Deterministic properties of separable and cross median filters with an application to block truncation coding

In this paper, we present some deterministic properties of separable and cross median filters. It is proved that in the absence of vertical binary oscillations, the roots of a separable median filter are included in a subset of root signals of the corresponding cross median filter. Moreover, the sufficient and necessary condition is given for a point to be invariant to cross median filtering. On the root structures of cross median filters, we indicate that there exist three different types of regions based on the one-dimensional features of rows and columns. Finally, an application example is discussed where the roots of separable and cross median filters are used in block truncation coding (BTC) for image compression.     

基于形态学和OTSU算法的红外图像降噪及分割

为了在去除红外图像的脉冲噪声的同时,有效保持和恢复图像的边缘细节,提出了基于灰度特征和众数原则的迭代双边中值滤波方法。此方法根据脉冲噪声的灰度特征以及众数原则,将取最小和最大值、而在邻域的灰度分布上孤立的像素识别为噪声。根据基于空间距离和灰度相似的加权系数,对邻域中的无噪像素与已经去噪恢复的像素进行频次加权,用频次加权中值作为噪声像素的估计值。其中,以迭代遍历的方式执行去噪处理,充分利用前次遍历处理的结果,以去除高密度噪声。实验数据证明,此方法去噪所得的PSNR和EPI值以及视觉效果均优于现有方法,具有更好的去噪性能。     

Convergence properties of median and weighted median filters

It has been shown that assuming the first and last value carry-on appending strategy, a finite number of passes of the same median filter to an arbitrary signal of finite length results in a root signal that will be invariant to additional filtering passes. This so-called convergence property is reproven using an extremely simple approach. In addition, the well-known idempotent property (i.e., where convergence is achieved with only one filtering pass) of a recursive median filter is reproven similarly, and the convergence behavior of weighted median filters is studied     

基于噪声估计和双加权的彩色图像矢量中值滤波

针对彩色图像椒盐噪声滤除中保护色彩和细节这个关键问题,提出了一种基于噪声估计和双加权的滤波新算法.噪声估计采用二级估计策略,第1级基于灰度最大、最小值进行粗估计,第2级采用加权方向算子进行精估计.对非噪声点保持像素灰度不变,对噪声点设计了空间和灰度双加权的矢量中值滤波算法(VMF).实验结果表明,新算法对低、中密度的彩...     

Analysis of weighted median filters based on inequalities relating the weights

By considering all orderings of the input samples, which are discrete-time continuous-valued, it is shown here that a weighted median (WM) filter of spanN can be specified unambiguously by 2^N–1 consistent linear inequalities relating the weights. This specification is identical to that of a self-dual threshold function with the same weights. It is also shown that WM filters with symmetric weights can be specified by ternary threshold functions. Based on these inequalities, properties of WM filters which can be used to check equivalence of some WM filters are derived.This work was supported in part by the National Science Foundation under Grant DCI-8611859. A portion of this work was presented at the IEEE International Symposium on Circuits and Systems, Portland, Oregon, May 1989.     

Fast adaptive optimization of weighted vector median filters

Weighted vector median (WVM) filters are effective tools for multichannel signal processing. To obtain the desired filtering behavior and characteristic, the WVM filter weights must be determined in an appropriate manner. In this paper, we first analyze previously defined approaches for WVM filter optimization and show their drawbacks related to derivative computation and vector direction information utilization. Based on this analysis, we propose two fast adaptive algorithms for WVM filter design. Proposed Algorithm I computes locally optimal weight changes at each iteration and updates the filter weights accordingly. This algorithm does not involve derivative computation, thus eliminating the instability caused by derivative approximations utilized in previous approaches. Proposed Algorithm II extends the results from established marginal weighted median optimization methods to the vector case by error metric generalization. Both algorithms can be applied to WVM filters using the L/sub p/ norm, while Algorithm I can operate on more general distance metrics. The presented simulation results show that both algorithms are effective, fast, and stable; they perform well under a wide range of circumstances.     

Impulse noise reduction based on improved median ϵ-filter

Impulse noise reduction has been a challenge for Image Processing researchers for many decades. Median filter had been the most popular denoising methods. However, owing to its edge jittering and removing image detail properties, numerous efforts have been taken in order to improve its performance. Median ?-filter is one of the modified median filters. Median ?-filter and median filter behave in a like manner in the presence of noise. Thus, it has all disadvantageous things of median filter. In this article, we improve median ?-filter's efficiency by giving weights to the outcomes of ?-filter. The experimental results show the excellent performance of our method. Other than that, in the absence of noise, our method preserves the original image's details more than others.     

On root structures and convergence properties of weighted median filters

A weighted median filter is a nonlinear digital filter consisting of a window of length 2N + 1 and a weight vector W=(W_? N,..., W₀,..., W_N). A root signal of a median type filter is a signal that is invariant to the filter. However, not all weighted median filters possess the convergence property. In this paper, we shall study the root structures and the convergence behavior of a subclass of weighted median filters, calledclass- 1 filters, which is symmetric in its weight vector. We shall introduce an important parameter, calledfeature value, and show that any one-dimensional unappended signal of lengthL will converge to a root signal in at most $$3\left\lceil {\frac{{L - 2}}{{2(2N + 2 - p)}}} \right\rceil$$ passes of aclass ?1 filter with window width 2N + 1 and thefeature value p.     

Quadratic weighted median filters for edge enhancement of noisy images.

Quadratic Volterra filters are effective in image sharpening applications. The linear combination of polynomial terms, however, yields poor performance in noisy environments. Weighted median (WM) filters, in contrast, are well known for their outlier suppression and detail preservation properties. The WM sample selection methodology is naturally extended to the quadratic sample case, yielding a filter structure referred to as quadratic weighted median (QWM) that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers arising in the higher order statistics of environment noise. Through statistical analysis of higher order samples, it is shown that, although the parent Gaussian distribution is light tailed, the higher order terms exhibit heavy-tailed distributions. The optimal combination of terms contributing to a quadratic system, i.e., cross and square, is approached from a maximum likelihood perspective which yields the WM processing of these terms. The proposed QWM filter structure is analyzed through determination of the output variance and breakdown probability. The studies show that the QWM exhibits lower variance and breakdown probability indicating the robustness of the proposed structure. The performance of the QWM filter is tested on constant regions, edges and real images, and compared to its weighted-sum dual, the quadratic Volterra filter. The simulation results show that the proposed method simultaneously suppresses the noise and enhances image details. Compared with the quadratic Volterra sharpener, the QWM filter exhibits superior qualitative and quantitative performance in noisy image sharpening.     

Some extremal properties of Daubechies filters and other orthonormal filters

New extremal properties of Daubechies 4-tap orthonormal filters are given: they maximize a certain functional, have the largest gain in (0,π/2), and allow maximum energy compaction in [0,π/2]. These properties do not carry over to Daubechies filters of arbitrary length. They complement what is known about Daubechies filters and highlight the specific role of the 4-tap filter. Moreover, we demonstrate that these properties cannot be fulfilled by any other orthonormal lowpass filter, regardless of its length.     

Stability determination of two-dimensional discrete-time systems

In determining root distribution of univariate polynomials with real or complex-valued coefficients, the Bistritz tabular form offers a significant computational advantage. Stability studies of two-dimensional (2-D) discrete-time systems involve univariate polynomials possessing parameter-dependent coefficients, where the parameter takes values on the unit circle in the complex plane. This paper investigates the application of Bistritz tabular form in determining stability of 2-D discrete-time systems, and for this purpose we present two algorithms. Both algorithms utilize a recent result that has established the relationship between Schur-Cohn minors and the entries of the Bistritz tabular form corresponding to a given polynomial. A comparison between the use of the modified Jury table and the Bistritz table in stability checking of 2-D discrete-time systems is also presented.     

改进的中值滤波去噪算法分析

通过对传统中值滤波的分析,针对传统中值滤波在图像去噪过程中的不足,提出了一种改进算法,根据图像细节特征进行阈值设定,给出噪声与复杂图像细节的判断方法。通过实验仿真该算法对椒盐噪声的抑制和复杂图像细节保护具有很好的鲁棒性和适应性。     

Design of smallest size two-dimensional linear-phase FIR filters with magnitude error constraint

This paper presents an online procedure that produces the smallest feasible size of two-dimensional FIR filters with prescribed magnitude error constraint. The procedure uses the mean square normalized error of constrained and unconstrained least-square filters to produce the initial and the subsequent sizes that converge to the smallest feasible one in a few iterations, where the constrained least-square filters are defined as the least-square filters satisfying the magnitude error constraint. The procedure finally returns a smallest size filter that satisfies the magnitude error constraint and has least total squared magnitude error. Design examples of diamond-shaped, rectangular, and elliptic filters are provided, and comparisons with an exhaustive search are given.     

基于中值PCA和加权PCA数据分类的研究

在分析了传统主成分分析（PCA）方法的原理和实现方法上,提出了基于中值的主成分分析新方法（MPCA）.另外,针对多类高维数据分类问题,较深入地研究了权函数对分类问题的影响,对传统PCA模型进行加权处理得到加权主成分分析（WPCA）.实验结果表明,MPCA比传统PCA具有较好的分类效果,不同权函数对数据的分类结果影响较大,且WPCA比传统PCA在分类效果上有明显的优势.     

可规划相位FIR滤波器的神经网络设计方法

本文针对可规划相频响应的实系数FIR滤波器的逼近问题,采用一个三层复激活函数前馈神经网络来实现。该网络隐层各神经元的激活函数为复指数函数,将滤波器系数作为隐层各神经元到输出层的连接权值,通过对误差函数的最小化来调整权值,并根据网络特性与所要设计的滤波器的特点,提出了一些实际设计中训练样本集选取与误差加权值设置的规则。依托所采用的神经网络,根据上述规则,进行了两例可规划相频特性的实系数FIR滤波器的设计,结果表明所设计滤波器的相频响应较好地满足了设计要求。     

基于自适应神经网络的二维线性相位FIR滤波器优化设计

提出一种基于自适应三角函数基神经网络的二维线性相位FIR滤波器优化设计方法.该方法根据二维线性相位FIR滤波器幅频响应特性,采用三角函数基神经网络优化算法计算滤波器系数,同时在神经网络训练过程引入自适应学习率算法,提高神经网络的学习效率和收敛速度.通过训练神经网络的权值,使二维线性相位FIR滤波器幅频响应与理想幅频响应...     

基于图像增强的改进自适应加权均值滤波算法

为了尽可能滤除图像中的椒盐噪声同时改善图像视觉效果,将改进自适应加权均值滤波与小波域图像增强技术有机结合,提出了一种具有增强效果的图像滤波算法。该算法分为滤波和滤波后处理两个阶段。滤波阶段,对经典均值滤波分别从噪声检测策略、权值计算机方法噪声滤波模版设计等方面进行适当改进,给出了具体实现步骤;滤波后处理阶段,首先将滤波后图像进行三层小波分解;然后构造出一种小波图像增强模型,根据小波系数的幅度值将其分为三个部分,分别进行不同程度的拉伸处理;最后进行拉伸后小波系数重构。将该滤波算法与经典均值滤波,加权均值滤波、自适应加权中值滤波等性能比较,实验结果表明,本文滤波算法在噪声滤除和图像细节保持方面,效果较好。     

Universal filters of arbitrary order and type employing square-root-domain technique

Novel Single Input Multiple Output (SIMO) and Multiple Input Single Output (MISO) universal filter topologies of arbitrary order and type are introduced in this paper. The proposed topologies have been realised by employing Square-Root Domain (SRD) technique. An offered benefit of the universal filter topologies is that only grounded capacitors are required for their implementations and the resonant frequency of the filters can be electronically controlled by an appropriate dc current. The proposed universal filters simultaneously offer all the five standard filtering functions i.e. Lowpass (LP), Highpass (HP) and Bandpass (BP), Bandstop (BS) and Allpass (AP) frequency responses. In addition, the SIMO topology is generic in the sense that it can yield four different stable filter configurations. Two design examples are provided in each configuration and the correct operation of the corresponding topologies has been evaluated through the PSPICE software with BSIM 0.35-µm CMOS process model parameters.     

On the practical realization of higher-order filters with fractional stepping

We propose the use of a compact integer-order transfer function approximation of the fractional-order Laplacian operator s^α to realize fractional-step filters. Lowpass and bandpass filters of orders (n+α) and 2(n+α), where n is an integer and 0<α<1, can, respectively, be designed. A 5th-order lowpass filter with fractional steps from 0.1 to 0.9 (i.e. 5.1→5.9) is given as an example with its characteristics compared to 5th- and 6th-order Butterworth filters. Spice simulations and experimental results are shown.