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。     

Blind deconvolution of medical ultrasound images: a parametric inverse filtering approach.

The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a "hybridization" of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the "hybrid" approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolutioh algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used.     

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 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 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 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 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     

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.     

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.     

Maritime filtering for images and videos

Maritime signal processing technologies have emerged as an important area of study because of the increasing popularity of autonomous ships and automatic maritime surveillance systems. However, the various techniques developed for detecting or tracking objects remain unable to address various maritime noise challenges that cause several types of false positives in maritime visual surveillance. Maritime signal processing is challenging because of the prevalence of noise sources such as severe dynamic backgrounds, wakes, and reflections, owing to the complex, unconstrained, and diverse nature of such scenes caused by the surface properties of water. Moreover, few studies have investigated specific maritime noise filtering as a general integrated processing approach with image and video technologies in the context of maritime visual surveillance. In this study, we propose a novel maritime noise prior (MNP) based on a dark channel prior and observations of the characteristics of the sea. A general maritime filtering technique is developed to suppress noise originating from the properties of water in maritime images and videos. The proposed method employs a noniterative, nonlinear, and simple maritime filtering approach based on MNP that does not require specialized knowledge of application scene conditions or structure. We conducted image and video experiments by applying our approach to three publicly available databases. In experiments with color images, our method successfully filtered related background noise and water, i.e., severe boat wakes and reflections, while preserving objects other than water in color images. In the experiments with video sequences, the results demonstrated that the proposed filter improved the overall performance of state-of-the-art background subtraction (BS) algorithms from 36.60%–50.63%. By combining BS algorithms and filtering to enhance foreground detection in video sequences, the proposed method ensures the universal applicability and flexibility required to eliminate noise from images and videos obtained in challenging maritime environments. The results indicate that the proposed method is appropriate for maritime surveillance applications implementing image segmentation and foreground detection, and it can potentially increase the accuracy of maritime visual surveillance.     

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.     

Least squares decoding in binomial frequency division multiplexing

This paper proposes a method that can reduce the complexity of a system matrix by analyzing the characteristics of a pseudoinverse matrix to receive a binomial frequency division multiplexing (BFDM) signal and decode it using the least squares (LS) method. The system matrix of BFDM can be expressed as a band matrix, and as this matrix contains many zeros, its amount of calculation when generating a transmission signal is quite small. The LS solution can be obtained by multiplying the received signal by the pseudoinverse matrix of the system matrix. The singular value decomposition of the system matrix indicates that the pseudoinverse matrix is a band matrix. The signal-to-interference ratio is obtained from their eigenvalues. Meanwhile, entries that do not contribute to signal generation are erased to enhance calculation efficiency. We decode the received signal using the pseudoinverse matrix and the removed pseudoinverse matrix to obtain the bit error rate performance and to analyze the difference.     

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     

Constrained least squares filtering algorithm for ultrasound image deconvolution

A new medical ultrasound tissue model is considered in this paper, which incorporates random fluctuations of the tissue response and provides more realistic interpretation of the received pulse-echo ultrasound signal. Using this new model, we propose an algorithm for restoration of the degraded ultrasound image. The proposed deconvolution is a modification of the classical regularization technique which combines Wiener filter and the constrained least squares (LS) algorithm for restoration of the ultrasound image. The performance of the algorithm is evaluated based on both the simulated phantom images and real ultrasound radio frequency (RF) data. The results show that the algorithm can provide improved ultrasound imaging performance in terms of the resolution gain. The deconvolved images visually show better resolved tissue structures and reduce speckle, which are confirmed by a medical expert.     

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.