Modeling SAR images with a generalization of the Rayleigh distribution

Synthetic aperture radar (SAR) imagery has found important applications due to its clear advantages over optical satellite imagery one of them being able to operate in various weather conditions. However, due to the physics of the radar imaging process, SAR images contain unwanted artifacts in the form of a granular look which is called speckle. The assumptions of the classical SAR image generation model lead to a Rayleigh distribution model for the histogram of the SAR image. However, some experimental data such as images of urban areas show impulsive characteristics that correspond to underlying heavy-tailed distributions, which are clearly non-Rayleigh. Some alternative distributions have been suggested such as the Weibull, log-normal, and the k-distribution which had success in varying degrees depending on the application. Recently, an alternative model namely the alpha-stable distribution has been suggested for modeling radar clutter. In this paper, we show that the amplitude distribution of the complex wave, the real and the imaginery components of which are assumed to be distributed by the alpha-stable distribution, is a generalization of the Rayleigh distribution. We demonstrate that the amplitude distribution is a mixture of Rayleighs as is the k-distribution in accordance with earlier work on modeling SAR images which showed that almost all successful SAR image models could be expressed as mixtures of Rayleighs. We also present parameter estimation techniques based on negative order moments for the new model. Finally, we test the performance of the model on urban images and compare with other models such as Rayleigh, Weibull, and the k-distribution.     

A new approach to speech segmentation based on the maximum likelihood

Successful speech recognition is highly dependent on appropriate speech segmentation. The poor efficiency of the sequential detection of abrupt changes in the signals with relatively short stationary intervals, as is the case with speech signals, can be improved by the off-line maximum likelihood segmentation algorithm. In this paper the new segmentation algorithm is presented. For the a priori known number of segments, the algorithm determines such signal partitions for which the sum of segment distortion is minimal. The generalized maximum likelihood distortion measure has been introduced, and has proven to be particularly efficient on short signal segments. In the case of an unknown number of segments, its estimate is obtained comparing the reduction of the distortion. The asymptotic properties of the distortion sequence have been analyzed, which led to the definition of the presented segmentation algorithm. The introduced measure can be applied both to the AR and ARMA models. The segmentation algorithm is verified on test signals as well as on the natural speech signal, for which the pitch synchronous framing scheme is applied. The experimental results also include a comparison of the AR and ARMA model-based segmentations. The first results show that ARMA model-based segmentation gives somewhat better results than the AR model algorithm.Research supported in part by the Mathematical Institute of the Serbian Science Academy and Serbian Science Foundation.     

Attenuation compensation of cone beam SPECT images using maximum likelihood reconstruction

Attenuation compensation for cone beam single-photon emission computed tomography (SPECT) imaging is performed by cone beam maximum likelihood reconstruction with attenuation included in the transition matrix. Since the transition matrix is too large to be stored in conventional computers, the E-M maximum likelihood estimator is implemented with a ray-tracing algorithm, efficiently recalculating each matrix element as needed. The method was applied and tested in both uniform and nonuniform density phantoms. Test projections sets were obtained from Monte Carlo simulations and experiments using a commercially available cone beam collimator. For representative regions of interest. reconstruction of a uniform sphere is accurate to within 3% throughout, in comparison to a reference image simulated and reconstructed without attenuation. High- and low-activity regions in a uniform density are reconstructed accurately, except that low-activity regions in a more active background have a small error. This error is explainable by the nonnegativity constraints of the E-M estimator and the image statistical noise     

Uniqueness of maximum likelihood estimators of the 2-parameterWeibull distribution

We present a simple statistic, calculated from either complete failure data or from right-censored data of type-I or -II. It is useful for understanding the behavior of the parameter maximum likelihood estimates (MLE) of a 2-parameter Weibull distribution. The statistic is based on the logarithms of the failure data and can be interpreted as a measure of variation in the data. This statistic provides: (a) simple lower bounds on the parameter MLE, and (b) a quick approximation for parameter estimates that can serve as starting points for iterative MLE routines; it can be used to show that the MLE for the 2-parameter Weibull distribution are unique     

On maximum likelihood estimation for the two parameter Weibull distribution

This paper examines recent results presented on maximum likelihood estimation for the two parameter Weibull distribution. In particular, we seek to explain some recently reported values for estimator bias when the data for analysis contains both times to failure and censored times in operation; our discussion centres on the generation of sample data sets. We conclude that, under appropriate conditions, estimators are asymptotically unbiased, with relatively low bias in small to moderate samples. We then present the results of some further experiments which suggest that the previously reported values for estimator bias can be attributed to the method of generating sample data sets in simulation experiments.     

Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies

The work presented evaluates the statistical characteristics of regional bias and expected error in reconstructions of real positron emission tomography (PET) data of human brain fluoro-deoxiglucose (FDG) studies carried out by the maximum likelihood estimator (MLE) method with a robust stopping rule, and compares them with the results of filtered backprojection (FBP) reconstructions and with the method of sieves. The task of evaluating radioisotope uptake in regions-of-interest (ROIs) is investigated. An assessment of bias and variance in uptake measurements is carried out with simulated data. Then, by using three different transition matrices with different degrees of accuracy and a components of variance model for statistical analysis, it is shown that the characteristics obtained from real human FDG brain data are consistent with the results of the simulation studies.     

Predictive source coding techniques using maximum likelihood prediction for compression of digitized images

A predictive compression technique is examined, using maximum likelihood prediction of the image pixel based on the Markov mesh model, that encodes the differences via Gordon block-bit-plane (GBBP) encoding. The procedure is very efficient in that it requires a bit rate near the entropy of the source. For images with many quantization levels, maximum likelihood prediction can be cumbersome to implement. Thus, a suboptimal procedure called differential bit-plane coding (DBPC) is investigated. This is easily implemented, even for a large number of quantization levels, and is reasonably efficient.     

Developments with maximum likelihood X-ray computed tomography

An approach to the maximum-likelihood estimation of attenuation coefficients in transmission tomography is presented as an extension of earlier theoretical work by K. Lange and R. Carson (J. Comput. Assist. Tomography, vol.8, p.306-16, 1984). The reconstruction algorithm is based on the expectation-maximization (EM) algorithm. Several simplifying approximations are introduced which make the maximization step of the algorithm available. Computer simulations are presented using noise-free and Poisson randomized projections. The images obtained with the EM-type method are compared to those reconstructed with the EM method of Lange and Carson and with filtered backprojection. Preliminary results show that there are potential advantages in using the maximum likelihood approaches in situations where a high-contrast object, such as bone, is embedded in low-contrast soft tissue.     

The use of maximum likelihood estimation for forming images ofdiffuse radar targets from delay-Doppler data

An approach to high-resolution imaging that starts with a model of the radar echo signal derived from the physics governing radar reflections is presented. The model has been used in the past to describe radar targets that are rough compared to the wavelength of the transmitted radiation. Without specifying precisely what the transmitted signal is, a general estimation-based procedure is derived for obtaining images. After discretizing the model, the radar imaging problem reduces to the task of estimating discretized second-order statistics of the reflectance process of the target. Maximum-likelihood estimates of these statics are obtained as the limit point of an expectation-maximization algorithm     

Accelerated penalized weighted least-squares and maximum likelihood algorithms for reconstructing transmission images from PET transmission data

We present penalized weighted least-squares (PWLS) and penalized maximum-likelihood (PML) methods for reconstructing transmission images from positron emission tomography transmission data. First, we view the problem of minimizing the weighted least-squares (WLS) and maximum likelihood objective functions as a sequence of nonnegative least-squares minimization problems. This viewpoint follows from using certain quadratic functions as surrogate functions for the WLS and maximum likelihood objective functions. Second, we construct surrogate functions for a class of penalty functions that yield closed form expressions for the iterates of the PWLS and PML algorithms. Due to the slow convergence of the PWLS and PML algorithms, accelerated versions of them are developed that are theoretically guaranteed to monotonically decrease their respective objective functions. In experiments using real phantom data, the PML images produced the most accurate attenuation correction factors. On the other hand, the PWLS images produced images with the highest levels of contrast for low-count data.     

Constrained maximum likelihood solution of linear equations

The total least squares (TLS) is used to solve a set of inconsistent linear equations Ax≈y when there are errors not only in the observations y but in the modeling matrix A as well. The TLS seeks the least squares perturbation of both y and A that leads to a consistent set of equations. When y and A have a defined structure, we usually want the perturbations to also have this structure. Unfortunately, standard TLS does not generally preserve the perturbation structure, so other methods are required. We examine this problem using a probabilistic framework and derive an approach to determining the most probable set of perturbations, given an a priori perturbation probability density function. While our approach is applicable to both Gaussian and non-Gaussian distributions, we show in the uncorrelated Gaussian case that our method is equivalent to several existing methods. Our approach is therefore more general and can be applied to a wider variety of signal processing problems     

Nonlinear maximum likelihood estimation of autoregressive timeseries

Describes an algorithm for finding the exact, nonlinear, maximum likelihood (ML) estimators for the parameters of an autoregressive time series. The authors demonstrate that the ML normal equations can be written as an interdependent set of cubic and quadratic equations in the AR polynomial coefficients. They present an algorithm that algebraically solves this set of nonlinear equations for low-order problems. For high-order problems, the authors describe iterative algorithms for obtaining a ML solution     

Automatic segmentation of color images with transitive closure

In this paper, a mask based automatic segmentation algorithm for color images which uses pixel similarity has been presented. Main concept of the algorithm relies on spatial mask for course segmentation and the Warshall's transitive closure (TC) computation algorithm for region merging. Although the proposed spatial mask approach reduces the computational burden required for segmentation or clustering techniques such as seeded region growing (SRG) or fuzzy c-means (FCM) in which user supplied parameters are essential, it has over segmentation drawback. Therefore, the transitive closure algorithm, which uses adjacency and similarity matrix associated to undirected graph of the over segmented image, has been employed to merge the regions. After comparing to existing methods, the obtained experimental results confirmed that the color images as well as gray level images could be segmented with considerable accuracy. Also computational complexity of image segmentation is significantly reduced. Furthermore, there is no need any user supplied parameter such as the number of clusters or seed points.     

Asymptotic results for maximum likelihood estimation with an arrayof sensors

In many cases, the maximum likelihood (ML) estimator is consistent and asymptotically normal with covariance equal to the inverse of the Fisher's information matrix. It does not follow, though, that the covariance of the ML estimator approaches the Cramer-Rao lower bound as the sample size increases. However, it is possible to draw such a conclusion for the adaptive array problem in which direction of arrival and signal magnitude are being estimated. Proofs of w-asymptotic efficiency, which comes with a convergence-of-moments condition, and strong consistency (almost-sure convergence) of the ML estimator are given. Strong consistency is also proved for a popular quasi-ML estimator     

Knowledge-based segmentation of Landsat images

A knowledge-based approach for Landsat image segmentation is proposed. The image segmentation problem is solved by extracting kernel information from the input image to provide an initial interpretation of the image and by using a knowledge-based hierarchical classifier to discriminate between major land-cover types in the study area. The proposed method is designed in such a way that a Landsat image can be segmented and interpreted without any prior image-dependent information. The general spectral land-cover knowledge is constructed from the training land-cover data, and the road information of an image is obtained through a road-detection program     

Intensity-based segmentation of microarray images

The underlying principle in microarray image analysis is that the spot intensity is a measure of the gene expression. This implicitly assumes the gene expression of a spot to be governed entirely by the distribution of the pixel intensities. Thus, a segmentation technique based on the distribution of the pixel intensities is appropriate for the current problem. In this paper, clustering-based segmentation is described to extract the target intensity of the spots. The approximate boundaries of the spots in the microarray are determined by manual adjustment of rectilinear grids. The distribution of the pixel intensity in a grid containing a spot is assumed to be the superposition of the foreground and the local background. The k-means clustering technique and the partitioning around medoids (PAM) were used to generate a binary partition of the pixel intensity distribution. The median (k-means) and the medoid (PAM) of the cluster members are chosen as the cluster representatives. The effectiveness of the clustering-based segmentation techniques was tested on publicly available arrays generated in a lipid metabolism experiment (Callow et al., 2000). The results are compared against those obtained using the region-growing approach (SPOT) (Yang et al., 2001). The effect of additive white Gaussian noise is also investigated.     

Optimal segmentation of cell images

An optimal segmentation algorithm for light microscopic cell images is presented. The image segmentation is performed by thresholding a parametric image approximating the original image. Using the mean squared error between the original and the constructed image as the cost function, the segmentation problem is transformed into an optimisation process where parametric parameters are determined that minimise the defined cost function. The cost function is iteratively minimised using an unsupervised learning rule to adjust the parameters, and a parametric image is constructed at each iteration, based on the obtained parameters. The cell region is extracted by thresholding the final parametric image, where the threshold is one of the image parameters. Application results to real cervical images are provided to show the performance of the proposed segmentation approach. Experimental segmentation results are presented for the proposed optimal algorithm for synthetic cell images corrupted by variant levels of noise; these results are compared with the K-means clustering method and Bayes classifier in terms of classification errors     

Application of maximum likelihood estimation to radar imaging

An efficient maximum likelihood (ML) estimator to obtain the scattering center locations of a target and the relative scattering level of these scattering centers from the scattered field data is described. In the proposed method, ML estimation is carried out in the image domain rather than in the frequency-aspect domain. A two-dimensional (2-D) inverse Fourier transform is used to transfer the scattered field data from frequency-aspect domain to the image domain (down-range/cross-range). As expected, the scattered field data in the image domain has some regions with high energy. The samples in the high-energy regions are used to obtain the initial guess for the ML estimator as well as for ML estimation. The ML estimator in the image domain is applied to both simulated and experimental scattered fields of some targets     

Threshold performance analysis of maximum likelihood DOA estimation

The purpose of this paper is to investigate the nonasymptotic behavior of the maximum likelihood method in the context of lacunar array processing. We derive an analytical expression of the maximum likelihood mean square error, which is now valid for all signal-to-noise ratio (SNR) ranges. We also provide an analysis of the SNR threshold phenomena, which allows us to derive closed-form formulas for the threshold values. Computer simulations confirm the validity of the theoretical investigations.