THE METHOD OF SEPARATING HARMONIC SIGNALS FROM MULTIPLICATIVE AND ADDITIVE NOISES

This paper focuses on the extraction of a harmonic signal from multiplicative and additive noises. A method is proposed in two stages: (1) to square the original discrete time series, which in- cludes both signals and noises, and form a new time series. By this means, the multiplicative noise is converted to additive noise; and (2) to filter out the noise by using existing noise removal schemes. With a large amount of simulation, experimental results demonstrated the efficiency and effective- ness of this newly developed method in terms of Signal-to-Noise Ratio (SNR) and other criteria. From the experiment, it is also found that: the two kinds of noises affect the SNR differently. In gen- eral, the SNR is not influenced by multiplicative Gaussian noise regardless of its variance. However, if both kinds of noise exist, the SNR decreases with the incensement of the Variance of Additive Noise to Multiplicative Noise Ratio (VAMNR). This analysis is also supported by simulation work.     

Unbiased homomorphic system and its application in reducing multiplicative noise

The problem of reducing the multiplicative noise corrupting a signal is discussed. A generalisation of the existing sampled function weighted order (SFWO) filter is proposed by relaxing the symmetry condition on the probability density function (PDF) of the noise. This generalised SFWO filter is then used within a homomorphic system to reduce the multiplicative noise. It is shown that the output from such a system is biased, and hence, a suitable bias compensation technique is suggested. An unbiased homomorphic system, whose design is based on the PDF of the corrupting multiplicative noise, is proposed to reduce the noise. Images generated by coherent imaging systems are always corrupted by speckle, a kind of multiplicative noise having a lognormal distribution. A filter called the mean median filter, to reduce additive white Gaussian noise, is first proposed and then used within the unbiased homomorphic system to reduce the speckle in images. The effectiveness of the various proposed algorithms is demonstrated and compared with that of some of the existing schemes through extensive simulations     

Two-dimensional adaptive block Kalman filtering of SAR imagery

A method for removing speckle from synthetic aperture radar (SAR) imagery by using 2-D adaptive block Kalman filtering is introduced. The image process is represented by an autoregressive model with a nonsymmetric half-plane (NSHP) region of support. New 2-D Kalman filtering equations are derived which taken into account not only the effect of speckles as multiplicative noise but also the effects of the additive receiver thermal noise and the blur. This method assumes local stationarity within a processing window, whereas the image can be assumed to be globally nonstationary. A recursive identification process using the stochastic Newton approach is also proposed which can be used on-line to estimate the filter parameters based upon the information within each new block of the image. Simulation results on several images are provided to indicate the effectiveness of the proposed method when used to remove the effects of speckle noise as well as those of the additive noise     

自适应正则化项去除乘性噪声

针对乘性噪声去噪算法研究,乘性噪声多出现在合成孔径雷达、超声波和激光等相干图像系统中,与标准高斯加性噪声不同,乘性噪声符合瑞利和伽马分布函数。文中通过:(1)取对数把乘性噪声模型转变成相加形模型;(2)改进正则化项成为自适应扩散模型;(3)将数学模型应用于图像处理的实践当中。在解决了阶梯效应的同时保持了图像的边缘。     

一种文本图像水印的算法研究

该文提出了一种文本图像水印的新算法。首先将文本中选定嵌入水印的区域视为一个彩色图像,对其进行离散余弦变换（DCT）,并将变换系数进行加密排序之后,则经典的乘性水印算法转变为加性算法。将排序之后的DCT系数视为分叉噪声,而水印信号为弱信号,那么利用加性噪声中弱信号榆测理论推导出一种水印检测器来检测水印信号,并对其检测性能进行了理论和实验分析。实验表明这种检测器对于高斯加性噪声、中值滤波、乘性噪音以及低通滤波等多种攻击手段都具有较好的抗攻击能力。     

Analytic behavior of the LMS adaptive line enhancer for sinusoidscorrupted by multiplicative and additive noise

The least mean squares adaptive line enhancer (LMS ALE) has been widely used for the enhancement of coherent sinusoids in additive wideband noise. This paper studies the behavior of the LMS ALE when applied to the enhancement of sinusoids that have been corrupted by both colored multiplicative and white additive noise. The multiplicative noise decorrelates the sinusoid, spreads its power spectrum, and acts as an additional corrupting noise. Closed-form expressions are derived for the optimum (Wiener filter) ALE output SNR as a function of the residual coherent sine wave power, the noncoherent sine wave power spectrum, and the background additive white noise. When the coherent to noncoherent sine wave power ratio is sufficiently small, it is shown that a nonlinear (e.g., square law) transformation of the ALE input results in a larger optimum ALE output SNR     

Robust NL-Means Filter With Optimal Pixel-Wise Smoothing Parameter for Statistical Image Denoising

Most denoising methods require that some smoothing parameters be set manually to optimize their performance. Among these methods, a new filter based on nonlocal weighting (NL-means filter) has been shown to have a very attractive denoising capacity. In this paper, we propose fixing the smoothing parameter of this filter automatically. The smoothing parameter corresponds to the bandwidth h of a local constant regression. We use the C_p statistic embedded in Newton's method to optimize h in a point-wise fashion. This statistic also has the advantage of being a reliable measure of the quality of the denoising process for each pixel. In addition, we introduce a robust regression in the NL-means filter designed to greatly reduce the blur yielded by the weighting. Finally, we show how the automatic denoising model can be extended to images degraded by multiplicative noise. Experiments conducted on images with additive and multiplicative noise demonstrate a high denoising power with a degree of detail preservation...     

乘性噪声环境下基于符号秩统计量的非参伪码捕获方法

扩频系统常常工作在多径环境中,伴随着加性噪声的同时往往还存在着乘性噪声.该文提出了一种乘性噪声环境下基于符号秩统计量的非参伪码捕获方法,将伪码捕获等价为假设检验问题,利用局部最佳检测算法推导出了乘性噪声环境下基于符号秩的检测统计量,通过简化记分函数进一步给出了局部次佳秩检测器.将局部次佳秩检测器与局部最佳检测器和平方和检测器的性能进行了仿真对比,结果表明该文所提出的捕获方法在乘性噪声环境下检测性能接近于乘性噪声环境下的局部最佳检测器,而较平方和检测器则有较大幅度的提高.     

基于均匀圆阵的信号二维方向角互相关估计

针对复值乘性和加性噪声同时存在的情况,提出一种基于均匀圆阵的信号二维方向角互相关估计方法.本文推导出互相关估计公式,分析了估计的统计性能,给出了最优参数选择原则.在不改变均匀圆阵阵列流形的情况下,此方法抑制了信号中的乘性和加性噪声,且计算量小.计算机仿真证明了此方法的有效性.     

Quantization and roundoff noises in fixed-point FIR digital filters

The errors in a fixed-point finite impulse response (FIR) filter due to quantization (analog-to-digital conversion) and roundoff are considered. Expressions for the exact moments of the filter output noise are derived. It is well known that, when the input signal satisfies certain conditions, the popular additive white noise model can be valid in describing the quantization noise. The characteristics of multiplicative roundoff noises, however, differ from what this model predicts, even under conditions where the roundoff noises are white. Hence the additive white noise model does not provide accurate results on the characteristics of the output error in an FIR filter. Using the exact formulas for the moments, the author computes the exact power spectrum of the filter output error. These results agree well with those obtained from simulation     

乘性噪声环境下基于局部最佳检测器的伪码捕获方法

扩频系统常常工作在多径环境中,伴随着加性噪声的同时往往还存在着乘性噪声。该文提出了一种乘性噪声环境下伪码捕获方法,将伪码捕获等价为假设检验问题,利用局部最佳检测算法推导出乘性噪声环境下的伪码捕获检测统计量,文中给出了基于局部最佳检测算法的捕获结构,并与传统的平方和检测器进行了性能仿真对比,结果表明该文所提出的捕获方法在乘性噪声环境下检测性能较平方和检测器有较大幅度的提高,而在无乘性噪声的环境下检测性能只较传统的平方和检测器检测性能稍有降低。     

基于Curvelet变换的ESPI图像散斑噪声抑制算法研究

重点研究了Curvelet变换的去噪原理及方法,并结合ESPI条纹图中散斑乘性噪声的特性,提出了改进的Curvelet变换去噪方法,即在去噪之前,先将图像进行对数变换,使得乘性噪声变成加性噪声,然后再进行Curvelet变换去噪,这样会更有利于噪声与边缘信息的分离。并把该方法应用在对轮胎的激光无损检测图像处理系统中,实验结果表明该方法在有效去除散斑噪声的同时,较好地保持了条纹图的边缘细节信息。     

PN code acquisition using signed-rank-based non-parametric detector in a multiplicative noise model

Multiplicative noise is known to be useful in modelling an environment that is difficult to describe with an additive noise model. In this article, signed-rank-based non-parametric detectors are used for pseudonoise (PN) code acquisition in multiplicative noise. First, a locally optimum (LO) detector based on the signs and ranks of observations is derived, and then the locally suboptimum rank (LSR) detector is proposed by using approximate score functions. The finite sample-size performance of the LSR detector is considered. Numerical results show that the LSR detector asymptotically has almost the same performance as the LO detector for multiplicative noise.     

乘性和加性噪声中二维谐波频率估计

噪声中的谐波恢复问题是信号处理领域的一个典型问题,在众多领域中有着广泛的应用。本文主要研究零均值乘性和加性噪声并存下的二维谐波信号频率估计问题,提出了一种基于数据矩阵的奇异值分解和子空间的旋转不变性的零均值乘性和加性噪声中的谐波频率的估计方法。乘性噪声为零均值情形下传统的估计方法往往难以直接应用或估计失效。本文利用谐波模型信号特征,通过对观测信号进行平方运算构造了一个数据矩阵。通过对数据矩阵的特征值进行理论分析,结合子空间旋转不变性,得到了零均值乘性和加性噪声中的谐波频率和数据矩阵之间的一种内在关系。这个性质可以用于零均值乘性和加性噪声并存下的二维谐波信号频率估计,并且所得的二维频率能自动配对。仿真实验验证了本文所提算法的有效性。      

红外焦平面非均匀校正的综合处理算法

时域高通滤波的算法具有简单，易于实现的优点。但其在既有加性噪声，又有乘性噪声时校正效果难以令人满意。神经元网络算法在噪声较强时，校正效果受到了限制。针对既有加性噪声，又有乘性噪声，且加性噪声较强的情况，提出了红外焦平面非均匀校正的综合处理算法。仿真证明，新算法具有较好的校正效果。     

Simulation Results for the Decision-Directed MAP Receiver for M-ary Signals in Mulitiplicative and Additive Gaussian Noise

Simulation results are presented for the error-rate performance of the recursive digital maximum a posteriori probability (MAP) detector for knownM-ary signals in multiplicative and additive Gaussian noise. The structure of the digital simulation of the optimum detector is generally described, with specific results obtained for a quaternary signal and 2500 digit per second transmission rate. The simulation is focused on the aeronautical multipath communication problem. Plots of detection error rate versus additive signal-to-noise ratio are given, with the power ratio of multiplicative process to desired signal as a parameter. Results are presented for the cases where the detector has perfect knowledge of the first- and second-order statistics of the multiplicative and additive processes and also where these statistics are estimated in near real time. For comparison, the error rates of conventional coherent and noncoherent digital MAP detectors are also obtained. It is shown that with nonzero multiplicative noise, the error rates of the conventional detectors saturate at a level that is irreducible for increasing additive signal-to-noise ratio. The error rate of the optimum detector having perfect statistical knowledge continues to decrease rapidly with increasing additive signal-to-noise ratio. In the absence of multiplicative noise, the conventional coherent detector and the optimum detector are shown to exhibit identical performance. Suboptimum detectors, having less than perfect statistical knowledge, yield error rates bounded below by the optimum detector rates and bounded above by the conventional detector rates.     

Nonlinear quantization and the design of coded and uncoded signalconstellations

The author analyzes the effects of nonlinear quantizers, used in T1 carrier systems, on the performance of QAM (quadrature amplitude modulation) and TCM (trellis coded modulation) voiceband data communication modems, and introduces a method to counteract the effects of these nonlinearities. The effect of nonlinear quantizers is modeled as a source of multiplicative noise whose variance is proportional to the amplitude of the quantized signal. The relation between variance of the multiplicative noise, characteristics of the nonlinear quantizer, and impulse response of the pulse shaping filters used in the modems is derived. Effects of multiplicative noise on the performance of QAM and TCM modems are analyzed. A method for the design of QAM and TCM signal constellations is introduced which counteracts the harmful effects of nonlinear quantizers. The new constellations provide 2-3 dB performance improvements in multiplicative noise channels while losing less than 0.5 dB in additive noise channels     

Locally optimum detection of signals in a generalized observationmodel: the known signal case

A generalized observation model for signal detection problems is proposed. The model allows consideration of several interesting special cases including additive noise, multiplicative noise, and signal-dependent noise, and includes both deterministic and random signals. Locally optimum (LO) detectors are interesting generalizations of those for the additive noise model. Under the proposed observation model the performance of the LO detectors is compared with that of other common detectors     

Novel color demosaicking for noisy color filter array data

Single sensor digital color still/video cameras use color demosaicking to reproduce full color images from color filter array (CFA) data. The quality of interpolated image will be degraded due to the sensor noise introduced during the image capture process. Many conventional demosaicking-denoising solutions adopt the channel-dependent noise model, which may fit the CMOS/CCD image sensor less than signal-dependent noise model. In this paper, the wavelet sub-band decomposition and synthesis are applied to interpolate the CFA data with signal-dependent noise model. The major contributions of this work include: (1) The combination of LMMSE and statistical calculation in wavelet domain are utilized to suppress the signal-dependent noise, which is separated into additive noise and multiplicative noise. (2) In CFA data, it has been verified that the quantitative relationship between the current pixel and the adjacent pixel, which locate in the same edge. Both simulated and real CFA images are employed to compare the proposed algorithm with the state-of-the-art techniques reported in the literature. The experimental results confirm that our method outperforms them both on demosaicking performance and on computational cost, when they process the noisy color filter array data.     

LUM filters: a class of rank-order-based filters for smoothing andsharpening

A new class of rank-order-based filters, called lower-upper-middle (LUM) filters, is introduced. The output of these filters is determined by comparing a lower- and an upper-order statistic to the middle sample in the filter window. These filters can be designed for smoothing and sharpening, or outlier rejection. The level of smoothing done by the filter can range from no smoothing to that of the median filter. This flexibility allows the LUM filter to be designed to best balance the tradeoffs between noise smoothing and signal detail preservation. LUM filters for enhancing edge gradients can be designed to be insensitive to low levels of additive noise and to remove impulsive noise. Furthermore, LUM filters do not cause overshoot or undershoot. Some statistical and deterministic properties of the LUM filters are developed, and a number of experimental results are presented to illustrate the performance. These experiments include applications to 1D signals and to images