TRIO a technique for reconstruction using intensity order: application to undersampled MRI

Long acquisition times are still a limitation for many applications of magnetic resonance imaging (MRI), specially in 3-D and dynamic imaging. Several undersampling reconstruction techniques have been proposed to overcome this problem. These techniques are based on acquiring less samples than specified by the Nyquist criterion and estimating the nonacquired data by using some sort of prior information. Most of these reconstruction methods use prior information based on estimations of the pixel intensities of the images and therefore they are prone to introduce spatial or temporal blurring. Instead of using the pixel intensities, we propose to use information that allows us to sort the pixels of an image from darkest to brightest. The set of order relations which sort the pixels of an image has been called intensity order. The intensity order of an image can be estimated from low-resolution images, adjacent slices in volumetric acquisitions, temporal correlation in dynamic sequences or from prior reconstructions. Our technique for reconstruction using intensity order (TRIO) consists of looking for an image that satisfies the intensity order and minimizes the discrepancy between the acquired and reconstructed data. Results show that TRIO can effectively reconstruct 2-D-cine cardiac MR images (under-sampling factor of 4), estimating correctly the temporal evolution of the objects. Furthermore, TRIO is used as a second stage reconstruction after reconstructing with other techniques, keyhole, sliding window and k-t BLAST, to estimate the order information. In all cases the images are improved by TRIO.     

J-substitution algorithm in magnetic resonance electrical impedance tomography (MREIT): phantom experiments for static resistivity images

Recently, a new static resistivity image reconstruction algorithm is proposed utilizing internal current density data obtained by magnetic resonance current density imaging technique. This new imaging method is called magnetic resonance electrical impedance tomography (MREIT). The derivation and performance of J-substitution algorithm in MREIT have been reported as a new accurate and high-resolution static impedance imaging technique via computer simulation methods. In this paper, we present experimental procedures, denoising techniques, and image reconstructions using a 0.3-tesla (T) experimental MREIT system and saline phantoms. MREIT using J-substitution algorithm effectively utilizes the internal current density information resolving the problem inherent in a conventional EIT, that is, the low sensitivity of boundary measurements to any changes of internal tissue resistivity values. Resistivity images of saline phantoms show an accuracy of 6.8%-47.2% and spatial resolution of 64 x 64. Both of them can be significantly improved by using an MRI system with a better signal-to-noise ratio.     

Feature-directed spiral coding of magnetic resonance images

The authors investigate the encoding of magnetic resonance (MR) images of the human body using various lossless techniques, and presents a new form of spiral encoding. The algorithm used relies partially on the overall shape of the bounding contour of the image in achieving the compression and uses a traditional run-based technique combined with an adaptive Huffman coder to encode the complete image. Comparisons are made between the feature-directed spiral encoding and the traditional paths; the latter include the scanning pattern associated with the normal raster scanned display and the path for a display that could be used in following a linearised quadtree encoding. The new method tracks the `greater' contour of the overall image and, once the path has been established and tuples recorded, the inner contours are automatically generated. The process is repeated for each of the inner contours with a reducing radius towards the centre. The results are given for the various techniques in terms of compression ratios. The new spiralling method achieves an approximate 5.29% saving over the traditional techniques and also gives structure to the compressed image     

Algebraic reconstruction for magnetic resonance imaging underB0 inhomogeneity

In magnetic resonance imaging, spatial localization is usually achieved using Fourier encoding which is realized by applying a magnetic field gradient along the dimension of interest to create a linear correspondence between the resonance frequency and spatial location following the Larmor equation. In the presence of B₀ inhomogeneities along this dimension, the linear mapping does not hold and spatial distortions arise in the acquired images. In this paper, the problem of image reconstruction under an inhomogeneous field is formulated as an inverse problem of a linear Fredholm equation of the first kind. The operators in these problems are estimated using field mapping and the k-space trajectory of the imaging sequence. Since such inverse problems are known to be ill-posed in general, robust solvers, singular value decomposition and conjugate gradient method, are employed to obtain corrected images that are optimal in the Frobenius norm sense. Based on this formulation, the choice of the imaging sequence for well-conditioned matrix operators is discussed, and it is shown that nonlinear k-space trajectories provide better results. The reconstruction technique is applied to sequences where the distortion is more severe along one of the image dimensions and the two-dimensional reconstruction problem becomes equivalent to a set of independent one-dimensional problems. Experimental results demonstrate the performance and stability of the algebraic reconstruction methods     

High-resolution NMR chemical-shift imaging with reconstruction by the chirp z-transform

A study of a novel nuclear magnetic resonance (NMR) chemical-shift image reconstruction method with a high chemical-shift resolution achieved by the chirp z-transform (CZT) is presented. Phase encoding is used for the spatial coordinates x and y, and the frequency coordinate is reserved especially for the chemical shift. The Fourier transform (FT) image reconstruction algorithm, which forms the basis of the new CZT image reconstruction method, is introduced. The novel method, using the CZT instead of the FT to evaluate the chemical-shift spectrum at a much higher resolution, is studied. The chemical-shift resolutions, achieved by the FT and the CZT, are studied theoretically from the aspect of the peak height and the peak width of chemical-shift spectra. The chemical-shift spectra calculated at a selected point in the image plane, and the chemical shift-images reconstructed by this method, are shown for a simple phantom containing ethanol and methanol at different locations. The results obtained by this method and by the FT method are compared and discussed. The experimental results have shown that a chemical-shift as small as 39 Hz, relative to the proton resonance frequency of 21.34 MHz, can be resolved successfully by this method without improvements in magnetic field homogeneity.     

On the choice of Compressed Sensing priors and sparsifying transforms for MR image reconstruction: An experimental study

Recently Compressed Sensing (CS) based techniques are being used for reconstructing magnetic resonance (MR) images from partially sampled k-space data. CS based reconstruction techniques can be categorized into three categories based on the objective function: (i) synthesis prior, (ii) analysis prior and (iii) mixed (analysis+synthesis) prior. Each of these can be further subdivided into convex and non-convex forms. There is also a wide choice available for the sparsifying transforms, viz. Daubechies wavelets (orthogonal and redundant), fractional spline wavelet (orthogonal), complex dualtree wavelet (redundant), contourlet (redundant) and finite difference (redundant). Previous studies in MR image reconstruction have used a various combinations of objective functions (priors) and sparsifying transforms; and each of these studies claimed the superiority of their method over others. In this work, we will review and evaluate the popular MR image reconstruction techniques and show that analysis prior with complex dualtree wavelets yields the best reconstruction results. We have evaluated our experimental results on real data. The metric for quantitative evaluation is the Normalized Mean Squared Error. Our qualitative evaluation is based both on the reconstructed and the difference images.The other significant contribution of this paper is the development of convex and non-convex versions of synthesis, analysis and mixed prior algorithms from a uniform majorization-minimization framework. The algorithms are compared with a state-of-the-art CS based techniques; the proposed ones have better reconstruction accuracy and are only fractionally slow. The algorithms that are derived in this paper are all efficient first order algorithms that are easy to implement.     

Estimating Motion From MRI Data

Magnetic resonance imaging (MRI) is an ideal imaging modality to measure blood flow and tissue motion. It provides excellent contrast between soft tissues, and images can be acquired at positions and orientations freely defined by the user. From a temporal sequence of MR images, boundaries and edges of tissues can be tracked by image processing techniques. Additionally, MRI permits the source of the image signal to be manipulated. For example, temporary magnetic tags displaying a pattern of variable brightness may be placed in the object using MR saturation techniques, giving the user a known pattern to detect for motion tracking. The MRI signal is a modulated complex quantity, being derived from a rotating magnetic field in the form of an induced current. Well-defined patterns can also be introduced into the phase of the magnetization, and could be thought of as generalized tags. If the phase of each pixel is preserved during image reconstruction, relative phase shifts can be used to directly encode displacement, velocity and acceleration. New methods for modeling motion fields from MRI have now found application in cardiovascular and other soft tissue imaging. In this review, we shall describe the methods used for encoding, imaging, and modeling motion fields with MRI.     

一种新的边界增强型图像先验模型

在各种超分辨率图像重构算法中，最大后验概率（Maxlmum a Posteriori，MAP）算法因其具有优异的重构性能而受到广泛关注。但由于目前在MAP算法中普遍采用的是平滑型图像先验模型，导致重构出来的图像边界不明锐，一些细节不清晰。本文提出了一种新的边界增强型图像先验模型。不同于已有的图像模型，新模型对图像中的非连续性不是进行惩罚，而是进行增强。实验结果表明，新模型能够获得优于平滑型图像先验模型的重构效果。     

一种基于L_∞范式的求解已知旋转相机重建算法

基于多幅图像序列的三维重建过程中,相机模型的坐标统一是非常重要的基础。在已知两两相机之间的相对关系的情况下,将相机模型统一至同一世界坐标系,并恢复特征点的三维坐标。本文给出了一种基于L∞范式的求解已知旋转相机重建方法。给出了一种基于L∞范式的几何结构和运动问题的新框架,并用实验证明了算法能够达到很好的性能。     

A fast and efficient hybrid fractal-wavelet image coder.

The excellent visual quality and compression rate of fractal image coding have limited applications due to exhaustive inherent encoding time. This paper presents a new fast and efficient image coder that applies the speed of the wavelet transform to the image quality of the fractal compression. Fast fractal encoding using Fisher's domain classification is applied to the lowpass subband of wavelet transformed image and a modified set partitioning in hierarchical trees (SPIHT) coding, on the remaining coefficients. Furthermore, image details and wavelet progressive transmission characteristics are maintained, no blocking effects from fractal techniques are introduced, and the encoding fidelity problem common in fractal-wavelet hybrid coders is solved. The proposed scheme promotes an average of 94% reduction in encoding-decoding time comparing to the pure accelerated Fractal coding results. The simulations also compare the results to the SPIHT wavelet coding. In both cases, the new scheme improves the subjective quality of pictures for high-medium-low bitrates.     

单次曝光频域振幅编码压缩成像

超分辨率被认为是光学成像和图像处理的“圣杯”之一.有别于传统的多幅亚像素图像配准融合实现超分辨率的方法面临的配准误差以及高成本问题,得益于大多数图像普遍具有的稀疏表示特性,本文将压缩传感理论引入超分辨率成像,提出一种新的单次曝光频域振幅编码压缩成像方法.利用4-f傅里叶光学架构实现图像信息的频域0/1振幅随机调制,然后可以使用低分辨率CCD器件实现积分下采样记录对应的测量值,最后利用优化方法从少量的测量值中重建原高分辨率图像.模拟实验验证了本文提出的方法可以有效地实现二维图像信息的获取与重构.此外,本文的方法可以有效地处理大尺寸图像的压缩成像问题,具有重要的应用前景.     

Image Reconstruction in a Wide Aspect Ratio HDTV System

One of the important characteristics of a high-definition television (HDTV) image is a wide aspect ratio. In some HDTV systems the image is segmented and different formats are used to transmit portions of the image. We address the problem of image reconstruction at the receiver and present an analysis of a wide aspect ratio HDTV system. Several image reconstruction techniques are described, including a channel-dependent design, and their effectiveness discussed. We also present a channel-independent system for image reconstruction that utilizes a vertical interval test line. Performance has been evaluated, via computer simulation, using still images. The results indicate an imperceptible amount of artifacts at the edge-center joints with an overlap as small as one picture element for the channel-independent reconstruction technique.     

Conjugate phase MRI reconstruction with spatially variant sample density correction

A new image reconstruction method to correct for the effects of magnetic field inhomogeneity in non-Cartesian sampled magnetic resonance imaging (MRI) is proposed. The conjugate phase reconstruction method, which corrects for phase accumulation due to applied gradients and magnetic field inhomogeneity, has been commonly used for this case. This can lead to incomplete correction, in part, due to the presence of gradients in the field inhomogeneity function. Based on local distortions to the k-space trajectory from these gradients, a spatially variant sample density compensation function is introduced as part of the conjugate phase reconstruction. This method was applied to both simulated and experimental spiral imaging data and shown to produce more accurate image reconstructions. Two approaches for fast implementation that allow the use of fast Fourier transforms are also described. The proposed method is shown to produce fast and accurate image reconstructions for spiral sampled MRI.     

Ultrasonic transmission tomography in refracting media: reduction of refraction artifacts by curved-ray techniques

The present work concerns the problem of refraction artifacts in ultrasonic transmission tomography. The reconstruction is improved by curved-ray methods, combined with algebraic reconstruction techniques. The problem of acoustic ray tracing and image interpolation has been carefully studied, and different reconstruction algorithms have been developed and compared. The effect of the geometrical characteristics of the set-up and the studied medium characteristics (geometry and acoustical properties) on the reconstruction accuracy are considered. Some simulation results are presented which show an encouraging reduction of the refraction artifacts. The results have been confirmed by experiments carried out with agar-gel phantoms. The experimental device and procedure are described and straight- and curved-ray reconstructions are shown. Reconstruction quality can be improved significantly for refractive index variations of up to 10%, which seems sufficient for soft tissue imaging; yet there are some limiting factors, such as multipath propagation, if any, or the difficulty of choosing an initial value for the reconstruction.     

Speed-up in fractal image coding: comparison of methods

Fractal image compression has received much attention from the research community because of some desirable properties like resolution independence, fast decoding, and very competitive rate-distortion curves. Despite the advances made, the long computing times in the encoding phase still remain the main drawback of this technique. So far, several methods have been proposed in order to speed-up fractal image coding. We address the problem of choosing the best speed-up techniques for fractal image coding, comparing some of the most effective classification and feature vector methods-namely Fisher (1994), Hurtgen (1993), and Saupe (1995, 1996)-and a new feature vector coding scheme based on the block's mass center. Furthermore, we introduce two new coding schemes combining Saupe with Fisher, and Saupe with mass center coding scheme. Experimental results demonstrate both the superiority of feature vector techniques on classification and the effectiveness of combining Saupe and the mass center coding scheme, an approach that exhibits the best time-distortion curves.     

Ultra fast symmetry and SIMD-based projection-backprojection (SSP) algorithm for 3-D PET image reconstruction

Remarkable progress in positron emission tomography (PET) development has occurred in recent years, in hardware, software, and computer implementation of image reconstruction. Recent development in PET scanners such as the high-resolution research tomograph (HRRT) developed by CTI (now Siemens) represents such a case and is capable of greatly enhanced resolution as well as sensitivity. In these PET scanners, the amount of coincidence line data collected contains more than 4.5 x 10(9) coincidence lines of response generated by as many nuclear detectors as 120 000. This formidable amount of data and the reconstruction of this data set pose a real problem in HRRT and have also been of the major bottle neck in further developments of high resolution PET scanners as well as their applications. In these classes of PET scanners, therefore, obtaining one set of reconstructed images often requires many hours of image reconstruction. For example, in HRRT with full data collection in a normal brain scan (using SPAN 3), the image reconstruction time is close to 80 min, making it practically impossible to attempt any list-mode-based dynamic imaging since the image reconstruction time would take many days (as much as 43 h or more for 32-frame dynamic image reconstruction). To remedy this data-handling problem in image reconstruction, we developed a new algorithm based on the symmetry properties of the projection and backprojection processes, especially in the 3-D OSEM algorithm where multiples of projection and back-projection are required. In addition, the single-instruction multiple-data (SIMD) technique also allowed us to successfully incorporate the symmetry properties mentioned above, thereby effectively reducing the total image reconstruction time to a few minutes. We refer to this technique as the symmetry and SIMD-based projection-backprojection (SSP) technique or algorithm and the details of the technique will be discussed and an example of the application of the technique to the HRRT's OSEM algorithm will be presented as a demonstration.     

Compression of facial images using the K-SVD algorithm

The use of sparse representations in signal and image processing is gradually increasing in the past several years. Obtaining an overcomplete dictionary from a set of signals allows us to represent them as a sparse linear combination of dictionary atoms. Pursuit algorithms are then used for signal decomposition. A recent work introduced the K-SVD algorithm, which is a novel method for training overcomplete dictionaries that lead to sparse signal representation. In this work we propose a new method for compressing facial images, based on the K-SVD algorithm. We train K-SVD dictionaries for predefined image patches, and compress each new image according to these dictionaries. The encoding is based on sparse coding of each image patch using the relevant trained dictionary, and the decoding is a simple reconstruction of the patches by linear combination of atoms. An essential pre-process stage for this method is an image alignment procedure, where several facial features are detected and geometrically warped into a canonical spatial location. We present this new method, analyze its results and compare it to several competing compression techniques.     

Linear inverse problems in imaging

Classical techniques for solving linear inverse problems have been presented. Our aim was to show how these classical techniques are applied in current state-of-the-art imaging systems. Moreover, we have provided a classification of the techniques into four families: FT-based, direct reconstruction, indirect reconstruction, and interpolation. We hope that this classification will guide the curious reader into a discipline with a rich bibliography and sometimes sophisticated mathematics. In this survey, we skipped complicated methods to solve inverse problems. Through our examples, we have tried to emphasize the large variety of applications of linear inverse problems in imaging. Two main examples have been examined more deeply in this survey. We hope they have helped the reader to understand the application of the general techniques in two interesting contexts: multispectral imaging and magnetic resonance imaging.     

A unified approach to statistical tomography using coordinatedescent optimization

Over the past years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms take an indirect approach based on the expectation maximization (EM) algorithm. We propose a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion. The key to this direct optimization approach is greedy pixel-wise computations known as iterative coordinate decent (ICD). We propose a novel method for computing the ICD updates, which we call ICD/Newton-Raphson. We show that ICD/Newton-Raphson requires approximately the same amount of computation per iteration as EM-based approaches, but the new method converges much more rapidly (in our experiments, typically five to ten iterations). Other advantages of the ICD/Newton-Raphson method are that it is easily applied to MAP estimation of transmission tomograms, and typical convex constraints, such as positivity, are easily incorporated.     

Electromagnetic brain mapping

There has been tremendous advances in our ability to produce images of human brain function. Applications of functional brain imaging extend from improving our understanding of the basic mechanisms of cognitive processes to better characterization of pathologies that impair normal function. Magnetoencephalography (MEG) and electroencephalography (EEG) (MEG/EEG) localize neural electrical activity using noninvasive measurements of external electromagnetic signals. Among the available functional imaging techniques, MEG and EEG uniquely have temporal resolutions below 100 ms. This temporal precision allows us to explore the timing of basic neural processes at the level of cell assemblies. MEG/EEG source localization draws on a wide range of signal processing techniques including digital filtering, three-dimensional image analysis, array signal processing, image modeling and reconstruction, and, blind source separation and phase synchrony estimation. We describe the underlying models currently used in MEG/EEG source estimation and describe the various signal processing steps required to compute these sources. In particular we describe methods for computing the forward fields for known source distributions and parametric and imaging-based approaches to the inverse problem