Least squares subspace projection approach to mixed pixelclassification for hyperspectral images

An orthogonal subspace projection (OSP) method using linear mixture modeling was recently explored in hyperspectral image classification and has shown promise in signature detection, discrimination, and classification. In this paper, the OSP is revisited and extended by three unconstrained least squares subspace projection approaches, called signature space OSP, target signature space OSP, and oblique subspace projection, where the abundances of spectral signatures are not known a priori but need to be estimated, a situation to which the OSP cannot be directly applied. The proposed three subspace projection methods can be used not only to estimate signature abundance, but also to classify a target signature at subpixel scale so as to achieve subpixel detection. As a result, they can be viewed as a posteriori OSP as opposed to OSP, which can be thought of as a priori OSP. In order to evaluate these three approaches, their associated least squares estimation errors are cast as a signal detection problem ill the framework of the Neyman-Pearson detection theory so that the effectiveness of their generated classifiers can be measured by receiver operating characteristics (ROC) analysis. All results are demonstrated by computer simulations and Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data     

Least squares restoration of multichannel images

Multichannel restoration using both within- and between-channel deterministic information is considered. A multichannel image is a set of image planes that exhibit cross-plane similarity. Existing optimal restoration filters for single-plane images yield suboptimal results when applied to multichannel images, since between-channel information is not utilized. Multichannel least squares restoration filters are developed using the set theoretic and the constrained optimization approaches. A geometric interpretation of the estimates of both filters is given. Color images (three-channel imagery with red, green, and blue components) are considered. Constraints that capture the within- and between-channel properties of color images are developed. Issues associated with the computation of the two estimates are addressed. A spatially adaptive, multichannel least squares filter that utilizes local within- and between-channel image properties is proposed. Experiments using color images are described     

Least squares approach to blind channel equalization

We present a least squares (LS) algorithm for blind channel equalization based on a reformulation of the Godard algorithm. A transformation for the equalizer parameters is considered to convert the nonlinear LS problem inherent in the Godard algorithm to a linear LS problem. Unlike the Godard (1980) algorithm, the proposed LS approach does not suffer from ill-convergence to closed-eye local minima. Methods for extracting the equalizer parameters from their transformed version are developed. Offline and recursive implementations of the LS algorithm are presented. The algorithm requires only a small number of channel output observations to estimate the equalizer parameters and is therefore fast vis-a-vis the Godard algorithm. The channel input correlation does not impose any restriction on the application of the algorithm, as long as a weak sufficient-excitation condition is satisfied. Simulation examples are presented to demonstrate the LS approach and to compare it with the Godard algorithm     

最小二乘Unscented卡尔曼滤波在伪卫星定位中的应用

为了提高伪卫星的定位精度,在研究伪卫星星历误差传递规律和伪距观测方程线性化误差的基础上,提出一种最小二乘Unscented卡尔曼滤波算法。该算法首先利用最小二乘法估计出伪卫星的位置误差,并对伪卫星的位置进行修正,以减小伪卫星位置误差对导航解算精度的影响;然后利用无迹卡尔曼滤波算法对用户位置进行解算。仿真结果表明,与传统的扩展卡尔曼滤波算法相比,提出的算法能够有效减小伪卫星位置误差对用户定位精度的影响,提高独立组网伪卫星系统的定位精度。     

Least squares algorithms for time-of-arrival-based mobile location

Localization of mobile phones is of considerable interest in wireless communications. In this correspondence, two algorithms are developed for accurate mobile location using the time-of-arrival measurements of the signal from the mobile station received at three or more base stations. The first algorithm is an unconstrained least squares (LS) estimator that has implementation simplicity. The second algorithm solves a nonconvex constrained weighted least squares (CWLS) problem for improving estimation accuracy. It is shown that the CWLS estimator yields better performance than the LS method and achieves both the Crame/spl acute/r-Rao lower bound and the optimal circular error probability at sufficiently high signal-to-noise ratio conditions.     

Least squares pattern synthesis for conformal arrays

The problem of synthesising low sidelobe beams from conformal arrays consisting of few elements and large radius of curvature is addressed. Experimental results are presented for a 12 element array of linearly polarised elements forming a faceted array with radius of curvature 1.5 m. It is shown that by calculation of an aperture correcting matrix, sidelobe levels of 40 dB can be obtained from the array by application of conventional linear array Taylor weights. Beam steering is achieved by aperture phase tapering while low sidelobe levels are maintained     

Least squares order-recursive lattice smoothers

Conventional least squares order-recursive lattice (LSORL) filters use present and past data values to estimate the present value of a signal. This paper introduces LSORL smoothers which use past, present and future data for that purpose. Except for an overall delay needed for physical realization, LSORL smoothers can substantially outperform LSORL filters while retaining all the advantages of an order-recursive structure     

Least squares algorithm for region-of-interest evaluation in emission tomography

An accurate model of the nonstationary geometrical response of a camera-collimator system is discussed. The algorithm is compared to three other algorithms that are specialized for region-of-interest evaluation, as well as to the conventional method for summing the reconstructed quantity over the regions of interest. For noise-free data and for regions of accurate shape, least-squares estimates were unbiased within roundoff errors. For noisy data, estimates were still unbiased but precision worsened for regions smaller than resolution: simulating typical statistics of brain perfusion studies performed with a collimated camera, the estimated standard deviation for a 1-cm-square region was 10% with an ultra-high-resolution collimator and 7% with a low-energy all-purpose collimator. Conventional region-of-interest estimates show comparable precision but are heavily biased if filtered backprojection is used for image reconstruction. Using the conjugate-gradient iterative algorithm and the model of nonstationary geometrical response, bias of estimates decreased on increasing the number of iterations, but precision worsened, thus achieving an estimated standard deviation of more than 25% for the same 1-cm region.     

Least squares acceleration filtering for the estimation of signalderivatives and sharpness at extrema [and application to biologicalsignals]

A family of finite impulse-response (FIR) filters is derived which estimate the second derivative or "acceleration" of a digitized signal. The acceleration is obtained from parabolas that are continuously fit to the signal using a least squares optimization criterion. A closed-form solution for the filter coefficients is obtained. The general approach is computationally simple, can be performed in real-time, and is robust in the presence of noise. An important application of the method, that of measuring sharpness in biologic signals, is presented using the electroencephalogram (EEG) and electrocardiogram (EKG) signals as examples. Furthermore, the design method is extended to derive FIR filters for estimating derivatives of arbitrary order in digital signals of biologic or other origins.     

Least squares phase unwrapping in wavelet domain

Two-dimensional phase unwrapping is an important processing step in some coherent imaging applications. Least squares phase unwrapping is one of the robust techniques used to solve two-dimensional phase unwrapping problems. However, owing to its sparse structure, the convergence rate is very slow, and some practical methods have been applied to improve this condition. A new method for solving the least squares two-dimensional phase unwrapping problem is presented. This technique is based on the multiresolution representation of a linear system using the discrete wavelet transform. By applying the wavelet transform, the original system is decomposed into its coarse and fine resolution levels. Fast convergence in separate coarse resolution levels makes the overall system convergence very fast.     

Least mean squares algorithm for fractionally spaced blind channelestimation

The authors consider the problem of blind estimation and equalisation of digital communication finite impulse response (FIR) channels using fractionally spaced samples. The system input is assumed to be a deterministic but unknown data sequence. Exploiting the periodicity of the transmitted data sequence in the frequency domain in the noise free case, it is shown that it is possible to form a linear system in terms of the unknown channel impulse response. In the presence of noise, a least mean squares (LMS) criterion is used to resolve the channel. The resulting algorithm has an appealing interpretation and can be considered as a single channel counterpart of the multi-channel cross-relation (CR) method. Finally, it is shown that the latter can be derived from the proposed algorithm     

Least squares adaptive antenna for angle of arrival estimation

The least squares formulation of an adaptive antenna is presented, which (with the aid of a calibration curve) may be used to estimate the angle of arrival in the presence of multipath as encountered in a low-angle tracking radar environment. A procedure (based on the Eckart-Young theorem) is proposed for improving the noise performance of the estimator.     

A mixed transform approach for efficient compression of medical images

A novel technique is presented to compress medical data employing two or more mutually nonorthogonal transforms. Both lossy and lossless compression implementations are considered. The signal is first resolved into subsignals such that each subsignal is compactly represented in a particular transform domain. An efficient lossy representation of the signal is achieved by superimposing the dominant coefficients corresponding to each subsignal. The residual error, which is the difference between the original signal and the reconstructed signal is properly formulated. Adaptive algorithms in conjunction with an optimization strategy are developed to minimize this error. Both two-dimensional (2-D) and three-dimensional (3-D) approaches for the technique are developed. It is shown that for a given number of retained coefficients, the discrete cosine transform (DCT)-Walsh mixed transform representation yields a more compact representation than using DCT or Walsh alone. This lossy technique is further extended for the lossless case. The coefficients are quantized and the signal is reconstructed. The resulting reconstructed signal samples are rounded to the nearest integer and the modified residual error is computed. This error is transmitted employing a lossless technique such as the Huffman coding. It is shown that for a given number of retained coefficients, the mixed transforms again produces the smaller rms-modified residual error. The first-order entropy of the error is also smaller for the mixed-transforms technique than for the DCT, thus resulting in smaller length Huffman codes.     

最小二乘与加权最小二乘空域矩阵滤波器设计

空域矩阵滤波器是一种新的信号处理技术,通过一个滤波矩阵与接收到的阵列数据相乘,可实现保留通带目标信号,抑制阻带干扰的目的.本文主要研究了最小二乘和加权最小二乘两类的空域矩阵滤波器.给出了空域滤波器设计基本原理,通过最优化问题得出了最优解.最小二乘空域矩阵滤波器是加权系数为1的加权加权最小二乘空域矩阵滤波器的特列.由加权最小二乘迭代仿真结果可以看出,迭代次数的增加使滤波器阻带响应极大值逐渐变小,可实现恒定阻带抑制效果,设计效率较高.     

Regularized fast recursive least squares algorithms for finitememory filtering

Novel fast recursive least squares algorithms are developed for finite memory filtering, by using a sliding data window. These algorithms allow the use of statistical priors about the solution, and they maintain a balance between a priori and data information. They are well suited for computing a regularized solution, which has better numerical stability properties than the conventional least squares solution. The algorithms have a general matrix formulation, such that the same equations are suitable for the prewindowed as well as the covariance case, regardless of the a priori information used. Only the initialization step and the numerical complexity change through the dimensions of the intervening matrix variables. The lower bound of O (16m) is achieved in the prewindowed case when the estimated coefficients are assumed to be uncorrelated, m being the order of the estimated model. It is shown that a saving of 2m multiplications per recursion can always be obtained. The lower bound of the resulting numerical complexity becomes O(14m ), but then the general matrix formulation is lost     

Robust adaptive estimator for filtering noise in images

Provides three new methods for storing images corrupted by additive noise. One is the adaptive mean median filter for preserving the details of images when restored from additive Gaussian noise. Another is the minimum-maximum method for moving outlier noise. The third method, the robust adaptive mean p-median filter, is based on a combination of the previous two methods. In the past, proposed restoration methods have generally proven to be inadequate for both detail preservation and noise suppression, but the new adaptive mean p-median filter is shown to be good at both of these tasks, while the robust adaptive mean p-median filter can give good performance even in the presence of outliers. Degraded images are processed by the proposed algorithms, with the results compared with a selection of other median-based algorithms that have been proposed in the literature.     

Multidimensional filtering approaches for pre-processing thermal images

Demand for sharpened thermal images drives research into pre-processing techniques. This paper describes two fast multi-frame image-processing techniques for reducing noise and some blurring effects that are typically exhibited in thermal images. The first technique cleans the thermal image from random and fixed-pattern noises. The random noise is considerably reduced by the simple principle of averaging corresponding pixels of a multi-frame sequence. For eliminating fixed-noise like effects, the technique performs, at first, conventional arithmetic mean filters within each local region of the noise pattern. Then, weighted versions of these values are subtracted from the corrupted image. The second technique attempts to recover the information hidden at a sub-pixel level. It sharpens the previously processed thermal image by down-sampling and matching a set of sub-pixel shifted frames, and finally calculating the statistical weighted average within the correspondent aligned pixels of the multi-frame set. Some variants that combine it with conventional filters are also presented. This technique effectively corrects some blurring effects typically found in thermal infrared images. For the case of a single frame image determines the direction and width of the blur slope and re-assigns the max and min values to the correspondent pixels in the gradient direction. Then, the area is shifted and the same process is done again, up to cover the full image. Image evaluation methods demonstrate the accuracy and quality of the results. In addition to reducing the hardware requirements of present designs, these algorithms increase the utility of present sensors.     

An efficient recursive total least squares algorithm for FIRadaptive filtering

An algorithm for recursively computing the total least squares (TLS) solution to the adaptive filtering problem is described. This algorithm requires O(N) multiplications per iteration to effectively track the N-dimensional eigenvector associated with the minimum eigenvalue of an augmented sample covariance matrix. It is shown that the recursive least squares (RLS) algorithm generates biased adaptive filter coefficients when the filter input vector contains additive noise. The TLS solution on the other hand, is seen to produce unbiased solutions. Examples of standard adaptive filtering applications that result in noise being added to the adaptive filter input vector are cited. Computer simulations comparing the relative performance of RLS and recursive TLS are described     

Least squares approximation of perfect reconstruction filter banks

Designing good causal filters for perfect reconstruction (PR) filter banks is a challenging task due to the unusual nature of the design constraints. We present a new least squares (LS) design methodology for approximating PRFBs that avoids most of these difficult constraints. The designer first selects a set of subband analysis filters from an almost unrestricted class of rational filters. Then, given some desired reconstruction delay, this design procedure produces the causal and rational synthesis filters that result in the best least squares approximation to a PRFB. This technique is built on a multi-input multi-output (MIMO) system model for filter banks derived from the filter bank polyphase representation. Using this model, we frame the LS approximation problem for PRFBs as a causal LS equalization problem for MIMO systems. We derive the causal LS solution to this design problem and present an algorithm for computing this solution. The resulting algorithm includes a MIMO spectral factorization that accounts for most of the complexity and computational cost for this design technique. Finally, we consider some design examples and evaluate their performance     

Rayleigh-maximum-likelihood filtering for speckle reduction of ultrasound images

Speckle is a multiplicative noise that degrades ultrasound images. Recent advancements in ultrasound instrumentation and portable ultrasound devices necessitate the need for more robust despeckling techniques, for both routine clinical practice and teleconsultation. Methods previously proposed for speckle reduction suffer from two major limitations: 1) noise attenuation is not sufficient, especially in the smooth and background areas; 2) existing methods do not sufficiently preserve or enhance edges--they only inhibit smoothing near edges. In this paper, we propose a novel technique that is capable of reducing the speckle more effectively than previous methods and jointly enhancing the edge information, rather than just inhibiting smoothing. The proposed method utilizes the Rayleigh distribution to model the speckle and adopts the robust maximum-likelihood estimation approach. The resulting estimator is statistically analyzed through first and second moment derivations. A tuning parameter that naturally evolves in the estimation equation is analyzed, and an adaptive method utilizing the instantaneous coefficient of variation is proposed to adjust this parameter. To further tailor performance, a weighted version of the proposed estimator is introduced to exploit varying statistics of input samples. Finally, the proposed method is evaluated and compared to well-accepted methods through simulations utilizing synthetic and real ultrasound data.