Faming Fang

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.

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.

Single Image Dehazing and Denoising: A Fast Variational Approach

In this paper, we propose a new fast variational approach to dehaze and denoise simultaneously. The proposed method first estimates a transmission map using a windows adaptive method based on the celebrated dark channel prior. This transmission map can significantly reduce the edge artifact in the resulting image and enhance the estimation precision. The transmission map is then converted to a depth map, with which the new variational model can be built to seek the final haze- and noise-free image. The existence and uniqueness of a minimizer of the proposed variational model is further discussed. A numerical procedure based on the Chambolle--Pock algorithm is given, and the convergence of the algorithm is ensured. Extensive experimental results on real scenes demonstrate that our method can restore vivid and contrastive haze- and noise-free images effectively.

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.

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.

Similarity-Guided and

In this letter, we propose a novel sparse unmixing model combined with two effective regularization terms: one is a similarity-weighting constraint, and the other is the ℓp (0 <; p <; 1) norm sparse regularization. The former utilizes the spatial structural correlation, which is presented in the hyperspectral data, to guide the abundance estimation. When compared with the existing graph Laplacian regularization, our similarity-weighting constraint avoids large matrix inversion, and thus, it can be efficiently solved. As for the ℓp-norm, it has numerical advantages over the convex ℓ1-norm and better approximates the ℓ0-norm theoretically. Moreover, the ℓp-norm regularizer can simultaneously promote sparsity and enforce the abundance sum-to-one constraint. Therefore, this term yields more desirable results in practice. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed model.

\ell_p

In remote-sensing image processing, pan-sharpening is used to obtain a high-resolution multi-spectral image by combining a low-resolution multi-spectral image with a corresponding high-resolution panchromatic image. In this article, to preserve the geometry, spectrum, and correlation information of the original images, three hypotheses are presented, i.e. (1) the geometry information contained in the pan-sharpened image should also be contained in the panchromatic bands; (2) the upsampled multi-spectral image can be seen as a blurred form of the fused image with an unknown kernel; and (3) the fused bands should keep the correlation between each band of the upsampled multi-spectral image. A variational energy functional is then built based on the assumptions, of which the minimizer is the target fused image. The existence of a minimizer of the proposed energy is further analysed, and the numerical scheme based on the split Bregman framework is presented. To verify the validity, the new proposed method is compared with several state-of-the-art techniques using QuickBird data in subjective, objective, and efficiency aspects. The results show that the proposed approach performs better than some compared methods according to the performance metrics.

-Regularized Sparse Unmixing of Hyperspectral Data

ABSTRACT In this article, we propose a novel unsupervised change detection method for synthetic aperture radar (SAR) images. First, we generate a difference image as a weighted average of a log-ratio image and a mean-ratio image, which has the advantage of enhancing the information of changed regions and restraining the information of unchanged background regions simultaneously. Second, we propose a variational soft segmentation model based on non-differentiable curvelet regularization and L1-norm fidelity. Numerically, by using the split Bregman technique for curvelet regularization term and reformulating the L1-norm fidelity as weighted L2-norm fidelity, we get an effective algorithm in which each sub-problem has a closed-form solution. The numerical experiments and comparisons with several existing methods show that the proposed method is promising, with not only high robustness to non-Gaussian noise or outliers but also high change detection accuracy. Moreover, the proposed method is good at detecting fine-structured change areas. Especially, it outperforms other methods in preserving edge continuity and detecting curve-shaped changed areas.

Pan-sharpening of multi-spectral images using a new variational model

It is well known that the linear mixture model (LMM) is attracting much attention due to its simplicity. However, some theoretical analysis reveals that the traditional LMM also impedes the improvement of blind spectral unmixing. For this reason, we propose a novel blind spectral unmixing method (NBSUM) in this letter. NBSUM utilizes the conjugate gradient to calculate end-member spectral and abundance, which can not only overcome some shortcomings of the traditional LMM but also provide more accurate results. NBSUM is compared with some state-of-the-art approaches on both synthetic and real hyperspectral data sets, and the experimental results demonstrate the efficacy of the proposed method.