Array interferometric synthetic aperture radar (Array InSAR) has a 3-D resolution capability and solves the layover problem in interferometric SAR (InSAR) by arranging multiple antennas in the cross-orbit direction. Airborne Array InSAR point clouds are obtained from two scans for complete building information in urban areas, resulting in very low overlapping point cloud. The existing methods are difficult to extract the identical features for the registration of Array InSAR point clouds. To this end, a robust registration approach Array InSAR point clouds in urban areas is proposed in this study. The main contribution of this article is raising the theoretically optimal transformation for achieving point cloud registration, considering the constraint from parallel facades of a certain building. Point density estimation is adopted to retain building facade points for initial registration. The facade pairs of a specific building are then matched and divided into two categories by judging whether one contains the concave–convex features or not, for performing rotation rectification and fine shift fixation, respectively. Experimental results of both simulated and real data validate the feasibility and reliability of our approach. For the simulated data, the results reach an average rotation error of about 0.01° and an average translation error of less than 0.8 m. For the real data, two evaluation criteria are designed for the lack of reference data. The results reach an average of 0.4° of the defined angle difference and less 0.8-m distance difference from the source facades center to the normal extension of the target facades.

The blur kernel estimated by blind deblurring algorithm is hardly to be error-free. The blur kernel error is usually ignored in non-blind deconvolution stage, and may result in severe artifacts or other negative effects. In addition, the bias hidden in the blurry image formation model has not been found and investigated due to ignoring the existence of the blur kernel errors. To this end, we develop a non-blind deconvolution method by bias-correction for inaccurate blur kernel in this paper, which are constructed on the basis of the classic errors-in-variables model. Firstly, we analyze in detail the bias caused by errors of inaccurate blur kernel from blurry image formation model. Next, the latent sparsity property of jointed latent image and errors of inaccurate blur kernel is counted statistically, which is imposed as a new regularization term. Then, the objective function of the new non-blind method is established, and an alternative minimization algorithm is derived and employed to estimate the latent clear image. Furthermore, a filtering method is utilized to modify the bias term, which is added to amend intermediate image in each iteration. Finally, extensive experiments with benchmark datasets and blurred micro-nano satellite remote sensing images are carried out to evaluate the proposed method. Experimental results demonstrate that the proposed method can obtain high quality restored images, and it is comparable to or even better than some state-of-the-art non-blind deconvolution methods.

The partial errors-in-variables (PEIV) model is an structured errors-in-variables (SEIV) model reformulated by collecting all the random elements of the coefficient matrix into an auxiliary random error vector to better treat the case where the coefficient matrix (or ‘data matrix’) A and observation vector y share common elements. In the usual PEIV model, the case of A and y sharing common elements has not been treated explicitly. However, in some cases, A and y do have common elements, taking the autoregressive problem as an example. To apply the PEIV model to SEIV problems with correlated matrix A and vector y, we propose an extended model named general PEIV (GPEIV). We also provide a corresponding algorithm for the total least-squares solution within the GPEIV model. A weight-matrix construction method, which is suitable for PEIV and GPEIV models, is also presented. The GPEIV model, the algorithm and the weight-matrix construction method are tested using two groups of numerical examples. The results show that the proposed model and corresponding algorithm can solve both uncorrelated and correlated SEIV problems, and the weight-matrix construction method is simple and efficient.

The sparsity regularization based on the L₁ norm can significantly stabilize the solution of the ill-posed sparsity inversion problem, e.g., azimuth super-resolution of radar forward-looking imaging, which can effectively suppress the noise and reduce the blurry effect of the convolution kernel. In practice, the total variation (TV) and TV-sparsity (TVS) regularizations based on the L₁ norm are widely adopted in solving the ill-posed problem. Generally, however, the existence of bias is ignored, which is incomplete in theory. This paper places emphasis on analyzing the partially biased property of the L₁ norm. On this basis, we derive the partially bias-corrected solution of TVS and TV, which improves the rigor of the theory. Lastly, two groups of experimental results reflect that the proposed methods with partial bias correction can preserve higher quality than those without bias correction. The proposed methods not only distinguish the adjacent targets, suppress the noise, and preserve the shape and size of targets in visual terms. Its improvement of Peak Signal-to-Noise Ratio, Structure-Similarity, and Sum-Squared-Errors assessment indexes are overall 2.15%, 1.88%, and 4.14%, respectively. As such, we confirm the theoretical rigor and practical feasibility of the partially bias-corrected solution with sparsity regularization based on the L₁ norm.

Weighted mean temperature of the atmosphere, $T_m$, is a key parameter for retrieving the precipitable water vapor from Global Navigation Satellite System observations. It is commonly estimated by a linear model that relates to surface temperature $T_s$. However, the linear relationship between $T_m$ and $T_s$ is associated with geographic regions and affected by the weather. To better estimate the $T_m$ over China, we analyzed the region-specific and weather-dependent characteristics of this linear relationship using 860,054 radiosonde profiles from 88 Chinese stations between 2005 and 2018. The slope coefficients of site-specific linear models are 0.35~0.95, which generally reduce from northeast to southwest. Over southwest China, the slope coefficient changes drastically, while over the northwest, it shows little variation. We developed a $T_s\sim T_m$ linear model using the data from rainless days as well as a model using the data from rainy days for each station. At half the stations, mostly located in west and north China, the differences between the rainy-day and rainless-day $T_m$ models are significant and larger than 0.5% (1%) in mean (maximal) relative bias. The regression precisions of the rainy-day models are higher than that of the rainless-day models averagely by 28% for the stations. Radiosonde data satisfying $T_m-T_s>10\mathrm{K}$ and $T_s-T_m>30\mathrm{K}$ most deviate from linear regression models. Results suggest that the former situation is related to low surface temperature (280 K) and a distinct humidity inversion above 600 hPa.