Image Deblurring Via Combined Total Variation and Framelet

This paper presents a new approach to image deblurring, on the basis of total variation (TV) and wavelet frame. The Rudin–Osher–Fatemi model, which is based on TV minimization, has been proven effective for image restoration. The explicit exploitation of sparse approximations of natural images has led to the success of wavelet frame approach in solving image restoration problems. However, TV introduces staircase effects. Thus, we propose a new objective functional that combines the tight wavelet frame and TV to reconstruct images from blurry and noisy observations while mitigating staircase effects. The minimization of the new objective functional presents a computational challenge. We propose a fast minimization algorithm by employing the augmented Lagrangian technique. The experiments on a set of image deblurring benchmark problems show that the proposed method outperforms the previous state-of-the-art methods for image restoration.     

A modified multi-grid algorithm for a novel variational model to remove multiplicative noise

This paper proposes a novel variational model and a fast algorithm for its numerical approximation to remove multiplicative noise from digital images. By applying a maximum a posteriori (MAP), we obtained a strictly convex objective functional whose minimization leads to non-linear partial differential equations. As a result, developing a fast numerical scheme is difficult because of the high nonlinearity and stiffness of the associated Euler-Lagrange equation and standard unilevel iterative methods are not appropriate. To this end, we develop an efficient non-linear multi-grid algorithm with an improved smoother. We also discuss a local Fourier analysis of the associated smoothers which leads to a new and more effective smoother. Experimental results using both synthetic and realistic images, illustrate advantages of our proposed model in visual improvement as well as an increase in the peak signal-to-noise ratio over comparing to related recent corresponding PDE methods. We compare numerical results of new multigrid algorithm via modified smoother with traditional time marching schemes and with multigrid method via (local and global) fixed point smoother as well.     

Thresholding implied by truncated quadratic regularization

We address the problem of the estimation of an unknown signal that is known to involve sharp edges, from noisy data given at the output of a linear system. The sought solution is defined to be the global minimizer of an objective function combining a quadratic data-fidelity term and a regularization term. The latter term is a sum whose entries are obtained by applying a truncated quadratic potential function to every difference between adjacent samples. Such objective functions are naturally formulated either in a statistical framework, or in a variational framework, and they are customarily used in signal and image reconstruction. However, these objective functions are nonsmooth and highly nonconvex, and many questions related to their minimization, as well as to the features of the resulting solutions, remain open. We present some new facts characterizing the features exhibited by the minimizers of such objective functions. Our main result states that the magnitude of the differences between adjacent samples of a global minimizer are either smaller than a first threshold or larger than a second, strictly larger threshold. Conversely, no difference corresponding to a global minimizer of the objective function can be placed among these thresholds for any data. This explains how edges are recovered in a signal and estimated using truncated quadratic regularization. These thresholds are independent of the data but are related to the observation system and to the regularization parameters. They can be used to derive necessary conditions for the choice of the regularization parameters. We also show that the chance to get data for which the objective function has two or more global minimizers is . Numerical experiments corroborate the obtained theoretical results.     

Efficient Total Variation Minimization Methods for Color Image Restoration

In this paper, we consider and study a total variation minimization model for color image restoration. In the proposed model, we use the color total variation minimization scheme to denoise the deblurred color image. An alternating minimization algorithm is employed to solve the proposed total variation minimization problem. We show the convergence of the alternating minimization algorithm and demonstrate that the algorithm is very efficient. Our experimental results show that the quality of restored color images by the proposed method are competitive with the other tested methods.     

Amplitude spectrum estimation for two-dimensional gapped data

The amplitude and phase estimation (APES) approach to nonparametric spectrum estimation of uniformly sampled data has received considerable interest. We consider the extension of APES to gapped data, i.e., uniformly sampled data with missing samples. It has been shown that the APES estimate of the spectrum is the minimizer of a certain least-squares (LS) criterion, and our extension of APES is based on minimizing this LS criterion with respect to the missing data as well. A computationally efficient method for doing this based on cyclic minimization and the conjugate gradient algorithm is proposed. The new algorithm is called gapped-data APES (GAPES) and is developed for the two-dimensional (2-D) case, with the one-dimensional (1-D) case as a special instance. Numerical examples are provided to demonstrate the performance of the algorithm and to show the advantages of 2-D data processing over 1-D (row or column-wise) data processing, as well as to show the applicability of the algorithm to synthetic aperture radar (SAR) imaging     

Designing nonstandard filters with differential evolution

An alternative method for nonstandard filter design has been described. This method recasts the filter design problem as a minimization problem and solves the minimization via the DE minimizer, for which public domain software has been made available previously. The advantages of this method are its simplicity as well as the capability to design unconventional filter types. A great asset of this approach is that it can be applied with minimal knowledge of digital filter design theory.     

Unsupervised multi class segmentation of 3D images with intensity inhomogeneities

Intensity inhomogeneities in images cause problems in gray-value based image segmentation since the varying intensity often dominates over gray-value differences of the image structures. In this paper we propose a novel biconvex variational model that includes the intensity inhomogeneities to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. In our model we assume that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of the resulting biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images serving as a motivation for our work.     

Image segmentation via image decomposition and fuzzy region competition

Taking into account the morphological diversity of images, this paper presents a novel multiphase image segmentation method that combines image decomposition and fuzzy region competition into a unified model. To efficiently solve the minimization of the energy functional, we design an optimal iteration algorithm which integrates a modified cartoon-texture dictionary learning algorithm and wavelet shrinkage. Compared with the classical fuzzy region competition method, the proposed method not only improves the overall segmentation results, but also has more strong robustness. A series of experimental results demonstrate the applicability and effectiveness of the proposed method.     

Optimal fusion rule for cooperative spectrum sensing in cognitive radio networks

In this paper,we analyze performance of cooperative spectrum sensing under counting rules when exponential model is utilized to characterize the burst nature of primary user(PU) link.Our objective is to minimize the average error probability(AEP) so that the link utilization in the considered link achieves its maximum.We derive a closed-form expression of AEP as well as the probability of interference(PoI) by classifying cognitive transmission into six events.Then,we consider the minimization of AEP over counting rules under the constraint of interference.As the solution,we develop an efficient algorithm to evaluate the optimal fusion rule.Finally,we verify our analysis in numerical results.     

Obstacle-avoiding rectilinear minimum-delay Steiner tree construction toward IP-block-based SOC design

With system-on-chip design, IP blocks form routing obstacles that deteriorate global interconnect delay. In this paper, we present a new approach for obstacle-avoiding rectilinear minimal delay Steiner tree (OARMDST) construction. We formalize the solving of minimum delay tree through the concept of an extended minimization function, and trade the objective into a top-down recursion, which wisely produces delay minimization from source to critical sinks. We analyze the topology generation with treatment of obstacles and exploit the connection flexibilities. To our knowledge, this is the first in-depth study of OARMDST problem based on topological construction. Experimental results are given to demonstrate the efficiency of the algorithm.     

一种改进的各向异性扩散模型

各项异性扩散方程是一种经典的图像去噪方法,但该方法在去除噪声的过程中会造成一定程度的模糊边缘。对此文中提出了一种基于改进的各向异性扩散方程的图像去噪方法,通过在其能量泛函的目标函数中添加残差项,使能量泛函的极小解更加接近原始的函数,可取得比其更好的去噪效果。文中方法可看作是各项异性扩散方程和全变差模型的结合。实验表明,新提出的方程相对经典的方程有较好的边界处理效果和更高的信噪比。     

Patch-Based Nonlocal Functional for Denoising Fluorescence Microscopy Image Sequences

We present a nonparametric regression method for denoising 3-D image sequences acquired via fluorescence microscopy. The proposed method exploits the redundancy of the 3-D+time information to improve the signal-to-noise ratio of images corrupted by Poisson-Gaussian noise. A variance stabilization transform is first applied to the image-data to remove the dependence between the mean and variance of intensity values. This preprocessing requires the knowledge of parameters related to the acquisition system, also estimated in our approach. In a second step, we propose an original statistical patch-based framework for noise reduction and preservation of space-time discontinuities. In our study, discontinuities are related to small moving spots with high velocity observed in fluorescence video-microscopy. The idea is to minimize an objective nonlocal energy functional involving spatio-temporal image patches. The minimizer has a simple form and is defined as the weighted average of input data taken in spatially-varying neighborhoods. The size of each neighborhood is optimized to improve the performance of the pointwise estimator. The performance of the algorithm (which requires no motion estimation) is then evaluated on both synthetic and real image sequences using qualitative and quantitative criteria.      

Hessian-based norm regularization for image restoration with biomedical applications

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second-order differential operators. Specifically, we derive second-order regularizers that involve matrix norms of the Hessian operator. The definition of these functionals is based on an alternative interpretation of TV that relies on mixed norms of directional derivatives. We show that the resulting regularizers retain some of the most favorable properties of TV, i.e., convexity, homogeneity, rotation, and translation invariance, while dealing effectively with the staircase effect. We further develop an efficient minimization scheme for the corresponding objective functions. The proposed algorithm is of the iteratively reweighted least-square type and results from a majorization-minimization approach. It relies on a problem-specific preconditioned conjugate gradient method, which makes the overall minimization scheme very attractive since it can be applied effectively to large images in a reasonable computational time. We validate the overall proposed regularization framework through deblurring experiments under additive Gaussian noise on standard and biomedical images.     

一种处理分层有耗色散介质的时域逆散射方法

为了重建分层有耗色散介质的特征参数,我们应用泛函分析和变分法,提出一种时域逆散射新方法.该方法首先以最小二乘准则构造目标函数,将逆问题表示为约束最小化问题;接着应用罚函数法转化为无约束最小化问题;然后基于变分计算导出闭式的拉格朗日(Lagrange)函数关于特征参数的Fréchet导数;最后借助梯度算法和时域有限差分(...     

Full motion and flow field recovery from echo Doppler data

We present a new computational method for reconstructing a vector velocity field from scattered, pulsed-wave ultrasound Doppler data. The main difficulty is that the Doppler measurements are incomplete, for they do only capture the velocity component along the beam direction. We thus propose to combine measurements from different beam directions. However, this is not yet sufficient to make the problem well posed because 1) the angle between the directions is typically small and 2) the data is noisy and nonuniformly sampled. We propose to solve this reconstruction problem in the continuous domain using regularization. The reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms: 1) the sum of squared difference between the Doppler data and the projected velocities 2) a quadratic regularization functional that imposes some smoothness on the velocity field. We express our solution for this minimization problem in a B-spline basis, obtaining a sparse system of equations that can be solved efficiently. Using synthetic phantom data, we demonstrate the significance of tuning the regularization according to the a priori knowledge about the physical property of the motion. Next, we validate our method using real phantom data for which the ground truth is known. We then present reconstruction results obtained from clinical data that originate from 1) blood flow in carotid bifurcation and 2) cardiac wall motion.     

Diagnosis of array faults from far-field amplitude-only data

The diagnosis of the faulty elements of a planar array from noisy far-field power pattern data is considered in the case of “on-off” faults. The possible ambiguities of the solutions are considered both in the theoretical and practical sense and are shown to be intrinsically less relevant than in the widely studied continuous case. The probability of the occurrence of the practical ambiguities is inferred from a number of numerical examples and is shown to be negligible in all cases of interest. An effective algorithm is presented here based on an intersection set finding approach and involving the minimization of a suitable objective functional. The global minimization of the functional has been successfully performed by applying a properly modified genetic algorithm. A number of numerical examples shows the effectiveness of the approach whose computational complexity essentially increases linearly with the array size     

Task Scheduling and Lightpath Establishment in Optical Grids

Data-intensive Grid applications require huge data transferring between multiple geographically separated computing nodes where computing tasks are executed. For a future WDM network to efficiently support this type of emerging applications, neither the traditional approaches to establishing lightpaths between given source destination pairs are sufficient, nor are those existing application level approaches that consider computing resources but ignore the optical layer connectivity. Instead, lightpath establishment has to be considered jointly with task scheduling to achieve best performance. In this paper, we study the optimization problems of jointly scheduling both computing resources and network resources. We first present the formulation of two optimization problems with the objectives being the minimization of the completion time of a job and minimization of the resource usage/cost to satisfy a job with a deadline. When the objective is to minimize the completion time, we devise an optimal algorithm for a special type of applications. Furthermore, we propose efficient heuristics to deal with general applications with either optimization objective and demonstrate their good performances in simulation.     

Effective Level Set Image Segmentation With a Kernel Induced Data Term

This study investigates level set multiphase image segmentation by kernel mapping and piecewise constant modeling of the image data thereof. A kernel function maps implicitly the original data into data of a higher dimension so that the piecewise constant model becomes applicable. This leads to a flexible and effective alternative to complex modeling of the image data. The method uses an active curve objective functional with two terms: an original term which evaluates the deviation of the mapped image data within each segmentation region from the piecewise constant model and a classic length regularization term for smooth region boundaries. Functional minimization is carried out by iterations of two consecutive steps: 1) minimization with respect to the segmentation by curve evolution via Euler-Lagrange descent equations and 2) minimization with respect to the regions parameters via fixed point iterations. Using a common kernel function, this step amounts to a mean shift parameter update. We verified the effectiveness of the method by a quantitative and comparative performance evaluation over a large number of experiments on synthetic images, as well as experiments with a variety of real images such as medical, satellite, and natural images, as well as motion maps.     

Variational B-Spline Level-Set: A Linear Filtering Approach for Fast Deformable Model Evolution

In the field of image segmentation, most level-set-based active-contour approaches take advantage of a discrete representation of the associated implicit function. We present in this paper a different formulation where the implicit function is modeled as a continuous parametric function expressed on a B-spline basis. Starting from the active-contour energy functional, we show that this formulation allows us to compute the solution as a restriction of the variational problem on the space spanned by the B-splines. As a consequence, the minimization of the functional is directly obtained in terms of the B-spline coefficients. We also show that each step of this minimization may be expressed through a convolution operation. Because the B-spline functions are separable, this convolution may in turn be performed as a sequence of simple 1-D convolutions, which yields an efficient algorithm. As a further consequence, each step of the level-set evolution may be interpreted as a filtering operation with a B-spline kernel. Such filtering induces an intrinsic smoothing in the algorithm, which can be controlled explicitly via the degree and the scale of the chosen B-spline kernel. We illustrate the behavior of this approach on simulated as well as experimental images from various fields.