Semi-Blind Sparse Image Reconstruction With Application to MRFM

We propose a solution to the image deconvolution problem where the convolution kernel or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the PSF uncertainty in a high-dimensional space. Unlike recent developments on blind deconvolution of natural images, we assume the image is sparse in the pixel basis, a natural sparsity arising in magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian Metropolis-within-Gibbs sampling framework. The performance of our Bayesian semi-blind algorithm for sparse images is superior to previously proposed semi-blind algorithms such as the alternating minimization algorithm and blind algorithms developed for natural images. We illustrate our myopic algorithm on real MRFM tobacco virus data.     

A comparison of deconvolution and windowed subtraction techniques for scatter compensation in SPECT

Three procedures for the removal of Compton-scattered data in SPECT by constrained deconvolution are presented. The first is a deconvolution of a 2-D measured PSRF containing scatter from a single reconstructed transaxial image; the second is a deconvolution of a 2-D measured point-source response function (PSRF) from each frame of projection data prior to reconstruction; the third involves deconvolution of a 3-D measured PSRF from a stack of reconstructed slices. Results of applying these procedures to data obtained from a phantom containing cold cylinders and to data from a cold spot-resolution phantom are presented and are shown to be superior to the results of correcting for scatter by scatter-window substraction. Both 3-D deconvolution from reconstructed images and 2-D deconvolution from projection data show major improvements in image contrast, resolution, and quantitation. Improvements are especially marked for small (1.0-3.0 cm) cold sources.     

Generalized Linear Mixed Models for Reliability Analysis of Multi-Copy Repairable Systems

The power law process (PLP) is usually applied to failure data from a single repairable system. When a system has a number of copies for analysis, the usual approach is to assume homogeneity among all system copies, and then to pool data from these copies. In the real world, however, it may be more reasonable to assume heterogeneity among the system copies. Therefore, this paper proposes a new generalized linear mixed model (GLMM), called PLP-GLMM, to analyse failure data from multi-copy repairable systems. In the PLP-GLMM, the underlying model for each system copy is assumed to be a PLP at Stage 1, and parameters vary among copies at Stage 2. The PLP-GLMM can make inferences about both the population, and each system copy when accounting for copy-to-copy variance. A modified Anderson-Darling test is adapted to the goodness-of-fit test of the PLP-GLMM. A numerical application is given to show the effectiveness of the model     

On the efficient prediction of fractal signals

A novel prediction scheme for self-affine fractal signals is presented. The signal is modeled by self-affine linear mappings, whose contraction factors are assumed to follow an auto-regressive (AR) process. In this way, the highly nonlinear time evolution of the fractal signal is captured by the linear AR process of the contraction factors, thereby exploiting the simplicity and ease of computation inherent in the AR model. An adaptive version of the proposed scheme is applied in simulations using the Weierstrass-Mandelbrot cosine fractal, as well as, in practice, using real radar sea clutter data     

基于FGG NUFFT的穿墙成像雷达快速BP算法

针对穿墙成像雷达后向投影(Back Projection,BP)算法存在计算复杂度较高、内存需求较大等问题,本文提出了一种基于快速高斯网格化的非均匀快速傅里叶变换(Fast Gaussian Gridding Nonuniform Fast Fourier Transform,FGG NUFFT)成像算法,该算法能够有效加速BP算法。对经过联合熵值法抑制墙体杂波后得到的目标回波数据,首先将BP算法中像素点幅值与高斯核函数反卷积消除高斯平滑的影响,然后对均匀数据进行快速傅里叶变换,最后对得到的数据进行卷积运算实现对数据均匀平滑输出。该方法预先划分网格并存储系数,避免了重复运算。通过对基于时域有限差分法(Finite Different-Time Domain,FDTD)的仿真软件GprMax2D/3D所获得的穿墙雷达数据进行处理,仿真实验证明该方法在保证成像质量的情况下,有效降低计算复杂度与内存需求。     

Estimating fractal dimension with fractal interpolation functionmodels

Fractal dimension (FD) is a feature which is widely used to characterize medical images. Previously, researchers have shown that FD separates important classes of images and provides distinctive information about texture. The authors analyze limitations of two principal methods of estimating FD: box-counting (BC) and power spectrum (PS). BC is ineffective when applied to data-limited, low-resolution images; PS is based on a fractional Brownian motion (fBm) model-a model which is not universally applicable. The authors also present background information on the use of fractal interpolation function (FIF) models to estimate FD of data which can be represented in the form of a function. They present a new method of estimating FD in which multiple FIF models are constructed. The mean of the FD's of the FIF models is taken as the estimate of the FD of the original data. The standard deviation of the FD's of the FIF models is used as a confidence measure of the estimate. The authors demonstrate how the new method can be used to characterize fractal texture of medical images. In a pilot study, they generated plots of curvature values around the perimeters of images of red blood cells from normal and sickle cell subjects. The new method showed improved separation of the image classes when compared to BC and PS methods     

A Power Differentiation Method of Fractal Dimension Estimation for 2-D Signals

Fractal dimension has been used for texture analysis as it is highly correlated with the human perception of surface roughness. Several methods have been proposed for the estimation of the fractal dimension of an image. One of the most popular is via its power spectrum density, provided that it is modeled as a fractional Brownian function. In this paper, a new method, called the power differentiation method (PDM), for estimating the fractal dimension of a two-variable signal from its power spectrum density is presented. The method is first applied to noise-free data of known fractal dimension. It is also tested with noise-corrupted and quantized data. Particularly, in the case of noise-corrupted data, the modified power differentiation method (MPDM) is developed, resulting in more accurate estimation of the fractal dimension. The results obtained by the PDM and the MPDM are compared directly to those obtained using four other well-known methods of fractal dimension. Finally, preliminary results for the classification of ultrasonic liver images, obtained by applying the new method, are presented.     

Deconvolution filter design for fractal signal transmissionsystems: a multiscale Kalman filter bank approach

A deconvolution filtering design is proposed for the 1/f fractal signal transmission systems, with its design philosophy being based on multiscale Kalman deconvolution filter bank equipped in the analysis/synthesis wavelet filter bank, The role of wavelet transformation for 1/f fractal signal process is exploited as a multiscale whitening filter for removing the properties of self-similarity and long-range dependence from the fractal signals     

Electromagnetic scattering calculated from pair distributionfunctions retrieved from planar snow sections

Electromagnetic wave scattering in dense media, such as snow, depends on the three-dimensional (3D) pair distribution function of particle positions. In snow, two-dimensional (2D) stereological data can be obtained by analyzing planar sections. In this paper the authors calculate the volume 3D pair distribution functions from the 2D stereological data by solving Hanisch's integral equation. They first use Monte Carlo simulations for multisize particles to verify the procedure. Next they apply the procedure to available planar snow sections. A log-normal distribution of particle sizes is assumed for the ice grains in snow. To derive multisize pair functions, a least squares fit is used to recover pair functions for particles with sufficient number density and the hole correction approximation is assumed for the larger particles. A family of 3D pair distribution functions are derived. These are then substituted into dense media scattering theory to calculate scattering. It is found that the computed scattering rates are comparable to those calculated under the Percus-Yevick approximation of pair distribution functions of multiple sizes     

A novel approach to the 2-D blind deconvolution problem in medical ultrasound

The finite frequency bandwidth of ultrasound transducers and the nonnegligible width of transmitted acoustic beams are the most significant factors that limit the resolution of medical ultrasound imaging. Consequently, in order to recover diagnostically important image details, obscured due to the resolution limitations, an image restoration procedure should be applied. The present study addresses the problem of ultrasound image restoration by means of the blind-deconvolution techniques. Given an acquired ultrasound image, algorithms of this kind perform either concurrent or successive estimation of the point-spread function (PSF) of the imaging system and the original image. In this paper, a blind-deconvolution algorithm is proposed, in which the PSF is recovered as a preliminary stage of the restoration problem. As the accuracy of this estimation affects all the following stages of the image restoration, it is considered as the most fundamental and important problem. The contribution of the present study is twofold. First, it introduces a novel approach to the problem of estimating the PSF, which is based on a generalization of several fundamental concepts of the homomorphic deconvolution. It is shown that a useful estimate of the spectrum of the PSF can be obtained by applying a proper smoothing operator to both log-magnitude and phase of the spectra of acquired radio-frequency (RF) images. It is demonstrated that the proposed approach performs considerably better than the existing homomorphic (cepstrum-based) deconvolution methods. Second, the study shows that given a reliable estimate of the PSF, it is possible to deconvolve it out of the RF-image and obtain an estimate of the true tissue reflectivity function, which is relatively independent of the properties of the imaging system. The deconvolution was performed using the maximum a-posteriori (MAP) estimation framework for a number of statistical priors assumed for the reflectivity function. It is shown in a series of in vivo experiments that reconstructions based on the priors, which tend to emphasize the "sparseness" of the tissue structure, result in solutions of higher resolution and contrast.     

基于两维解卷积和稀疏回波去噪的高分辨雷达成像方法

该文提出了一种结合稀疏低秩矩阵恢复技术以及基于匹配滤波结果的反卷积算法的高分辨率雷达成像方法。对雷达回波信号进行匹配滤波操作可以最大化回波信噪比,通过推导发现经过匹配滤波操作后的回波信号可以建模为两维卷积的形式,对该结果做维纳滤波解卷积可以获得较高的分辨率。然而典型的解卷积算法面临着病态性问题,该问题会放大解卷积后的噪声、限制解卷积后的成像分辨率。文中证明了在目标稀疏分布的先验下,经过匹配滤波后的回波矩阵满足稀疏低秩的特性。在这种情况下,利用回波矩阵的稀疏低秩矩阵特征可以进一步提高信噪比,以减轻解卷积的病态性问题以及点扩散函数的平滑卷积造成目标散射低分辨率的影响。仿真实验以及实测数据证明了所提方法的有效性。      

H<Subscript>∞</Subscript> Deconvolution Filters for Stochastic Systems with Interval Uncertainties

This paper is concerned with the robust H_∞ deconvolution filtering problem for continuous- and discrete-time stochastic systems with interval uncertainties. The matrices of the system describing the signal transmissions are assumed to be uncertain within given intervals, and the stochastic perturbation is in the form of multiplicative Gaussian white noise with constant variance. The purpose of the addressed problem is to design a robust H_∞ deconvolution filter such that the input signal distorted by the transmission channel could recover to a specified extent γ. By using stochastic analysis techniques and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the asymptotical stability of the filtering error system. Then the filter parameters are characterized in terms of the solution to linear matrix inequalities, which can be easily solved by using available software packages. Two simulation examples are exploited to demonstrate the effectiveness of the proposed design procedures, respectively, for continuous- and discrete-time systems.     

Multichannel seismic deconvolution

Deals with Bayesian estimation of 2D stratified structures from echosounding signals. This problem is of interest in seismic exploration, but also for nondestructive testing or medical imaging. The proposed approach consists of a multichannel Bayesian deconvolution method of the 2D reflectivity based upon a theoretically sound prior stochastic model. The Markov-Bernoulli random field representation introduced by Idier et al. (1993) is used to model the geometric properties of the reflectivity, and emphasis is placed on representation of the amplitudes and on deconvolution algorithms. It is shown that the algorithmic structure and computational complexity of the proposed multichannel methods are similar to those of single-channel B-G deconvolution procedures, but that explicit modeling of the stratified structure results in significantly better performances. Simulation results and examples of real-data processing illustrate the performances and the practicality of the multichannel approach     

A new method for optimal deconvolution

Using an innovation analysis method in the time domain, the problem of optimal input estimation is considered, Two algorithms for calculating optimal deconvolution estimators are presented. A new tool for obtaining the estimators is described. It is based on the projection method and innovation theory. The approach covers input prediction, filtering, and smoothing problems. The solution is also applied to unstable linear systems, disturbances, or input models     

Assessment of perfusion by dynamic contrast-enhanced imaging using a deconvolution approach based on regression and singular value decomposition

The assessment of tissue perfusion by dynamic contrast-enhanced (DCE) imaging involves a deconvolution process. For analysis of DCE imaging data, we implemented a regression approach to select appropriate regularization parameters for deconvolution using the standard and generalized singular value decomposition methods. Monte Carlo simulation experiments were carried out to study the performance and to compare with other existing methods used for deconvolution analysis of DCE imaging data. The present approach is found to be robust and reliable at the levels of noise commonly encountered in DCE imaging, and for different models of the underlying tissue vasculature. The advantages of the present method, as compared with previous methods, include its efficiency of computation, ability to achieve adequate regularization to reproduce less noisy solutions, and that it does not require prior knowledge of the noise condition. The proposed method is applied on actual patient study cases with brain tumors and ischemic stroke, to illustrate its applicability as a clinical tool for diagnosis and assessment of treatment response.     

Optimal Cross-Layer Scheduling of Transmissions Over a Fading Multiaccess Channel

We consider the problem of several users transmitting packets to a base station, and study an optimal scheduling formulation involving three communication layers, namely, the medium access control, link, and physical layers. We assume Markov models for the packet arrival processes and the channel gain processes. Perfect channel state information is assumed to be available at the transmitter and the receiver. The transmissions are subject to a long-run average transmitter power constraint. The control problem is to assign power and rate dynamically as a function of the fading and the queue lengths so as to minimize a weighted sum of long run average packet transmission delays.     

Optimal and self-tuning deconvolution in time domain

This paper is concerned with both the optimal (minimum mean square error variance) and self-tuning deconvolution problems for discrete-time systems. When the signal model, measurement model, and noise statistics are known, a novel approach for the design of the optimal deconvolution filter, predictor, and smoother is proposed based on projection theory and innovation analysis in the time domain. The estimators are given in terms of an autoregressive moving average (ARMA) innovation model and one unilateral linear polynomial equation, where the ARMA innovation model is obtained by performing one spectral factorization. A self-tuning scheme can be incorporated when the noise statistics, the input model, and/or colored noise model are unknown. The self-tuning estimator is designed by identifying two ARMA innovation models