theory of binary wavelets is developed in terms of two-band perfect reconstruction filter banks in GF(2). By generalizing the corresponding real field constraints of bandwidth, vanishing moments, and spectral content in the filters, we construct a perfect reconstruction wavelet decomposition. We also demonstrate the potential use of the binary wavelet decomposition in lossless image coding.     

Speckle noise reduction of medical ultrasound images in complex wavelet domain using mixture priors

Speckle noise is an inherent nature of ultrasound images, which may have negative effect on image interpretation and diagnostic tasks. In this paper, we propose several multiscale nonlinear thresholding methods for ultrasound speckle suppression. The wavelet coefficients of the logarithm of image are modeled as the sum of a noise-free component plus an independent noise. Assuming that the noise-free component has some local mixture distribution (MD), and the noise is either Gaussian or Rayleigh, we derive the minimum mean squared error (MMSE) and the averaged maximum ${a quad posteriori}$ (AMAP) estimators for noise reduction. We use Gaussian and Laplacian MD for each noise-free wavelet coefficient to characterize their heavy-tailed property. Since we estimate the parameters of the MD using the expectation maximization (EM) algorithm and local neighbors, the proposed MD incorporates some information about the intrascale dependency of the wavelet coefficients. To evaluate our spatially adaptive despeckling methods, we use both real medical ultrasound and synthetically introduced speckle images for speckle suppression. The simulation results show that our method outperforms several recently and the state-of-the-art techniques qualitatively and quantitatively.      

Adaptive compression of medical ultrasound images

An adaptive image-coding algorithm for compression of medical ultrasound (US) images in the wavelet domain is presented. First, it is shown that the histograms of wavelet coefficients of the subbands in the US images are heavy-tailed and can be better modelled by using the generalised Student's t-distribution. Then, by exploiting these statistics, an adaptive image coder named JTQVS-WV is designed, which unifies the two approaches to image-adaptive coding: rate-distortion (R-D) optimised quantiser selection and R-D optimal thresholding, and is based on the varying-slope quantisation strategy. The use of varying-slope quantisation strategy (instead of fixed R-D slope) allows coding of the wavelet coefficients across various scales according to their importance for the quality of reconstructed image. The experimental results show that the varying-slope quantisation strategy leads to a significant improvement in the compression performance of the JTQVS-WV over the best state-of-the-art image coder, SPIHT, JPEG2000 and the fixed-slope variant of JTQVS-WV named JTQ-WV. For example, the coding of US images at 0.5 bpp yields a peak signal-to-noise ratio gain of >0.6, 3.86 and 0.3 dB over the benchmark, SPIHT, JPEG2000 and JTQ-WV, respectively.     

Analysis of speckle noise contribution on wavelet decomposition ofSAR images

This paper describes the use of the wavelet transform for multiscale texture analysis. One of the basic problems is that texture measures have to adapt to the peculiarity of radar images that contain multiplicative speckle noise. In this paper, the focus is on the effect of speckle on the wavelet transform. The effect is first assessed analytically. It is shown that the wavelet coefficients are modulated by the multiplicative character of the speckle in a manner that is proportional to the target mean backscattering coefficient. The effect of speckle correlation is also demonstrated. Wavelet decomposition is then applied to a simulated radar image generated by a Monte Carlo approach and based on a statistical model. Modeling shows that the correlation properties of speckle have an effect up to a scale that corresponds to its granular size. The results also show that the main contribution to the wavelet transform for an homogeneous area is the first-order statistical distribution of speckle, which remains important even at large scales. The results are then compared to a ERS-1 synthetic aperture radar (SAR) image of a primary tropical forest region     

Time-varying lapped transforms and wavelet packets

The perfect reconstruction conditions for a time-varying lapped transform (paraunitary filter bank) are developed through the factorization of the transform matrix into sparse factors. A general formulation is presented allowing one to switch between two paraunitary filter banks. However, the extended lapped transform (ELT) is often used as an example. Furthermore, an adaptive wavelet packet is developed employing a time varying, tree association of ELTs. In all cases perfect reconstruction is inherently assured     

Theory of orthonormal M-band wavelet packets

In recent years, M-band orthonormal wavelet bases, due to their good characteristics, have attracted much attention. The ability of 2-band wavelet packets to decompose high frequency channels can be employed to improve the performance of wavelets for time-frequency localization, which makes more kinds of signals for analyzing by wavelets. Similar to the notations from the extension of 2-band wavelets to 2-band wavelet packets, the theoretic framework of M-band wavelet packets is developed, a generalization of the notations and properties of 2-band wavelet packets to that of M-band wavelet packets is made and the corresponding proofs are given.     

Time-frequency localisation of Shannon wavelet packets

It is well known that the 2/spl pi/ minimally supported frequency scaling function /spl phi//sup /spl alpha//(x) satisfying /spl phi//spl circ//sup /spl alpha//(/spl omega/)=/spl chi//sub (-/spl alpha/,2/spl pi/-/spl alpha/)/(/spl omega/), 0相似文献   

Despeckling of ultrasound images using novel adaptive wavelet thresholding function

Multidimensional Systems and Signal Processing - In the present work, a new thresholding function has been proposed for despeckling of ultrasound images. The main limitation of ultrasound images is...     

High-order wavelet packets and cumulant field analysis

In many applications it is necessary to characterize the statistical properties of the wavelet/wavelet packet coefficients of a stationary random signal. In particular, in a stationary non-Gaussian noise scenario it may be useful to determine the high-order statistics of the wavelet packet coefficients. In this work we prove that this task may be performed through multidimensional filter banks. In particular, we show how the cumulants of the M-band wavelet packet coefficients of a strictly stationary signal are derived from those of the signal and we provide scale-recursive decomposition and reconstruction formulae to compute these cumulants. High-order wavelet packets, associated with these multidimensional filter banks, are presented along with some of their properties. It is proved that under some conditions these high-order wavelet packets allow us to define frame multiresolution analyses. Finally, the asymptotic normality of the coefficients is studied by showing the geometric decay of their polyspectra/cumulants (of order greater than two) with respect to the resolution level     

Hybrid signal decomposition based on instantaneous harmonic parameters and perceptually motivated wavelet packets for scalable audio coding

The paper presents a complete framework for hybrid representation of audio and speech signals that can be used in coding applications. The parameterization approach is based on the three-part model (sinusoids, transients and noise). The essential contributions of the paper can be summarized as follows: (i) a precise mathematical solution to the problem of instantaneous harmonic parameters estimation that can be applied to nonstationary (amplitude and frequency modulated) signals. The instantaneous harmonic parameters (magnitude, frequency and phase) are calculated as the result of the narrow-band filtering of signals. The frequency-modulated filters synthesis with the closed form impulse response has been proposed. The filter frequency bounds can be determined during the components frequency tracking and can be adjusted according to the fundamental frequency modulations; (ii) a practical technique of instantaneous harmonic analysis and numerical evaluation of its performance; (iii) a new transient parameterization scheme based on matching pursuit with frame-based psychoacoustic optimized wavelet packet dictionary. The choice of most relevant coefficients is based on maximizing the matching between the auditory excitation scalograms of original and modeled signals; (iv) the given hybrid analysis system is applied to speech and audio signals in order to validate the proposed methods.     

Locally adaptive wavelet domain Bayesian processor for denoising medical ultrasound images using Speckle modelling based on Rayleigh distribution

The authors present a statistical approach to speckle reduction in medical ultrasound B-scan images based on maximum a posteriori (MAP) estimation in the wavelet domain. In this framework, a new class of statistical model for speckle noise is proposed to obtain a simple and tractable solution in a closed analytical form. The proposed method uses the Rayleigh distribution for speckle noise and a Gaussian distribution for modelling the statistics of wavelet coefficients in a logarithmically transformed ultrasound image. The method combines the MAP estimation with the assumption that speckle is spatially correlated within a small window and designs a locally adaptive Bayesian processor whose parameters are computed from the neighboring coefficients. Further, the locally adaptive estimator is extended to the redundant wavelet representation, which yields better results than the decimated wavelet transform. The experimental results show that the proposed method clearly outperforms the state-of-the-art medical image denoising algorithm of Pizurica et al., spatially adaptive single-resolution methods and band-adaptive multi-scale soft-thresholding techniques in terms of quantitative performance as well as in terms of visual quality of the images. The main advantage of the new method over the existing techniques is that it suppresses speckle noise well, while retaining the structure of the image, particularly the thin bright streaks, which tend to occur along boundaries between tissue layers.     

Nonlinear multiscale wavelet diffusion for speckle suppression and edge enhancement in ultrasound images

This paper introduces a novel nonlinear multiscale wavelet diffusion method for ultrasound speckle suppression and edge enhancement. This method is designed to utilize the favorable denoising properties of two frequently used techniques: the sparsity and multiresolution properties of the wavelet, and the iterative edge enhancement feature of nonlinear diffusion. With fully exploited knowledge of speckle image models, the edges of images are detected using normalized wavelet modulus. Relying on this feature, both the envelope-detected speckle image and the log-compressed ultrasonic image can be directly processed by the algorithm without need for additional preprocessing. Speckle is suppressed by employing the iterative multiscale diffusion on the wavelet coefficients. With a tuning diffusion threshold strategy, the proposed method can improve the image quality for both visualization and auto-segmentation applications. We validate our method using synthetic speckle images and real ultrasonic images. Performance improvement over other despeckling filters is quantified in terms of noise suppression and edge preservation indices.     

利用小波分解和顶点成分分析的高光谱异常检测

针对高光谱图像复杂背景影响异常检测结果的问题,提出了一种新的抑制背景的异常检测算法。首先对高光谱图像采用小波分解,将高光谱图像分解成高频图像和低频图像;然后使用顶点成分分析(VCA)方法提取高频图像的端元光谱图;最后使用光谱角匹配(SAM)技术对高光谱图像进行异常检测。实验结果表明,KRX算法相比,本文算法像素目标个数增加32.35%;虚拟个数减少12.12%,计算时间少2个数量级;本文方法的ROC曲线一直位于KRX、PCA-KPX算法的异常检测方法之上,有利于高光谱图像的实时异常检测应用。     

Wavelet packets and spatial adaptive intraband coding of images

In this work, we present a coding scheme based on a rate-distortion optimum wavelet packets decomposition and on an adaptive coding procedure that exploits spatial non-stationarity within each subband. We show, by means of a generalization of the concept of coding gain to the case of non-stationary signals, that it may be convenient to perform subband decomposition optimization in conjunction with intraband optimal bit allocation. In our implementation, each subband is partitioned into blocks of coefficients that are coded using a geometric vector quantizer with a rate determined on the basis of spatially local statistical characteristics. The proposed scheme appears to be simpler than other wavelet packets-based schemes presented in the literature and achieves good results in terms of both compression and visual quality.     

Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition

Since Chavez proposed the highpass filtering procedure to fuse multispectral and panchromatic images, several fusion methods have been developed based on the same principle: to extract from the panchromatic image spatial detail information to later inject it into the multispectral one. In this paper, we present new fusion alternatives based on the same concept, using the multiresolution wavelet decomposition to execute the detail extraction phase and the intensity-hue-saturation (IHS) and principal component analysis (PCA) procedures to inject the spatial detail of the panchromatic image into the multispectral one. The multiresolution wavelet decomposition has been performed using both decimated and undecimated algorithms and the resulting merged images compared both spectral and spatially. These fusion methods, as well as standard IHS-, PCA-, and wavelet-based methods have been used to merge Systeme Pour l'Observation de la Terre (SPOT) 4 XI and SPOT 4 M images with a ratio 4:1. We have estimated the validity of each fusion method by analyzing, visually and quantitatively, the quality of the resulting fused images. The methodological approaches proposed in this paper result in merged images with improved quality with respect to those obtained by standard IHS, PCA, and standard wavelet-based fusion methods. For both proposed fusion methods, better results are obtained when an undecimated algorithm is used to perform the multiresolution wavelet decomposition.     

Despeckling of medical ultrasound images using data and rate adaptive lossy compression

A novel technique for despeckling the medical ultrasound images using lossy compression is presented. The logarithm of the input image is first transformed to the multiscale wavelet domain. It is then shown that the subband coefficients of the log-transformed ultrasound image can be successfully modeled using the generalized Laplacian distribution. Based on this modeling, a simple adaptation of the zero-zone and reconstruction levels of the uniform threshold quantizer is proposed in order to achieve simultaneous despeckling and quantization. This adaptation is based on: (1) an estimate of the corrupting speckle noise level in the image; (2) the estimated statistics of the noise-free subband coefficients; and (3) the required compression rate. The Laplacian distribution is considered as a special case of the generalized Laplacian distribution and its efficacy is demonstrated for the problem under consideration. Context-based classification is also applied to the noisy coefficients to enhance the performance of the subband coder. Simulation results using a contrast detail phantom image and several real ultrasound images are presented. To validate the performance of the proposed scheme, comparison with two two-stage schemes, wherein the speckled image is first filtered and then compressed using the state-of-the-art JPEG2000 encoder, is presented. Experimental results show that the proposed scheme works better, both in terms of the signal to noise ratio and the visual quality.