Maximum entropy methods in coherent radar imaging

There are some compelling reasons for viewing the problem of image reconstruction from noisy or incomplete data as one of statistical estimation, i.e., of choosing, from the infinity of images consistent with the data, that image which, in some statistical sense, is most plausible. Among these reasons are the soundness of the philosophical underpinning of the resulting image reconstruction process, a greater realization of the image resolution which is inherent in the data, and freedom from many of the artifacts encountered in commonly used ad hoc reconstruction schemes. One successful technique employing a principle of statistical inference is the maximum entropy technique, in which the data-consistent image with maximum configurational entropy is chosen. It is a computationally intensive approach involving a conjugate gradient search over a convex function of a vector in a space of dimensionality equal to the number of image pixels. This technique has been employed with success in situations where the data samples are modeled as linearly related to a real non-negative object. We investigate application of maximum entropy image reconstruction to the problem of high-resolution radar diagnostic imaging. The problem differs from others in which maximum entropy has been applied in that the object to be imaged is complex. Although the desired image is of the magnitude of the complex object and is thus real and non-negative, there is no linear relationship beween object magnitude and data. Rather, the data are linearly related to the complex object. Several earlier proposed methods for applying the maximum entropy principle to this problem are identified and analyzed. A method that more closely approximates true Bayesian estimation is proposed.     

High-resolution restoration of dynamic image sequences

We investigated an approach to reconstructing high-resolution images from dynamic image sequences using local spectral analysis. High-resolution reconstruction from linearly shifted multiple static image frames has previously been studied, in which the aliasing relationship between the spectrum of the original signal and the DFTs of shifted and sampled signals is exploited. In the high-resolution reconstruction of dynamic image sequences, difficulties occur as a result of nonuniform shifts in the frames. We use loca spectral analysis to achieve high-resolution reconstruction by overlapped block decomposition and motion compensation. For each block image in a reference frame in the sequence, motion estimation and subpixel registrations are performed against adjacent frames. High resolution reconstruction is performed on such motion-compensated block-image sequences. For some blocks containing motion boundaries, high resolution reconstruction is difficult; a new scene emerges or disappears producing inconsistent information. An interpolation technique is used in such blocks to generate the number of pixels consistent with other high-resolution blocks. The flower-garden image sequence is used for the computer simulations. The quality of the restored images are very encouraging; the aliasing effects in the original frames are significantly reduced and sharper edges are produced. The overall procedure to generate such higher-resolution images from a dynamic image sequence is described in detail. The result can be applied to various image sequence restoration applications including up-conversion of conventional video signals.©1994 John Wiley & Sons Inc     

3-D ultrasound volume reconstruction using the direct frame interpolation method

A new method for 3-D ultrasound volume reconstruction using tracked freehand 3-D ultrasound is proposed. The method is based on solving the forward volume reconstruction problem using direct interpolation of high-resolution ultrasound B-mode image frames. A series of ultrasound B-mode image frames (an image series) is acquired using the freehand scanning technique and position sensing via optical tracking equipment. The proposed algorithm creates additional intermediate image frames by directly interpolating between two or more adjacent image frames of the original image series. The target volume is filled using the original frames in combination with the additionally constructed frames. Compared with conventional volume reconstruction methods, no additional filling of empty voxels or holes within the volume is required, because the whole extent of the volume is defined by the arrangement of the original and the additionally constructed B-mode image frames. The proposed direct frame interpolation (DFI) method was tested on two different data sets acquired while scanning the head and neck region of different patients. The first data set consisted of eight B-mode 2-D frame sets acquired under optimal laboratory conditions. The second data set consisted of 73 image series acquired during a clinical study. Sample volumes were reconstructed for all 81 image series using the proposed DFI method with four different interpolation orders, as well as with the pixel nearest-neighbor method using three different interpolation neighborhoods. In addition, volumes based on a reduced number of image frames were reconstructed for comparison of the different methods' accuracy and robustness in reconstructing image data that lies between the original image frames. The DFI method is based on a forward approach making use of a priori information about the position and shape of the B-mode image frames (e.g., masking information) to optimize the reconstruction procedure and to reduce computation times and memory requirements. The method is straightforward, independent of additional input or parameters, and uses the high-resolution B-mode image frames instead of usually lower-resolution voxel information for interpolation. The DFI method can be considered as a valuable alternative to conventional 3-D ultrasound reconstruction methods based on pixel or voxel nearest-neighbor approaches, offering better quality and competitive reconstruction time.     

Experimental demonstration of the spectral interference between two linearly polarized modes at the output of a fibre waveguide excited by a low-coherence source

Abstract

The mutual interference of two linearly polarized (LP) modes in the frequency domain has been demonstrated experimentally at the output of a fibre waveguide excited by a low-coherence source when the optical path difference between both LP modes exceeds the coherence length of the source. The spectral interference between two LP modes, which shows up a periodic modulation of the source spectrum, serves as an illustration of the experimental verification of conclusions we have made in previous theoretical works. Consequently, the feasibility of a novel experimental method utilizing a high-resolution spectrometer in the evaluation of the group-delay time difference between both LP modes has been confirmed.     

基于多帧"差分"图像的分辨率提高算法

介绍了一种基于多帧"差分"图像重建高分辨率图像技术,并从CCD数字化采样能量的角度分析了多幅低分辨率的"差分"图像与高分辨率图像各像素灰度值的对应关系,给出了通过图像"差分"技术提高探测图像分辨率的倍数与所需CCD最少数目之间的一般规律.最后,采用Matlab软件以一幅黑白条纹均匀分布的图像作为目标物,模拟了图像"差分"技术的实现过程,仿真结果表明了该技术的可行性.     

Investigation of multi-frame image super-resolution based on adaptive self-learning methods

The goal of this paper is to introduce and demonstrate a new high-performance super-resolution (SR) method for multi-frame images. By combining learning-based and reconstruction-based SR methods, this paper proposes a multi-frame image super-resolution method based on adaptive self-learning. Using the adaptive self-learning method and recovery of high-frequency edge information, an initial high-resolution (HR) image containing effective texture information is obtained. The edge smoothness prior is then used to satisfy the global reconstruction constraint and enhance the quality of the HR image. Our results indicate that this method achieves better performance than several other methods for both simulated data and real-scene images.     

高分辨率SAR与光学图像融合的建筑物三维重建研究

分析了用于建筑物测量的高分辨率SAR叠掩及角反射器效应等成像要素,并将其与高分辨率快鸟卫星图像融合,实现了建筑物屋顶信息的提取。进一步利用SAR叠掩得到的建筑物高度信息和快鸟图像得到的建筑物屋顶信息实现了建筑物的三维重建。与实地测量数据相比较,计算结果精度较高,从而验证了这种三维重建方法的可行性。     

Blind multichannel reconstruction of high-resolution images using wavelet fusion

We developed an approach to the blind multichannel reconstruction of high-resolution images. This approach is based on breaking the image reconstruction problem into three consecutive steps: a blind multichannel restoration, a wavelet-based image fusion, and a maximum entropy image interpolation. The blind restoration step depends on estimating the two-dimensional (2-D) greatest common divisor (GCD) between each observation and a combinational image generated by a weighted averaging process of the available observations. The purpose of generating this combinational image is to get a new image with a higher signal-to-noise ratio and a blurring operator that is a coprime with all the blurring operators of the available observations. The 2-D GCD is then estimated between the new image and each observation, and thus the effect of noise on the estimation process is reduced. The multiple outputs of the restoration step are then applied to the image fusion step, which is based on wavelets. The objective of this step is to integrate the data obtained from each observation into a single image, which is then interpolated to give an enhanced resolution image. A maximum entropy algorithm is derived and used in interpolating the resulting image from the fusion step. Results show that the suggested blind image reconstruction approach succeeds in estimating a high-resolution image from noisy blurred observations in the case of relatively coprime unknown blurring operators. The required computation time of the suggested approach is moderate.     

一种改进的视频序列超分辨率重建算法及应用

在凸集优化基础上,充分利用最大后验概率和凸集投影技术,提出了一种高效强鲁棒性视频序列分辨率提升算法。首先,在空域设计一个简单的预处理共轭梯度估计器,预测原始高分辨率图像;然后,在小波域分别创建帧间和帧内两个不同的凸集,并实施不同的投影运算,提取出隐含在相邻低分辨率图像中的细节信息;最后,利用空域估计器中相邻因子间的关系约束凸集投影解的可行域,保证快速获得图像重建的唯一最优解。仿真实验和实际交通监测系统应用结果均表明,该方法较其他方法不仅可获得更高的峰值信噪比和更好的可视化效果,而且收敛更快,鲁棒性更强。     

Adaptive framework for robust high-resolution image reconstruction in multiplexed computational imaging architectures

In multiplexed computational imaging schemes, high-resolution images are reconstructed by fusing the information in multiple low-resolution images detected by a two-dimensional array of low-resolution image sensors. The reconstruction procedure assumes a mathematical model for the imaging process that could have generated the low-resolution observations from an unknown high-resolution image. In practical settings, the parameters of the mathematical imaging model are known only approximately and are typically estimated before the reconstruction procedure takes place. Violations to the assumed model, such as inaccurate knowledge of the field of view of the imagers, erroneous estimation of the model parameters, and/or accidental scene or environmental changes can be detrimental to the reconstruction quality, even if they are small in number. We present an adaptive algorithm for robust reconstruction of high-resolution images in multiplexed computational imaging architectures. Using robust M-estimators and incorporating a similarity measure, the proposed scheme adopts an adaptive estimation strategy that effectively deals with violations to the assumed imaging model. Comparisons with nonadaptive reconstruction techniques demonstrate the superior performance of the proposed algorithm in terms of reconstruction quality and robustness.     

Magnetic resonance scan‐time reduction using echo prediction

A linear prediction (LP) filter derived from a complete echo with zero‐phase encoding amplitude is used for recovering anatomical details from a partially acquired echo sequence. The LP filter is shown to reconstruct missing k‐space phase and amplitude information, with errors sufficiently low so as to provide image reconstruction with a contrast‐to‐noise ratio (CNR) ≥ 3. For volume imaging using multislice acquisition, the partial‐echo sequence enables more number of slices to be acquired for a given repetition time period T_R. For such sequences, separate predictors are used for reconstruction of missing k‐space data corresponding to each individual slice in the volume. The proposed filtering scheme is shown to achieve results comparable to other partial k‐space approaches such as singularity function analysis (SFA), when the noise content is less than about 0.4%. For higher noise levels, this technique is recommended as a preprocessing step for SFA to track the singularity locations more accurately. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 1–8, 2013     

Multiframe image super-resolution adapted with local spatial information

Super-resolution image reconstruction, which has been a hot research topic in recent years, is a process to reconstruct high-resolution images from shifted, low-resolution, degraded observations. Among the available reconstruction frameworks, the maximum a posteriori (MAP) model is widely used. However, existing methods usually employ a fixed prior item and regularization parameter for the entire HR image, ignoring local spatially adaptive properties, and the large computation load caused by the solution of the large-scale ill-posed problem is another issue to be noted. In this paper, a block-based local spatially adaptive reconstruction algorithm is proposed. To reduce the large computation load and realize the local spatially adaptive process of the prior model and regularization parameter, first the target image is divided into several same-sized blocks and the structure tensor is used to analyze the local spatial properties of each block. Different property prior items and regularization parameters are then applied adaptively to different properties' blocks. Experimental results show that the proposed method achieves better performance than methods with a fixed prior item and regularization parameter.     

High-resolution multiband polarization epithelial tissue imaging method by sparse representation and fusion

Multiband polarization epithelial tissue imaging is an effective tool to measure tissue's birefringence and structure for quantitative pathology analysis. To discriminate the pathology accurately, high-resolution multiband polarization images are essential. But it is difficult to acquire high-resolution polarization images because of the limitations of imaging systems. The polarization image calculation process can be regarded as image fusion with fixed rules, and multiband polarization images are intrinsically sparse. In this paper, we propose a novel high-resolution multiband polarization image calculation method by utilizing the sparse representation and image fusion method. The multiband images are first represented in the sparse domain and we further introduce total-variation-regularization terms into the sparse representation framework. Then, polarization parameter images are calculated by simultaneous fusion and reconstruction. Higher quality multiband polarization images can be obtained through additional regularization constraint in the fusion process. Extensive experiments validate that the proposed method achieves much better results than many state-of-the-art algorithms in terms of both peak signal-to-noise-ratio and visual perception.     

Robust MR image super-resolution reconstruction with cross-modal edge-preserving regularization

In this article, we propose a novel image super-resolution (SR) reconstruction method in the field of magnetic resonance imaging, which is based on a cross-modal edge-preserving regularization integrating the internal gradient prior from the target-modal image itself and the external gradient prior from the reference-modal image obtained by pre-scan in many medical imaging scenes. The reference-modal image is a high-resolution guidance image that has much shareable information such as gradient orientation on edge regions, which can be used to improve the image resolution of the target modal. In addition, to be robust against the misalignment between the target-modal image and reference-modal image, a multimodal registration is incorporated in the SR reconstruction process. In this work, the proposed SR method can be formulated as an alternating optimization problem, that is, the target-modal and reference-modal images are alternately updated through iterations. Experimental results on simulated and realistic images show the superior performance of the proposed approach over several state-of-the-art SR techniques.     

Accurate image reconstruction from few-view and limited-angle data in diffraction tomography

We present a method for obtaining accurate image reconstruction from highly sparse data in diffraction tomography (DT). A practical need exists for reconstruction from few-view and limited-angle data, as this can greatly reduce required scan times in DT. Our method does this by minimizing the total variation (TV) of the estimated image, subject to the constraint that the Fourier transform of the estimated image matches the measured Fourier data samples. Using simulation studies, we show that the TV-minimization algorithm allows accurate reconstruction in a variety of few-view and limited-angle situations in DT. Accurate image reconstruction is obtained from far fewer data samples than are required by common algorithms such as the filtered-backpropagation algorithm. Overall our results indicate that the TV-minimization algorithm can be successfully applied to DT image reconstruction under a variety of scan configurations and data conditions of practical significance.     

Reconstruction of a high-resolution image on a compound-eye image-capturing system

The authors have proposed an architecture for a compact image-capturing system called TOMBO (thin observation module by bound optics), which uses compound-eye imaging for a compact hardware configuration [Appl. Opt. 40, 1806 (2001)]. The captured compound image is decomposed into a set of unit images, then the pixels in the unit images are processed with digital processing to retrieve the target image. A new method for high-resolution image reconstruction, called a pixel rearrange method, is proposed. The relation between the target object and the captured signals is estimated and utilized to rearrange the original pixel information. Experimental results show the effectiveness of the proposed method. In the experimental TOMBO system, the resolution obtained is four times higher than that of the unit image that did not undergo reconstruction processing.     

Quantum-implementable selective reconstruction of high-resolution images

This paper, written for interdisciplinary audience, presents computational image reconstruction implementable by quantum optics. The input-triggered selection of a high-resolution image among many stored ones, and its reconstruction if the input is occluded or noisy, has been successfully simulated. The original algorithm, based on the Hopfield associative neural net, was transformed in order to enable its quantum-wave implementation based on holography. The main limitations of the classical Hopfield net are much reduced with the simulated new quantum-optical implementation.     

Depth extraction of three-dimensional objects using block matching for slice images in synthetic aperture integral imaging

We describe a computational method for depth extraction of three-dimensional (3D) objects using block matching for slice images in synthetic aperture integral imaging (SAII). SAII is capable of providing high-resolution 3D slice images for 3D objects because the picked-up elemental images are high-resolution ones. In the proposed method, the high-resolution elemental images are recorded by moving a camera; a computational reconstruction algorithm based on ray backprojection generates a set of 3D slice images from the recorded elemental images. To extract depth information of the 3D objects, we propose a new block-matching algorithm between a reference elemental image and a set of 3D slice images. The property of the slices images is that the focused areas are the right location for an object, whereas the blurred areas are considered to be empty space; thus, this can extract robust and accurate depth information of the 3D objects. To demonstrate our method, we carry out the preliminary experiments of 3D objects; the results indicate that our method is superior to a conventional method in terms of depth-map quality.     

Spatial analysis of time of flight-secondary ion mass spectrometric images by ordinary kriging and inverse distance weighted interpolation techniques

Ordinary kriging and inverse distance weighted (IDW) are two interpolation methods for spatial analysis of data and are commonly used to analyze macroscopic spatial data in the fields of remote sensing, geography, and geology. In this study, these two interpolation techniques were compared and used to analyze microscopic chemical images created from time of flight-secondary ion mass spectrometry images from a patterned polymer sample of fluorocarbon (C(x)F(y)) and poly(aminopropyl siloxane) (APS, a.k.a. siloxane). Data was eliminated from the original high-resolution data set by successive random removal, and the image file was interpolated and reconstructed with a random subset of points using both methods. The statistical validity of the reconstructed image was determined by both standard geographic information system (GIS) validation statistics and evaluating the resolution across an image boundary using ASTM depth and image resolution methodology. The results show that both ordinary kriging and IDW techniques can be used to accurately reconstruct an image using substantially fewer sample points than the original data set. Ordinary kriging performed better than the IDW technique, resulting in fewer errors in predicted intensities and greater retention of original image features. The size of the data set required for the most accurate reconstruction of the original image is directly related to the autocorrelation present within the data set. When 10% of the original siloxane data set was used for an ordinary kriging interpolation, the resulting image still retained the characteristic gridlike pattern. The C(x)F(y) data set exhibited stronger spatial correlation, resulting in reconstruction of the image with only 1% of the original data set. The removal of data points does result in a loss of image resolution; however, the resolution loss is not directly related to the percentage of sample points removed.     

Quadratic cost functional for wave-front reconstruction

A quadratic cost functional for reconstruction of a high-resolution wave front from a coarse wave front is presented. The functional uses as data the position and the direction of the coarse wave front that had previously been computed with a ray-tracing method. This functional uses an optical relationship between the ray information and the wave front's shape to reconstruct a high-density wave front. The performance of the proposed functional is illustrated by reconstruction of complicated wave fronts for which this functional has an accuracy that is superior to that of conventional interpolation methods.