Superresolution reconstruction using nonlinear gradient-based regularization

This paper discusses the problem of superresolution reconstruction. To preserve edges accurately and efficiently in the reconstruction, we propose a nonlinear gradient-based regularization that uses the gradient vector field of a preliminary high resolution image to configure a regularization matrix and compute the regularization parameters. Compared with other existing methods, it not only enhances the spatial resolution of the resulting images, but can also preserve edges and smooth noise to a greater extent. The advantages are shown in simulations and experiments with synthetic and real images.

Edge-preserving tomographic reconstruction with nonlocal regularization

Tomographic image reconstruction using statistical methods can provide more accurate system modeling, statistical models, and physical constraints than the conventional filtered backprojection (FBP) method. Because of the ill posedness of the reconstruction problem, a roughness penalty is often imposed on the solution to control noise. To avoid smoothing of edges, which are important image attributes, various edge-preserving regularization methods have been proposed. Most of these schemes rely on information from local neighborhoods to determine the presence of edges. In this paper, we propose a cost function that incorporates nonlocal boundary information into the regularization method. We use an alternating minimization algorithm with deterministic annealing to minimize the proposed cost function, jointly estimating region boundaries and object pixel values. We apply variational techniques implemented using level-sets methods to update the boundary estimates; then, using the most recent boundary estimate, we minimize a space-variant quadratic cost function to update the image estimate. For the positron emission tomography transmission reconstruction application, we compare the bias-variance tradeoff of this method with that of a "conventional" penalized-likelihood algorithm with local Huber roughness penalty.     

基于小波基的压缩感知重构算法设计

针对传统重构理论下对硬件设备的高要求和高损耗问题,提出基于小波基的压缩感知重构算法,利用小波变换在图像压缩重构上的优势,选取合适的小波基作为稀疏基,对一维信号和二维图像采用正交匹配追踪(OMP)算法,进行信号的压缩和重构,并对算法进行相应的改进。实验表明,压缩感知理论用于数字信号和数字图像处理有着显著的优势。     

Super resolution image reconstruction through bregman iteration using morphologic regularization

Multiscale morphological operators are studied extensively in the literature for image processing and feature extraction purposes. In this paper, we model a nonlinear regularization method based on multiscale morphology for edge-preserving super resolution (SR) image reconstruction. We formulate SR image reconstruction as a deblurring problem and then solve the inverse problem using Bregman iterations. The proposed algorithm can suppress inherent noise generated during low-resolution image formation as well as during SR image estimation efficiently. Experimental results show the effectiveness of the proposed regularization and reconstruction method for SR image.     

Dynamic texture description using adapted bipolar-invariant and blurred features

Multidimensional Systems and Signal Processing - Encoding turbulent properties of dynamic textures (DTs) is a challenging issue of video understanding for various applications in computer vision....     

Diagonal preconditioners for the EFIE using a wavelet basis

The electric field integral equation (EFIE) has found widespread use and in practice has been accepted as a stable method. However, mathematically, the solution of the EFIE is an “ill-posed” problem. In practical terms, as one uses more and more expansion and testing functions per wavelength, the condition number of the resulting moment-method matrix increases (without bound). This means that for high-sampling densities, iterative methods such as conjugate gradients converge more slowly. However, there is a way to change all this. The EFIE is considered using a wavelet basis for expansion and for testing functions. Then, the resulting matrix is multiplied on both sides by a diagonal matrix. This results in a well-conditioned matrix which behaves much like the matrix for the magnetic field integral equation (MFIE). Consequences for the stability and convergence rate of iterative methods are described     

Image reconstruction using the wavelet transform for positronemission tomography

We conducted positron emission tomography (PET) image reconstruction experiments using the wavelet transform. The Wavelet-Vaguelette decomposition was used as a framework from which expressions for the necessary wavelet coefficients might be derived, and then the wavelet shrinkage was applied to the wavelet coefficients for the reconstruction (WVS). The performances of WVS were evaluated and compared with those of the filtered back-projection (FBP) using software phantoms, physical phantoms, and human PET studies. The results demonstrated that WVS gave stable reconstruction over the range of shrinkage parameters and provided better noise and spatial resolution characteristics than FBP.     

Multilayer perceptron trained using radial basis functions

An algebraic equation for the training of a multilayer perceptron using radial basis functions is derived. Examples using this technique for the training of a network for the exclusive-OR and related problems are presented. Suggestions on the choice of the number of centres are given.<>     

Computation of optical flow using basis functions

The issues governing the computation of optical flow in image sequences are addressed. The trade-off between accuracy versus computation cost is shown to be dependent on the redundancy of the image representation. This dependency is highlighted by reformulating Horn's (1986) algorithm, making explicit use of the approximations to the continuous basis functions underlying the discrete representation. The computation cost of estimating optical flow, for a fixed error tolerance, is shown to be a minimum for images resampled at twice the Nyquist rate. The issues of derivative calculation and multiresolution representation are also briefly discussed in terms of basis functions and information encoding. A multiresolution basis function formulation of Horn's algorithm is shown to lead to large improvements in dealing with high frequencies and large displacements.     

Evaluation of data reconstruction using Walsh functions

The reconstruction of a finite-length record taken from a band-limited stochastic process is described. An integral mean-square-error criterion is used to compare the reconstruction using Walsh functions, a zero-order hold, and the sampling function (sin x)/x.     

Efficient framework for model-based tomographic image reconstruction using wavelet packets

The use of model-based algorithms in tomographic imaging offers many advantages over analytical inversion methods. However, the relatively high computational complexity of model-based approaches often restricts their efficient implementation. In practice, many modern imaging modalities, such as computed-tomography, positron-emission tomography, or optoacoustic tomography, normally use a very large number of pixels/voxels for image reconstruction. Consequently, the size of the forward-model matrix hinders the use of many inversion algorithms. In this paper, we present a new framework for model-based tomographic reconstructions, which is based on a wavelet-packet representation of the imaged object and the acquired projection data. The frequency localization property of the wavelet-packet base leads to an approximately separable model matrix, for which reconstruction at each spatial frequency band is independent and requires only a fraction of the projection data. Thus, the large model matrix is effectively separated into a set of smaller matrices, facilitating the use of inversion schemes whose complexity is highly nonlinear with respect to matrix size. The performance of the new methodology is demonstrated for the case of 2-D optoacoustic tomography for both numerically generated and experimental data.     

Time-domain full-band method using orthogonal edge basis functions

A new time-domain numerical approach for two-dimensional vectorial wave equation solutions based on slow wave variation is presented. The algorithm incorporates finite-element discretization and uses orthogonal edge basis functions to describe pulse propagation in optical waveguides.     

Modelling 1-D signals using Hermite basis functions

The paper discusses a method for estimating the Hermite coefficients of a discrete-time one-dimensional signal. To estimate the Hermite coefficients a solution based on Gaussian quadratures is used. The paper also looks at various least mean squared (LMS) estimation methods to estimate two further parameters which are incorporated into the orthonormal Hermite basis function; a spread term and a shift term. In addition, the effects of scaling, dilation and translates of a signal on its Hermite coefficients, spread and shift terms are presented. The paper concludes with a brief discussion on the potential application of the Hermite parameters as features for use in problems requiring shape discrimination within a one-dimensional signal. It also mentions those applications where this was found to be appropriate     

Iterative reconstruction methods using regularization and optimal current patterns in electrical impedance tomography

An iterative reconstruction method which minimizes the effects of ill-conditioning is discussed. Based on the modified Newton-Raphson algorithm, a regularization method which integrates prior information into the image reconstruction was developed. This improves the conditioning of the information matrix in the modified Newton-Raphson algorithm. Optimal current patterns were used to obtain voltages with maximal signal-to-noise ratio (SNR). A complete finite element model (FEM) was used for both the internal and the boundary electric fields. Reconstructed images from phantom data show that the use of regularization optimal current patterns, and a complete FEM model improves image accuracy. The authors also investigated factors affecting the image quality of the iterative algorithm such as the initial guess, image iteration, and optimal current updating.     

基于动态全变差的动态磁共振图像重建

动态核磁共振(dMRI)成像技术要在极短的扫描时间内获取高时空精度的MR图像,目前仍然是一个难点。文中提出了一种新的基于动态全变差技术(DTV)的压缩感知(CS)动态磁共振图像重建方案,该方法充分利用dMRI数据在时空域的稀疏性。文中算法采用加权最小二乘算法解决重建速度过慢的问题。论文将该算法与目前比较先进的两种算法TV及k-t SLR做比较,实验数据来源于临床脑部电影数据集。实验结果显示该方法在重建精度上处于领先水平。     

Image reconstruction with locally adaptive sparsity and nonlocal robust regularization

Sparse representation based modeling has been successfully used in many image-related inverse problems such as deblurring, super-resolution and compressive sensing. The heart of sparse representations lies on how to find a space (spanned by a dictionary of atoms) where the local image patch exhibits high sparsity and how to determine the image local sparsity. To identify the locally varying sparsity, it is necessary to locally adapt the dictionary learning process and the sparsity-regularization parameters. However, spatial adaptation alone runs into the risk of over-fitting the data because variation and invariance are two sides of the same coin. In this work, we propose two sets of complementary ideas for regularizing image reconstruction process: (1) the sparsity regularization parameters are locally estimated for each coefficient and updated along with adaptive learning of PCA-based dictionaries; (2) a nonlocal self-similarity constraint is introduced into the overall cost functional to improve the robustness of the model. An efficient alternative minimization algorithm is present to solve the proposed objective function and then an effective image reconstruction algorithm is presented. The experimental results on image deblurring, super-resolution and compressive sensing demonstrate that the proposed image reconstruct method outperforms many existing image reconstruction methods in both PSNR and visual quality assessment.     

Three-dimensional tumor perfusion reconstruction using fractal interpolation functions

It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool. Also, it was concluded in a previous report that the blood perfusion in a two-dimensional (2-D) tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In this paper, the three-dimensional (3-D) tumor perfusion is reconstructed from the 2-D slices using the method of fractal interpolation functions (FIF), i.e., the piecewise self-affine fractal interpolation model (PSAFIM) and the piecewise hidden variable fractal interpolation model (PHVFIM). The fractal models are compared to classical interpolation techniques (linear, spline, polynomial) by means of determining the 2-D fractal dimension of the reconstructed slices. Using FIFs instead of classical interpolation techniques better conserves the fractal-like structure of the perfusion data. Among the two FIF methods, PHVFIM conserves the 3-D fractality better due to the cross correlation that exists between the data in the 2-D slices and the data along the reconstructed direction. The 3-D structures resulting from PHVFIM have a fractal dimension within 3%-5% of the one reported in literature for 3-D percolation. It is, thus, concluded that the reconstructed 3-D perfusion has a percolation-like scaling. As the perfusion term from bio-heat equation is possibly better described by reconstruction via fractal interpolation, a more suitable computation of the temperature field induced during hyperthermia treatments is expected.     

Regression on the basis of nonstationary Gaussian processes with Bayesian regularization

We consider the regression problem, i.e. prediction of a real valued function. A Gaussian process prior is imposed on the function, and is combined with the training data to obtain predictions for new points. We introduce a Bayesian regularization on parameters of a covariance function of the process, which increases quality of approximation and robustness of the estimation. Also an approach to modeling nonstationary covariance function of a Gaussian process on basis of linear expansion in parametric functional dictionary is proposed. Introducing such a covariance function allows to model functions, which have non-homogeneous behaviour. Combining above features with careful optimization of covariance function parameters results in unified approach, which can be easily implemented and applied. The resulting algorithm is an out of the box solution to regression problems, with no need to tune parameters manually. The effectiveness of the method is demonstrated on various datasets.     

Fast fully 3-D image reconstruction in PET using planograms

We present a method of performing fast and accurate three-dimensional (3-D) backprojection using only Fourier transform operations for line-integral data acquired by planar detector arrays in positron emission tomography. This approach is a 3-D extension of the two-dimensional (2-D) linogram technique of Edholm. By using a special choice of parameters to index a line of response (LOR) for a pair of planar detectors, rather than the conventional parameters used to index a LOR for a circular tomograph, all the LORs passing through a point in the field of view (FOV) lie on a 2-D plane in the four-dimensional (4-D) data space. Thus, backprojection of all the LORs passing through a point in the FOV corresponds to integration of a 2-D plane through the 4-D "planogram." The key step is that the integration along a set of parallel 2-D planes through the planogram, that is, backprojection of a plane of points, can be replaced by a 2-D section through the origin of the 4-D Fourier transform of the data. Backprojection can be performed as a sequence of Fourier transform operations, for faster implementation. In addition, we derive the central-section theorem for planogram format data, and also derive a reconstruction filter for both backprojection-filtering and filtered-backprojection reconstruction algorithms. With software-based Fourier transform calculations we provide preliminary comparisons of planogram backprojection to standard 3-D backprojection and demonstrate a reduction in computation time by a factor of approximately 15.