Wavelet transform domain filters: a spatially selective noisefiltration technique

Wavelet transforms are multiresolution decompositions that can be used to analyze signals and images. They describe a signal by the power at each scale and position. Edges can be located very effectively in the wavelet transform domain. A spatially selective noise filtration technique based on the direct spatial correlation of the wavelet transform at several adjacent scales is introduced. A high correlation is used to infer that there is a significant feature at the position that should be passed through the filter. The authors have tested the technique on simulated signals, phantom images, and real MR images. It is found that the technique can reduce noise contents in signals and images by more than 80% while maintaining at least 80% of the value of the gradient at most edges. The authors did not observe any Gibbs' ringing or significant resolution loss on the filtered images. Artifacts that arose from the filtration are very small and local. The noise filtration technique is quite robust. There are many possible extensions of the technique. The authors see its applications in spatially dependent noise filtration, edge detection and enhancement, image restoration, and motion artifact removal. They have compared the performance of the technique to that of the Weiner filter and found it to be superior.     

A new adaptive filtering scheme based on wavelet transform

Based on the scale function representation for a function in L ²(R), a new wavelet transform based adaptive system identification scheme is proposed. It can reduce the amount of computation by exploiting the decimation properties and keep the advantage of quasi-orthogonal transform of the discrete wavelet transform (DWT). The issue has been supported by computer simulations. Supported by the National Natural Science Foundation of China, no.69672039     

Performance of adaptive filters using combined lattice and transform techniques

A composite scheme combining lattice and transform techniques for implementation of adaptive filters is discussed. Results of the eigenvalue spreads and convergence time for simple correlation cancelers in combination with Walsh-Hadamard Transform (WHT) are reported.     

Adaptive median filters: new algorithms and results

Based on two types of image models corrupted by impulse noise, we propose two new algorithms for adaptive median filters. They have variable window size for removal of impulses while preserving sharpness. The first one, called the ranked-order based adaptive median filter (RAMF), is based on a test for the presence of impulses in the center pixel itself followed by a test for the presence of residual impulses in the median filter output. The second one, called the impulse size based adaptive median filter (SAMF), is based on the detection of the size of the impulse noise. It is shown that the RAMF is superior to the nonlinear mean L(p) filter in removing positive and negative impulses while simultaneously preserving sharpness; the SAMF is superior to Lin's (1988) adaptive scheme because it is simpler with better performance in removing the high density impulsive noise as well as nonimpulsive noise and in preserving the fine details. Simulations on standard images confirm that these algorithms are superior to standard median filters.     

一种基于Shearlet变换域改进自适应中值滤波算法

为了有效滤除图像中大量存在的脉冲噪声,提出了一种基于Shearlet变换域改进自适应中值滤波方法。首先在对Shearlet变换进行深入分析的基础上,给出了Shearlet分解和重构基本步骤;然后实现对含噪图像进行多尺度Shearlet变换,对获得多个尺度下的分解系数采用从噪声检测、噪声滤波等环节改进的自适应中值滤波算法(IAMF)进行噪声抑制;最后实现滤波后分解系数重构。分别与经典中值滤波(MF)、自适应中值滤波(AMF)以及Shearlet变换域阈值法进行比较,实验结果表明,该滤波算法滤波性能较好。     

A new design for digital adaptive filters

The design and operation of a digital adaptive filter based on a modified Widrow-Hoff algorithm is described. It uses LSI components as main elements. This filter realization converges faster than other realizations reported hitherto because its weight vector is updated at every sampling instant.     

Transient analysis of data-normalized adaptive filters

This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability, of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model provides information about the mean-square deviation and mean-square error performance of the filters. In addition to deriving earlier results in a unified manner, the approach leads to stability and performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and does not require an explicit recursion for the covariance matrix of the weight-error vector.     

Wavelet based image adaptive watermarking scheme

An image adaptive watermark casting method based on the wavelet transform is proposed. To increase the robustness and perceptual invisibility, the algorithm is combined with the quantisation model based on the human visual system. The number of factors that affect the noise sensitivity of the human eye are taken into consideration. Experimental results demonstrate the robustness of the algorithm to high compression environments     

Performance analysis of LMS adaptive prediction filters

The conditions required to implement real-time adaptive prediction filters that provide nearly optimal performance in realistic input conditions are delineated. The effects of signal bandwidth, input signal-to-noise ratio (SNR), noise correlation, and noise nonstationarity are explicitly considered. Analytical modeling, Monte Carlo simulations and experimental results obtained using a hardware implementation are utilized to provide performance bounds for specified input conditions. It is shown that there is a nonlinear degradation in the signal processing gain as a function of the input SNR that results from the statistical properties of the adaptive filter weights. The stochastic properties of the filter weights ensure that the performance of the adaptive filter is bounded by that of the optimal matched filter for known stationary input conditions     

Spectral analysis of subband adaptive digital filters

Subband adaptive digital filters at stationary points are analyzed in the frequency domain. Approximate expressions for the optimal subband filters are presented, and then, a spectral representation of the error variance is derived. These are expressed in the frequency domain and, hence, enable us to see the aliasing effects in subband adaptive filtering     

Envelope-constrained filters: adaptive algorithms

We consider an envelope-constrained (EC) optimal filter design problem involving a quadratic cost function and a number of linear inequality constraints. Using the duality theory and the space transformation function, the optimal solution of the dual problem can be computed by finding the limiting point of an ordinary differential equation given in terms of the gradient flow. An iterative algorithm is developed via discretizing the differential equation. From the primal-dual relationship, the corresponding sequence of approximate solutions in the original EC filtering problem is obtained. Based on these results, an adaptive algorithm is constructed for solving the stochastic EC filtering problem in which the input signal is corrupted by an additive random noise. For illustration,a practical example is solved for both noise-free and noisy cases     

Convergence analysis of alias-free subband adaptive filters based on a frequency domain technique

Convergence analysis of alias-free subband adaptive filters (SADFs) is presented based on a frequency-domain technique where instead of analyzing the adaptive algorithms in the time-domain, the averaging method and the ordinary differential equation (ODE) method are applied to the frequency-domain expressions of the adaptive algorithms converted by the discrete Fourier transform. As an alias-free SADF algorithm, the SADF proposed by Pradhan and Reddy is known. In this paper, this technique is first applied to the Pradhan's SADF. The stability of the Pradhan's SADF is verified in the frequency domain, and a simple formula to evaluate the mean square error (MSE) of the algorithm is theoretically derived. By using a slight modification, the technique can be applied to the two-band delayless subband adaptive filter (DLSADF) with the Hadamard transform. The stability condition and the MSE of the DLSADF with the Hadamard transform are also obtained. Simulation results of both algorithms show the validity of the theoretical results.     

On the block least squares adaptive digital filters realized usingthe fast Fourier transform

The authors formulate a block-based least-squares problem in the frequency domain. They then develop computationally efficient block least-squares algorithms that can be realized using the fast Fourier transform. They also present computer simulation results demonstrating the convergence characteristics of the proposed algorithms     

Transient analysis of adaptive filters with error nonlinearities

The paper develops a unified approach to the transient analysis of adaptive filters with error nonlinearities. In addition to deriving earlier results in a unified manner, the approach also leads to new performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and avoids the need for explicit recursions for the covariance matrix of the weight-error vector.     

Globally convergent adaptive IIR filters based on fixed polelocations

A new class of adaptive filters, dubbed fixed pole adaptive filters (FPAF's), is introduced. These adaptive filters have infinite impulse responses, yet their adaptation exhibits provable global convergence. Good filter performance with a relatively small number of adapted parameters is permitted by the new filter structure, thus reducing the computational burden needed to implement adaptive filters. The implementation and computational complexity of the FPAF is described, and its modeling capabilities are determined. Excitation conditions on the filter input are established that guarantee global convergence of a standard set of adaptive algorithms. Some methods are described for selecting the fixed pole locations based on a priori information regarding the operating environment of the adaptive filter. The FPAF is tailored to applications by such a procedure, enabling improved performance. In examples, the FPAF is shown to achieve a smaller minimum mean square error, given an equal number of adapted parameters, in comparison with adaptive FIR filters and adaptive filters based on Laguerre and Kautz models     

基于LMS的自适应去噪滤波器设计

讨论了自适应滤波去噪原理，采用LMS算法设计了自适应去噪滤波器，分析了MAT-LAB／SIMULINK中DSP Builder模块库在FPGA中的设计优点，最后应用DSP Builder模块库对自适应滤波器进行仿真。为自适应滤波器硬件实现提供了实验依据。     

A new method for low-rank transform domain adaptive filtering

This paper introduces a least squares, matrix-based framework for adaptive filtering that includes normalized least mean squares (NLMS), affine projection (AP) and recursive least squares (RLS) as special cases. We then introduce a method for extracting a low-rank underdetermined solution from an overdetermined or a high-rank underdetermined least squares problem using a part of a unitary transformation. We show how to create optimal, low-rank transformations within this framework. For obtaining computationally competitive versions of our approach, we use the discrete Fourier transform (DFT). We convert the complex-valued DFT-based solution into a real solution. The most significant bottleneck in the optimal version of the algorithm lies in having to calculate the full-length transform domain error vector. We overcome this difficulty by using a statistical approach involving the transform of the signal rather than that of the error to estimate the best low-rank transform at each iteration. We also employ an innovative mixed domain approach, in which we jointly solve time and frequency domain equations. This allows us to achieve very good performance using a transform order that is lower than the length of the filter. Thus, we are able to achieve very fast convergence at low complexity. Using the acoustic echo cancellation problem, we show that our algorithm performs better than NLMS and AP and competes well with FTF-RLS for low SNR conditions. The algorithm lies in between affine projection and FTF-RLS, both in terms of its complexity and its performance     

The gamma-filter-a new class of adaptive IIR filters withrestricted feedback

Generalized feedforward filters, a class of adaptive filters that combines attractive properties of finite impulse response (FIR) filters with some of the power of infinite impulse response (IIR) filters, are described. A particular case, the gamma filter, generalizes Widrow's adaptive transversal filter (adaline) to an infinite impulse response filter. Yet, the stability condition for the gamma filter is trivial, and LMS adaptation is of the same computational complexity as the conventional transversal filter structure. Preliminary results indicate that the gamma filter is more efficient than the adaptive transversal filter. The authors extend the Wiener-Kopf equation to the gamma filter and develop some analysis tools     

Stability analysis of adaptive filters with regression vector nonlinearities

We present a unified framework to analyze the mean and mean-square stability of a large class of adaptive filters. We do this without obtaining a full transient model, allowing us to acquire sufficient conditions on the stability without assuming a given statistical distribution for the input regressors. We also apply the proposed framework to some popular adaptive filtering schemes, showing that in some cases the sufficient conditions derived are very tight and even necessary too.     

可变树长混合小波和子树自量化分形视频编码

对可变树长混合小波和子树自量化分形视频编码方案进行了探讨。通过金字塔小波分解，每一频序列帧被分解为多频率子带，将它们按一定方式组织成小波子树结构来表示视频序列的运动特性。对这些小波子树者运动检测，分成运动树和非运动树两类。非运动树的编码直接、简单；运动树则采用可变树长混合小波和对自量化方法来进行编码。实验结果表明在低比特率情况下，所述的方案在ＰＳＮＲ和主观质量两方面均可获得较好的性能。