Maximum likelihood estimation of 2-D superimposed exponentialsignals

The problem of maximum likelihood estimation of the parameters (i.e. frequencies, amplitudes, and noise variance) of 2-D superimposed exponential signals is considered. In this paper, a polynomial rooting approach is proposed to obtain the estimates of the 2-D frequencies. Strong consistency and limiting distribution are established for the estimates of the parameters. Furthermore, the covariance matrix of the limiting distribution attains the Cramer-Rao lower bound     

Maximum likelihood estimation and MUSIC in array localization signal processing: A review

Algorithms to treat the maximum likelihood (ML) estimation problem in array localization signal processing are reviewed, including the alternating projection method, the iterative quadratic maximum likelihood method and the expectation-maximization method. The relationship of ML estimators and the MUSIC algorithm is presented. The Cramer-Rao bounds for the deterministic and stochastic models in array localization are summarized. Finally, the problem of the estimation of the number of sources is discussed.     

Scalability of 2-D wavelet transform algorithms: analytical and experimental results on MPPs

This paper studies the scalability of two-dimensional (2-D) discrete wavelet transform (DWT) algorithms on massively parallel processors (MPPs). The principal operation in the 2-D DWT is the filtering operation used to implement the filter banks of the 2-D subband decomposition. This filtering operation can be implemented as a convolution in the time domain or as a multiplication in the frequency domain. We demonstrate that there exist combinations of machine size, image size, and wavelet kernel size for which the time-domain algorithms outperform the frequency domain algorithms and vice-versa. We therefore demonstrate that a hybrid approach that combines time- and frequency-domain approaches can yield linear scalability for a broad range of problem and machine sizes. Furthermore, we show the effect of processor speed versus communication overhead and the use of separable versus nonseparable wavelets on the crossover points between the algorithm approaches.     

Maximum likelihood localization of sources in noise modeled as astable process

This paper introduces a new class of robust beamformers which perform optimally over a wide range of non-Gaussian additive noise environments. The maximum likelihood approach is used to estimate the bearing of multiple sources from a set of snapshots when the additive interference is impulsive in nature. The analysis is based on the assumption that the additive noise can be modeled as a complex symmetric α-stable (SαS) process. Transform-based approximations of the likelihood estimation are used for the general SαS class of distributions while the exact probability density function is used for the Cauchy case. It is shown that the Cauchy beamformer greatly outperforms the Gaussian beamformer in a wide variety of non-Gaussian noise environments, and performs comparably to the Gaussian beamformer when the additive noise is Gaussian. The Cramer-Rao bound for the estimation error variance is derived for the Cauchy case, and the robustness of the SαS beamformers in a wide range of impulsive interference environments is demonstrated via simulation experiments     

Maximum likelihood parameter estimation of F-ARIMA processes using the genetic algorithm in the frequency domain

This work aims to treat the parameter estimation problem for fractional-integrated autoregressive moving average (F-ARIMA) processes under external noise. Unlike the conventional approaches from the perspective of the time domain, a maximum likelihood (ML) method is developed in the frequency domain since the power spectrum of an F-ARIMA process is in a very explicit and more simple form. However, maximization of the likelihood function is a highly nonlinear estimation problem. Conventional searching algorithms are likely to converge to local maxima under this situation. Since the genetic algorithm (GA) tends to find the globally optimal solution without being trapped at local maxima, an estimation scheme based on the GA is therefore developed to solve the ML parameter estimation problem for F-ARIMA processes from the frequency domain perspective. In the parameter estimation procedure, stability of the F-ARIMA model is ensured, and convergence to the global optimum of the likelihood function is also guaranteed. Finally, several simulation examples are presented to illustrate the proposed estimation algorithm and exhibit its performance.     

Controllability and reachability of 2-D positive systems: a graph theoretic approach

When dealing with two-dimensional (2-D) discrete state-space models, controllability properties are introduced in two different forms: a local form, which refers to single local states, and a global form, which instead pertains the infinite set of local states lying on a separation set. In this paper, these concepts are investigated in the context of 2-D positive systems by means of a graph theoretic approach. For all these properties, necessary and sufficient conditions, which refer to the structure of the digraph, are provided. While the global reachability index is bounded by the system dimension n, the local reachability index may far exceed the system dimension. Upper bounds on the local reachability index for some special classes of positive systems are finally derived.     

Wavelet-based multifractal analysis of 1-D and 2-D signals: New results

During the past decade, new tools stemming from fractal geometry and wavelet analysis are meeting with great success in signal image processing. This paper will focus on these two topics: Wavelets and Multifractal. Both themes evolved towards self contained theories, and yet, a host of reasons justify for coupling them in same applications. It is well known that both analyses share the same conceptual backbone of “scale”: it is the “mathematical zoom” commonly associated to wavelet analysis and it is the “scaling laws” that underlie multifractal structures. Very naturally then, wavelets stood as a privileged tool for analyzing and characterizing multifractal signals and images. Hence, the purpose of this paper is to illuminate some of the issue involved in taking advantage of the current advances in wavelets and multifractals analysis. We discuss continuous, discrete, orthogonal wavelets and present applications to fracture processes and medical ultrasound imaging.     

List-mode likelihood: EM algorithm and image quality estimationdemonstrated on 2-D PET

Using a theory of list-mode maximum-likelihood (ML) source reconstruction presented recently by Barrett et al. (1997), this paper formulates a corresponding expectation-maximization (EM) algorithm, as well as a method for estimating noise properties at the ML estimate. List-mode ML is of interest in cases where the dimensionality of the measurement space impedes a binning of the measurement data. It can be advantageous in cases where a better forward model can be obtained by including more measurement coordinates provided by a given detector. Different figures of merit for the detector performance can be computed from the Fisher information matrix (FIM). This paper uses the observed FIM, which requires a single data set, thus, avoiding costly ensemble statistics. The proposed techniques are demonstrated for an idealized two-dimensional (2-D) positron emission tomography (PET) [2-D PET] detector. The authors compute from simulation data the improved image quality obtained by including the time of flight of the coincident quanta     

Maximum likelihood estimation of the K factor in Ricean fading channels

Estimation of the K factor in a Ricean fading channel is studied. Unlike most previous estimators which employ exclusively samples of the fading envelope, new maximum likelihood estimators that use samples of both the fading envelope and the fading phase, or samples of the fading phase only, are derived and examined. Simulation results show that these estimators have good performances when operating in a Ricean fading channel, and in some cases outperform envelope-sample-based estimators.     

Maximum likelihood positioning in the scintillation camera using depth of interaction

Specific effects of the depth of interaction (DOI) on the photomultiplier (PM) response in an Auger gamma camera were quantified. The method was implemented and tested on a Monte Carlo simulator with special care to the noise modeling. Two models were developed, one considering only the geometric aspects of the camera and used for comparison, and one describing a more realistic camera environment. In a typical camera configuration and 140-keV photons, the DOI alone can account for a 6.4-mm discrepancy in position and 12% in energy between two scintillations. Variation of the DOI can still bring additional distortions when photons do not enter the crystal perpendicularly such as in slant hole, cone beam and other focusing collimators. With a 0.95-cm crystal and a 30 degrees slant angle, the obliquity factor can be responsible for a 5.5-mm variation in the event position. Results indicate that both geometrical and stochastic effects of the DOI are definitely reducing the camera performances and should be included in the image formation process.     

Application of 2-D Hilbert transform in geophysical imaging withpotential field data

The relationship between two-dimensional (2-D) Hilbert transforms and three-dimensional (3-D) potential field data (gravity and magnetic) is reviewed and applied to quantitative interpretation of magnetic and gravity anomalies as well as their derivatives. The vertical and horizontal derivatives of potential field anomalies due to multiprism models were used to test the 2-D Hilbert transform algorithms and their application. The gravity and magnetic contour maps of the Sudbury area, Canada, were digitized and Hilbert-transformed to be correlated with satellite digital images and with the previously known geology. The results indicate that the 2-D Hilbert transform technique can, in a robust fashion, be utilized for the extrapolation of geological boundaries through overburdened areas and subsequently provide a mathematical tool for a step-by-step integration of potential field data and geological remote sensing     

Detection and elimination of 2-D transmission error patterns inDPCM images

The paper studies two methods for detecting and removing channel error patterns in images transmitted by two-dimensional differential-pulse-code-modulation (2-D DCM) with fixed-length words. The methods are based on statistical classification and filtering procedures. For the predictions A+(C-B)/2 and A+(D-B)/2 in combination with 4-b DPCM, it is demonstrated experimentally by computer simulation that the effect of channel errors can effectively be reduced at bit-error rates (BERs) up to approximately 0.1%     

Maximum likelihood soft decoding of binary block codes and decodersfor the Golay codes

Maximum-likelihood soft-decision decoding of linear block codes is addressed. A binary multiple-check generalization of the Wagner rule is presented, and two methods for its implementation, one of which resembles the suboptimal Forney-Chase algorithms, are described. Besides efficient soft decoding of small codes, the generalized rule enables utilization of subspaces of a wide variety, thereby yielding maximum-likelihood decoders with substantially reduced computational complexity for some larger binary codes. More sophisticated choice and exploitation of the structure of both a subspace and the coset representatives are demonstrated for the (24, 12) Golay code, yielding a computational gain factor of about 2 with respect to previous methods. A ternary single-check version of the Wagner rule is applied for efficient soft decoding of the (12, 6) ternary Golay code     

Maximum likelihood estimation of the Burr XII parameters with censored and uncensored data

This paper presents the methodology for obtaining point and interval estimates of the parameters of the Burr Type XII distribution with multiple-censored and singly-censored data (Type I censoring or Type II censoring) as well as complete data, using the maximum likelihood method. The basis is the likelihood expression for multiple-censored data. The other types of censoring and complete data are treated as special cases. A FORTRAN language program was used. Some illustrative examples are included.     

变换域窄带干扰抑制技术中变换基的选取研究

基于变换域窄带干扰抑制技术的基本思路,研究了几种常用变换基的性质及其对典型窄带干扰形式的识别能力。通过仿真对比了典型窄带干扰在各变换域的谱型,并以CV系数作为标准对各变换基窄带干扰抑制能力进行了比较。仿真结果表明,重叠变换对于单音、窄带等平稳干扰信号的识别能力较优,而对扫频干扰这种非平稳干扰类型,则更适合在分数阶傅里叶变换域进行检测和识别。     

New results in 2-D systems theory, part II: 2-D state-space models—Realization and the notions of controllability, observability, and minimality

In this part, a comparison between the different state-space models is presented. We discuss proper definitions of state, controllability and observability and their relations to minimality of 2-D systems. We also present new circuit realizations and 2-D digital filter hardware implementation of 2-D transfer functions.     

Formulation of the Fourier transform in the spectral domain technique

A way to formulate the transform in spectral domain technique is presented.     

Exact reduced-complexity maximum likelihood reconstruction of multiple 3-D objects from unlabeled unoriented 2-D projections and electron microscopy of viruses.

In cryo-electron microscopy, the data is comprised of noisy 2-D projection images of the 3-D electron scattering intensity of the object where the orientation of the projections is unknown. Often, the images show randomly selected objects from a mixture of different types of objects. Objects of different type may be unrelated, e.g., different species of virus, or related, e.g., different conformations of the same species of virus. Due to the low SNR and the 2-D nature of the data, it is challenging to determine the type of the object shown in an individual image. A statistical model and maximum likelihood estimator that computes simultaneous 3-D reconstruction and labels using an expectation maximization algorithm exists but requires extensive computation due to the numerical evaluation of 3-D or 5-D integrations of a square matrix of dimension equal to the number of degrees of freedom in the 3-D reconstruction. By exploiting the geometry of rotations in 3-D, the estimation problem can be transformed so that the inner-most numerical integral has a scalar rather than a matrix integrand. This leads to a dramatic reduction in computation, especially as the number of degrees of freedom in the 3-D reconstruction increases. Numerical examples of the 3-D reconstructions are provided based on synthetic and experimental images where the objects are small spherical viruses.