The main aim of this paper is to develop an algorithm for blending of multiple images in the image-stitching process. Our idea is to propose a variational method containing an energy functional to determine both a stitched image and weighting mask functions of multiple input images for image blending. The existence of the solution of the proposed energy functional is shown. We also present an alternative minimizing algorithm to solve the proposed model numerically and show the convergence of this algorithm. Experimental results show that the proposed model works effectively and efficiently and that the proposed method is competitive with the tested existing methods under noisy conditions.

In this paper, we propose and develop a novel nonlocal variational technique based on structural similarity (SS) information for image restoration problems. In the literature, patches extracted from images are compared according to their pixel values, and then nonlocal filtering can be employed for image restoration. The disadvantage of this approach is that intensity-based patch distance may not be effective in image restoration, especially for images containing texture or structural information. The main aim of this paper is to propose using SS between image patches to develop nonlocal regularization models. In particular, two types of nonlocal regularizing functions are studied: an SS-based nonlocal quadratic function (SS-NLH1) and an SS-based nonlocal total variation function (SS-NLTV) for regularization of image restoration problems. Moreover, we employ iterative algorithms to solve these SS-NLH1 and SS-NLTV variational models numerically and discuss the convergence of these algorithms. The experimental results are presented to demonstrate the effectiveness of the proposed models.

The ill-posed models are widely encountered in various inversions of geodesy and remote sensing. The regularization approaches can significantly stabilize the solution to ill-posed models since the high-frequency noise is effectively suppressed. Although the famous Tikhonov regularization and truncated singular value decomposition (TSVD) regularization have been widely applied in various geodetic applications, there still remain theoretical drawbacks for either single regularization. For Tikhonov regularization, given a regularization parameter, the low-frequency terms are over-regularized, and high-frequency terms are under-regularized. For TSVD regularization, some medium-frequency terms will be mistaken for high-frequency terms to be truncated and the hidden signals will be lost. For this reason, we propose an adaptive regularized solution in spectral form, which adaptively divides the terms of different frequencies into three kinds: 1) the low-frequency terms are not regularized; 2) the medium-frequency terms are regularized by the Tikhonov method; and 3) the high-frequency terms are regularized by the TSVD method. The analytical conditions for determining the term sets are derived based on the criteria that the introduced biases should be smaller than the reduced errors; in other words, the mean square error (MSE) should be reduced. The two examples are presented to demonstrate the performance of our adaptive regularization. The first numerical example is solving the Fredholm integral equation of the first kind, which is widely encountered in remote sensing inversions. The simulations clearly demonstrate that the adaptive regularized solution can improve the MSE of ordinary Tikhonov and TSVD regularized functions by 25.00% and 9.09%, respectively. In the second example, we apply the new method to investigate the mass variation of the Yangtze River Basin based on the Gravity Recovery and Climate Experiment (GRACE) time-variable gravity field model. The Tongji-Grace 2018 monthly gravity field solutions from April 2002 to December 2016 are used to construct the mascon observation equation. The results show that our method also outperforms the ordinary Tikhonov and TSVD regularized solutions, with mean MSE reductions of about 13.40% and 11.69%, respectively. Furthermore, the spatial resolution of secular trend derived by our method is improved and the signal-to-noise ratio (SNR) of mass variation series is higher than the other two regularizations.

The performance of contrast enhancement is degraded when input images are noisy. In this paper, we propose and develop a variational model for simultaneously image denoising and contrast enhancement. The idea is to propose a variational approach containing an energy functional to adjust the pixel values of an input image directly so that the resulting histogram can be redistributed to be uniform and the noise of the image can be removed. In the proposed model, a histogram equalization term is considered for image contrast enhancement, a total variational term is incorporate to remove the noise of the input image, and a fidelity term is added to keep the structure and the texture of the input image. The existence of the minimizer and the convergence of the proposed algorithm are studied and analyzed. Experimental results are presented to show the effectiveness of the proposed model compared with existing methods in terms of several measures: average local contrast, discrete entropy, structural similarity index, measure of enhancement, absolute measure of enhancement, and second derivative like measure of enhancement.