Advances in Calibration and Imaging Techniques in Radio Interferometry

This paper summarizes some of the major calibration and image reconstruction techniques used in radio interferometry and describes them in a common mathematical framework. The use of this framework has a number of benefits, ranging from clarification of the fundamentals, use of standard numerical optimization techniques, and generalization or specialization to new algorithms.     

Convergent incremental optimization transfer algorithms: application to tomography

No convergent ordered subsets (OS) type image reconstruction algorithms for transmission tomography have been proposed to date. In contrast, in emission tomography, there are two known families of convergent OS algorithms: methods that use relaxation parameters, and methods based on the incremental expectation-maximization (EM) approach. This paper generalizes the incremental EM approach by introducing a general framework, "incremental optimization transfer." The proposed algorithms accelerate convergence speeds and ensure global convergence without requiring relaxation parameters. The general optimization transfer framework allows the use of a very broad family of surrogate functions, enabling the development of new algorithms. This paper provides the first convergent OS-type algorithm for (nonconcave) penalized-likelihood (PL) transmission image reconstruction by using separable paraboloidal surrogates (SPS) which yield closed-form maximization steps. We found it is very effective to achieve fast convergence rates by starting with an OS algorithm with a large number of subsets and switching to the new "transmission incremental optimization transfer (TRIOT)" algorithm. Results show that TRIOT is faster in increasing the PL objective than nonincremental ordinary SPS and even OS-SPS yet is convergent.     

Measurement of a Three－dimensional Gas Temperature Field with Holographic Interferometry

ＭｅａｓｕｒｅｍｅｎｔｏｆａＴｈｒｅｅ－ｄｉｍｅｎｓｉｏｎａｌＧａｓＴｅｍｐｅｒａｔｕｒｅＦｉｅｌｄｗｉｔｈＨｏｌｏｇｒａｐｈｉｃＩｎｔｅｒｆｅｒｏｍｅｔｒｙ￥ＣＨＥＮＳｈａｏｈｕａ（ＹｉｂｉｎＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，Ｙｉｂｉｎ６４４００７...     

Image restoration in astronomy: a Bayesian perspective

When preparing an article on image restoration in astronomy, it is obvious that some topics have to be dropped to keep the work at reasonable length. We have decided to concentrate on image and noise models and on the algorithms to find the restoration. Topics like parameter estimation and stopping rules are also commented on. We start by describing the Bayesian paradigm and then proceed to study the noise and blur models used by the astronomical community. Then the prior models used to restore astronomical images are examined. We describe the algorithms used to find the restoration for the most common combinations of degradation and image models. Then we comment on important issues such as acceleration of algorithms, stopping rules, and parameter estimation. We also comment on the huge amount of information available to, and made available by, the astronomical community     

相似图像块逼近的人脸超分重建残差补偿框架

为了提高人脸图像超分辨率重建算法中残差补偿步骤的效果,提出一种通用的基于内容相似图像块线性组合逼近的残差补偿框架,不经过搜索步骤,使用训练集人脸图像同一内容的图像块来进行运算。所提框架中的全局重建步骤,可以使用不同的重建方法。实验结果表明,在这种框架下的残差补偿方法,相比经典的邻域嵌入残差补偿方法,可以更好地恢复出初步重建的人脸图像细节信息。因为这是一种通用的残差补偿方法,从而可以推测凡使用邻域残差补偿的算法,均可借助本算法框架将重建结果进一步的提升。     

Microwave holographic interferometry

Microwave holography is an extension of the optical holography to the microwave field. In fact, by using a well-known characteristic of the holographic process, it is possible to record the hologram at frequencies very far from the optical region (microwave) and to reconstruct a visible image by laser light. This paper describes the experimental apparatus and the technique used for obtaining a satisfactory optical wave reconstruction from microwave holograms. The resolving power of the system which was experimentally tested, and visible images of microwave transparencies and of a back scattering object are given. As an alternative application of the microwave holography together with the optical wave reconstruction, in this paper, extension of holographic interferometry to the microwave region is suggested, and the visible image of a deformed object crossed by fringes due to microwave interference is also shown. This technique can find applications, for instance, in the mapping of the earth's deformations or in that of the tides. Different aspects of the microwave holographic interferometry have been also discussed.     

Correlation estimation from compressed images

This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where the images are represented under the form of linear measurements due to low complexity sensing or security requirements. We assume that the images are correlated through the displacement of visual objects due to motion or viewpoint change and the correlation is effectively represented by optical flow or motion field models. The correlation is estimated in the compressed domain by jointly processing the linear measurements. We first show that the correlated images can be efficiently related using a linear operator. Using this linear relationship we then describe the dependencies between images in the compressed domain. We further cast a regularized optimization problem where the correlation is estimated in order to satisfy both data consistency and motion smoothness objectives with a Graph Cut algorithm. We analyze in detail the correlation estimation performance and quantify the penalty due to image compression. Extensive experiments in stereo and video imaging applications show that our novel solution stays competitive with methods that implement complex image reconstruction steps prior to correlation estimation. We finally use the estimated correlation in a novel joint image reconstruction scheme that is based on an optimization problem with sparsity priors on the reconstructed images. Additional experiments show that our correlation estimation algorithm leads to an effective reconstruction of pairs of images in distributed image coding schemes that outperform independent reconstruction algorithms by 2–4 dB.     

Penalized maximum-likelihood image reconstruction usingspace-alternating generalized EM algorithms

Most expectation-maximization (EM) type algorithms for penalized maximum-likelihood image reconstruction converge slowly, particularly when one incorporates additive background effects such as scatter, random coincidences, dark current, or cosmic radiation. In addition, regularizing smoothness penalties (or priors) introduce parameter coupling, rendering intractable the M-steps of most EM-type algorithms. This paper presents space-alternating generalized EM (SAGE) algorithms for image reconstruction, which update the parameters sequentially using a sequence of small "hidden" data spaces, rather than simultaneously using one large complete-data space. The sequential update decouples the M-step, so the maximization can typically be performed analytically. We introduce new hidden-data spaces that are less informative than the conventional complete-data space for Poisson data and that yield significant improvements in convergence rate. This acceleration is due to statistical considerations, not numerical overrelaxation methods, so monotonic increases in the objective function are guaranteed. We provide a general global convergence proof for SAGE methods with nonnegativity constraints.     

A nonlinear least square technique for simultaneous image registration and super-resolution.

This paper proposes a new algorithm to integrate image registration into image super-resolution (SR). Image SR is a process to reconstruct a high-resolution (HR) image by fusing multiple low-resolution (LR) images. A critical step in image SR is accurate registration of the LR images or, in other words, effective estimation of motion parameters. Conventional SR algorithms assume either the estimated motion parameters by existing registration methods to be error-free or the motion parameters are known a priori. This assumption, however, is impractical in many applications, as most existing registration algorithms still experience various degrees of errors, and the motion parameters among the LR images are generally unknown a priori. In view of this, this paper presents a new framework that performs simultaneous image registration and HR image reconstruction. As opposed to other current methods that treat image registration and HR reconstruction as disjoint processes, the new framework enables image registration and HR reconstruction to be estimated simultaneously and improved progressively. Further, unlike most algorithms that focus on the translational motion model, the proposed method adopts a more generic motion model that includes both translation as well as rotation. An iterative scheme is developed to solve the arising nonlinear least squares problem. Experimental results show that the proposed method is effective in performing image registration and SR for simulated as well as real-life images.     

Restoration of blurred star field images by maximally sparseoptimization

The problem of removing blur from, or sharpening, astronomical star field intensity images is discussed. An approach to image restoration that recovers image detail using a constrained optimization theoretic approach is introduced. Ideal star images may be modeled as a few point sources in a uniform background. It is argued that a direct measure of image sparseness is the appropriate optimization criterion for deconvolving the image blurring function. A sparseness criterion based on the l(p) is presented, and candidate algorithms for solving the ensuing nonlinear constrained optimization problem are presented and reviewed. Synthetic and actual star image reconstruction examples are presented to demonstrate the method's superior performance as compared with several image deconvolution methods.     

白光干涉法三维面型重构仿真研究

采用Twyman光路结构和LED为光源进行白光干涉三维测量,对干涉图像及元件面型的重构算法进行了仿真研究。使用Matlab软件,选取了两种面型结构函数,仿真得出重构的面型,选取5个参考点进行了对比。研究结果表明,白光干涉测量具有高精度、测量时间短、相对误差小于0.5%。     

Single-slice rebinning reconstruction in spiral cone-beam computed tomography

At the advent of multislice computed tomography ICT) a variety of approximate cone-beam algorithms have been proposed suited for reconstruction of small cone-angle CT data in a spiral mode of operation. The goal of this study is to identify a practical and efficient approximate cone-beam method, extend its potential for medical use, and demonstrate its performance at medium cone-angles required for area detector CT. We will investigate two different approximate single-slice rebinning algorithms for cone-beam CT: the multirow Fourier reconstruction (MFR) and an extension of the advanced single-slice rebinning method (ASSR), which combines the idea of ASSR with a z-filtering approach. Thus, both algorithms, MFR and ASSR, are formulated in the framework of z-filtering using optimized spiral interpolation algorithms. In each view, X-ray samples to be used for reconstruction are identified, which describe an approximation to a virtual reconstruction plane. The performance of approximate reconstruction should improve as the virtual reconstruction plane better fits the spiral focus path. The image quality of the respective reconstruction will be assessed with respect to image artifacts, spatial resolution, contrast resolution, and image noise. It turns out that the ASSR method using tilted reconstruction planes is a practical and efficient algorithm, providing image quality comparable to that of a single-row scanning system even with a 46-row detector at a table feed of 64 mm. Both algorithms tolerate any table feed below the maximum value associated to the detector height. Due to the z-filter approach, all detector data sampled can be used for image reconstruction.     

Parallel MR image reconstruction using augmented Lagrangian methods

Magnetic resonance image (MRI) reconstruction using SENSitivity Encoding (SENSE) requires regularization to suppress noise and aliasing effects. Edge-preserving and sparsity-based regularization criteria can improve image quality, but they demand computation-intensive nonlinear optimization. In this paper, we present novel methods for regularized MRI reconstruction from undersampled sensitivity encoded data--SENSE-reconstruction--using the augmented Lagrangian (AL) framework for solving large-scale constrained optimization problems. We first formulate regularized SENSE-reconstruction as an unconstrained optimization task and then convert it to a set of (equivalent) constrained problems using variable splitting. We then attack these constrained versions in an AL framework using an alternating minimization method, leading to algorithms that can be implemented easily. The proposed methods are applicable to a general class of regularizers that includes popular edge-preserving (e.g., total-variation) and sparsity-promoting (e.g., l(1)-norm of wavelet coefficients) criteria and combinations thereof. Numerical experiments with synthetic and in vivo human data illustrate that the proposed AL algorithms converge faster than both general-purpose optimization algorithms such as nonlinear conjugate gradient (NCG) and state-of-the-art MFISTA.     

会聚光横向剪切移相干涉

为了检测长光程情况或多组分光学镜头逐片装校中的波面,提出一种以会聚光波直接作为干涉测试光源的会聚光移相剪切干涉方法,阐述了基于迈克耳孙干涉仪原理的会聚光横向剪切干涉光路,建立了会聚光横向剪切波面的数学表达式,并与一般横向剪切干涉相比较,分析了剪切量和波面偏移量的特征,且引入移相干涉技术求取剪切波面.结果表明,会聚光横向剪切移相干涉测试,能够实时测试会聚光的波面质量,峰谷值(PV)的重复性为0.022λ,均方根(RMS)值的重复性为0.014λ,并与Zygo干涉仪的测量结果进行了对比,验证会聚光剪切移相干涉的可行性.     

Estimation in Gaussian Graphical Models Using Tractable Subgraphs: A Walk-Sum Analysis

Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure. These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as embedded trees, serial iterations such as block Gauss-Seidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walk-sum interpretation of Gaussian inference. We describe the walks ldquocomputedrdquo by the algorithms using walk-sum diagrams, and show that for iterations based on a very large and flexible set of sequences of subgraphs, convergence is guaranteed in walk-summable models. Consequently, we are free to choose spanning trees and subsets of variables adaptively at each iteration. This leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error. Simulation results demonstrate that these nonstationary algorithms provide a significant speedup in convergence over traditional one-tree and two-tree iterations.     

Arbitrary resizing of images in DCT space

Using the spatial relationship of the block discrete cosine transform (DCT) coefficients and subband approximations, algorithms for image halving and doubling operations are presented. The computational steps identified in the process provide a general framework for image resizing operations. Some of the previously reported image halving and doubling algorithms are shown to be special cases. The proposed approach is general enough to accommodate resizing operations with arbitrary factors, namely with integral and rational factors. The application of these methods to the conversion in the compressed domain of images (video frames) from one format to another is demonstrated.     

Radio Astronomy in the Early Twenty-First Century

This paper serves as an introduction to the contributions in this Special Issue on ldquoAdvances in Radio Telescopes.rdquo After a very short historical view of the emergence of Radio Astronomy, we refer to earlier IEEE special issues on this subject and mention recent instruments in the domain of millimeter wavelength radio telescopes, developments in very long baseline interferometry and the planned Square Kilometre Array (SKA). After a short discussion of site selection aspects for the new telescopes we conclude with a summary of the major astronomical and astrophysical problems which will be studied by the new instruments described in the following papers.     

Iterative tomographic image reconstruction using Fourier-based forward and back-projectors

Iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems, especially in emission tomography. With the fast increase of the sizes of the tomographic data, reduction of the computation demands of the reconstruction algorithms is of great importance. Fourier-based forward and back-projection methods have the potential to considerably reduce the computation time in iterative reconstruction. Additional substantial speed-up of those approaches can be obtained utilizing powerful and cheap off-the-shelf fast Fourier transform (FFT) processing hardware. The Fourier reconstruction approaches are based on the relationship between the Fourier transform of the image and Fourier transformation of the parallel-ray projections. The critical two steps are the estimations of the samples of the projection transform, on the central section through the origin of Fourier space, from the samples of the transform of the image, and vice versa for back-projection. Interpolation errors are a limitation of Fourier-based reconstruction methods. We have applied min-max optimized Kaiser-Bessel interpolation within the nonuniform FFT (NUFFT) framework and devised ways of incorporation of resolution models into the Fourier-based iterative approaches. Numerical and computer simulation results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic forward and back-projection than conventional interpolation methods. Our studies have further confirmed that Fourier-based projectors using the NUFFT approach provide accurate approximations to their space-based counterparts but with about ten times faster computation, and that they are viable candidates for fast iterative image reconstruction.