Guixu Zhang

A Variational Approach for Pan-Sharpening

Pan-sharpening is a process of acquiring a high resolution multispectral (MS) image by combining a low resolution MS image with a corresponding high resolution panchromatic (PAN) image. In this paper, we propose a new variational pan-sharpening method based on three basic assumptions: 1) the gradient of PAN image could be a linear combination of those of the pan-sharpened image bands; 2) the upsampled low resolution MS image could be a degraded form of the pan-sharpened image; and 3) the gradient in the spectrum direction of pan-sharpened image should be approximated to those of the upsampled low resolution MS image. An energy functional, whose minimizer is related to the best pan-sharpened result, is built based on these assumptions. We discuss the existence of minimizer of our energy and describe the numerical procedure based on the split Bregman algorithm. To verify the effectiveness of our method, we qualitatively and quantitatively compare it with some state-of-the-art schemes using QuickBird and IKONOS data. Particularly, we classify the existing quantitative measures into four categories and choose two representatives in each category for more reasonable quantitative evaluation. The results demonstrate the effectiveness and stability of our method in terms of the related evaluation benchmarks. Besides, the computation efficiency comparison with other variational methods also shows that our method is remarkable.

An MOEA/D with multiple differential evolution mutation operators

In evolutionary algorithms, the reproduction operators play an important role. It is arguable that different operators may be suitable for different kinds of problems. Therefore, it is natural to combine multiple operators to achieve better performance. To demonstrate this idea, in this paper, we propose an MOEA/D with multiple differential evolution mutation operators called MOEA/D-MO. MOEA/D aims to decompose a multiobjective optimization problem (MOP) into a number of single objective optimization problems (SOPs) and optimize those SOPs simultaneously. In MOEA/D-MO, we combine multiple operators to do reproduction. Three mutation strategies with randomly selected parameters from a parameter pool are used to generate new trial solutions. The proposed algorithm is applied to a set of test instances with different complexities and characteristics. Experimental results show that the proposed combining method is promising.

A variational method for multisource remote-sensing image fusion

With the increasing availability of multisource image data from Earth observation satellites, image fusion, a technique that produces a single image which preserves major salient features from a set of different inputs, has become an important tool in the field of remote sensing since usually the complete information cannot be obtained by a single sensor. In this article, we develop a new pixel-based variational model for image fusion using gradient features. The basic assumption is that the fused image should have a gradient that is close to the most salient gradient in the multisource inputs. Meanwhile, we integrate the inputs with the average quadratic local dispersion measure for the purpose of uniform and natural perception. Furthermore, we introduce a split Bregman algorithm to implement the proposed functional more effectively. To verify the effect of the proposed method, we visually and quantitatively compare it with the conventional image fusion schemes, such as the Laplacian pyramid, morphological pyramid, and geometry-based enhancement fusion methods. The results demonstrate the effectiveness and stability of the proposed method in terms of the related fusion evaluation benchmarks. In particular, the computation efficiency of the proposed method compared with other variational methods also shows that our method is remarkable.

A decomposition based estimation of distribution algorithm for multiobjective traveling salesman problems

The traveling salesman problem (TSP) is a well known NP-hard benchmark problem for discrete optimization. However, there is a lack of TSP test instances for multiobjective optimization and some current TSP instances are combined to form a multiobjective TSP (MOTSP). In this paper, we present a way to systematically design MOTSP instances based on current TSP test instances, of which the degree of conflict between the objectives is measurable. Furthermore, we propose an approach, named multiobjective estimation of distribution algorithm based on decomposition (MEDA/D), which utilizes decomposition based techniques and probabilistic model based methods, to tackle the newly designed MOTSP test suite. In MEDA/D, an MOTSP is decomposed into a set of scalar objective sub-problems and a probabilistic model, using both priori and learned information, is built to guide the search for each sub-problem. By the cooperation of neighbor sub-problems, MEDA/D could optimize all the sub-problems simultaneously and thus find an approximation to the original MOTSP in a single run. The experimental results show that MEDA/D outperforms MOACO and MOEA/D-ACO, two ant colony based methods, on most of the given test instances and MEDA/D is insensible to its control parameters.

Fast image inpainting and colorization by Chambolle’s dual method

Abstract In this paper, we propose to use Chambolle’s dual methods to solve Total Variation (TV) inpainting model and (weighted) TV colorization model. The fidelity coefficients in these two models are functions which taking zero in the inpainting region and a positive constant in the other region. Then Chambolle’s dual method can not be directly used to solve these models since the fidelity coefficient will be denominator in the algorithm. In order to overcome this drawback, we propose to approximate these models by adding new variables. Then the approximated problems can be solved by alternating minimization method with Chambolle’s dual method and closed form solutions which is fast and easy to implement. Mathematical results of existence of minimizers are proved for both the original and the approximated problems. Numerical results and comparison with other closely related methods demonstrate that our algorithms are quite efficient.

Variational denoising of partly textured images

The Rudin-Osher-Fatemi model is a widely used variational denoising algorithm which favors piecewise constant solutions. Although edge sharpness and location are well preserved, some local features such as textures and small details are often diminished with noise simultaneously. This paper aims to better preserve these local features using a similar variational framework. We introduce a texture detecting function according to the derivatives of the noisy textured image. Then this function is used to construct a spatially adaptive fidelity term, which adjusts the denoising extent in terms of the local features. Numerical results show that our method is superior to the Rudin-Osher-Fatemi model in both signal-to-noise ratio and visual quality. Moreover, part of our results are also compared with other state-of-the-art methods including a variational method and a non local means filter. The comparison shows that our method is competitive with these two methods in restoration quality but is much faster.

Framelet based pan-sharpening via a variational method

Pan-sharpening is a process of combining a low resolution multi-spectral (MS) image and a high resolution panchromatic (PAN) image to obtain a single high resolution MS image. In this paper, we propose two pan-sharpening methods based on the framelet framework. The first method, as a basic work, is called a framelet-based pan-sharpening (FP) method. In the FP method, we first decompose the MS and PAN images into framelet coefficients, then obtain a new set of coefficients by choosing the approximation coefficients in MS and detail coefficients in PAN, and finally construct the pan-sharpened image from the new set of coefficients. To overcome the inflexibility of FP, in the second method, by combining FP and other three fusion requirements, i.e., geometry keeping, spectral preserving and the sparsity of the image in the framelet domain, four assumptions are established. Based on these assumptions, a framelet based variational energy functional, whose minimizer is related to the final pan-sharpened result, is then formulated. To improve the numerical efficiency, the split Bregman iteration is further introduced, and the result of FP method is set as an initial value. We refer this method as the variational framelet pan-sharpening (VFP) method. To verify the effectiveness of our methods, we present the results of the two methods on the QuickBird and IKONOS images, compare them with five existing methods qualitatively and quantitatively, analyze the influence of parameters of VFP, and extend the VFP to hyperspectral data as well as comparison study. The experimental results demonstrate the superiority of our methods.

An estimation of distribution algorithm based on decomposition for the multiobjective TSP

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) has gained much attention recently. It is suitable to use scalar objective optimization techniques for dealing with multiobjective optimization problems. In this paper, we propose a new approach, named multiobjective estimation of distribution algorithm based on decomposition (MEDA/D), which combines MOEA/D with probabilistic model based methods for multiobjective traveling salesman problems (MOTSPs). In MEDA/D, an MOTSP is decomposed into a set of scalar objective sub-problems and a probabilistic model, using both priori and learned information, is built to guide the search for each subproblem. By the cooperation of neighbor sub-problems, MEDA/D could optimize all the sub-problems simultaneously and thus find an approximation to the original MOTSP in a single run. The experimental results show that MEDA/D outperforms BicriterionAnt, an ant colony based method, on a set of test instances and MEDA/D is insensible to its control parameters.

Framelet-Based Sparse Unmixing of Hyperspectral Images

Spectral unmixing aims at estimating the proportions (abundances) of pure spectrums (endmembers) in each mixed pixel of hyperspectral data. Recently, a semi-supervised approach, which takes the spectral library as prior knowledge, has been attracting much attention in unmixing. In this paper, we propose a new semi-supervised unmixing model, termed framelet-based sparse unmixing (FSU), which promotes the abundance sparsity in framelet domain and discriminates the approximation and detail components of hyperspectral data after framelet decomposition. Due to the advantages of the framelet representations, e.g., images have good sparse approximations in framelet domain, and most of the additive noises are included in the detail coefficients, the FSU model has a better antinoise capability, and accordingly leads to more desirable unmixing performance. The existence and uniqueness of the minimizer of the FSU model are then discussed, and the split Bregman algorithm and its convergence property are presented to obtain the minimal solution. Experimental results on both simulated data and real data demonstrate that the FSU model generally performs better than the compared methods.

Single image dehazing and denoising with variational method

In this paper, we propose an unified variational approach for image dehazing and denoising from a single input image. Total variation regularization terms are used in the energy functional. Also, we use the negative gradient descent method to solve the corresponding Euler-Lagrange equations. To obtain good initial values, we improve the estimation of transmission map with the windows adaptive method based on the dark channel prior which can overcomes the block effects. The numerical results demonstrate that our algorithm is effective and promising.