Search Results (4)

Recovering the relaxation spectrum, a fundamental rheological characteristic of polymers, from experiment data requires special identification methods since it is a difficult ill-posed inverse problem. Recently, a new approach relating the identification index directly with a completely unknown real relaxation spectrum has been proposed. The integral square error of the relaxation spectrum model was applied. This paper concerns regularization aspects of the linear-quadratic optimization task that arise from applying Tikhonov regularization to relaxation spectra direct identification problem. An influence of the regularization parameter on the norms of the optimal relaxation spectra models and on the fit of the related relaxation modulus model to the experimental data was investigated. The trade-off between the integral square norms of the spectra models and the mean square error of the relaxation modulus model, parameterized by varying regularization parameter, motivated the definition of two new multiplicative indices for choosing the appropriate regularization parameter. Two new problems of the regularization parameter optimal selection were formulated and solved. The first and second order optimality conditions were derived and expressed in the matrix-vector form and, alternatively, in finite series terms. A complete identification algorithm is presented. The usefulness of the new regularization parameter selection rules is demonstrated by three examples concerning the Kohlrausch–Williams–Watts spectrum with short relaxation times and uni- and double-mode Gauss-like spectra with middle and short relaxation times. Full article

The unmixing-based spatiotemporal fusion model is one of the effective ways to solve limitations in temporal and spatial resolution tradeoffs in a single satellite sensor. By using fusion data from different satellite platforms, high resolution in both temporal and spatial domains can be produced. However, due to the ill-posed characteristic of the unmixing function, the model performance may vary due to the different model setups. The key factors affecting the model stability most and how to set up the unmixing strategy for data downscaling remain unknown. In this study, we use the multisource land surface temperature as the case and focus on the three major factors to analyze the stability of the unmixing-based fusion model: (1) the definition of the homogeneous change regions (HCRs), (2) the unmixing levels, and (3) the number of HCRs. The spatiotemporal data fusion model U-STFM was used as the baseline model. The results show: (1) The clustering-based algorithm is more suitable for detecting HCRs for unmixing. Compared with the multi-resolution segmentation algorithm and k-means algorithm, the ISODATA clustering algorithm can more accurately describe LST’s temporal and spatial changes on HCRs. (2) For the U-STFM model, applying the unmixing processing at the change ratio level can significantly reduce the additive and multiplicative noise of the prediction. (3) There is a tradeoff effect between the number of HCRs and the solvability of the linear unmixing function. The larger the number of HCRs (less than the available MODIS pixels), the more stable the model is. (4) For the fusion of the daily 30 m scale LST product, compared with STARFM and ESTARFM, the modified U-STFM (iso_USTFM) achieved higher prediction accuracy and a lower error ($R{ }^2$: 0.87 and RMSE:1.09 k). With the findings of this study, daily fine-scale LST products can be predicted based on the unmixing-based spatial–temporal model with lower uncertainty and stable prediction. Full article

The extraction of landslide deformation using terrestrial laser scanning (TLS) has many important applications. The landslide deformation can be extracted based on a digital terrain model (DTM). However, such methods usually suffer from the ill-posed problem of a multiplicative error model as illustrated in previous studies. Moreover, the edge drift of commonly used spherical targets for point cloud registration (PCR) is ignored in the existing method, which will result in the unstable precision of the PCR. In response to these problems, we propose a method for extracting landslide deformations from TLS data. To archive the PCR of different period point clouds, a new triangular pyramid target is designed to eliminate the edge drift. If a fixed target is inconvenient, we also propose a PCR method based on total station orientation. Then, the use of the Tikhonov regularization method to derive the weighted least squares regularization solution is presented. Finally, the landslide deformation is extracted by DTM deference. The experiments are conducted on two datasets with more than 1.5 billion points. The first dataset takes Lashagou NO. 3 landslide in Gansu Province, China, as the research object; the point cloud data were collected on 26 February 2021 and 3 May 2021. The registration accuracy was 0.003 m based on the permanent triangular pyramid target and 0.005 m based on the total station orientation. The landslide deforms within 3 cm due to the ablation of the frozen soil. The second dataset is TLS data from the Lihua landslide in Chongqing, China, collected on 20 April 2021 and 1 May 2021. The overall deformation of the Lihua landslide is small, with a maximum value of 0.011 m. The result shows that the proposed method achieves a better performance than previous sphere-based registration and that the weighted least square regularization iterative solution can effectively reduce the ill-condition of the model. Full article

The monitoring of impervious surfaces in urban areas using remote sensing with fine spatial and temporal resolutions is crucial for monitoring urban development and environmental changes in urban areas. Spatiotemporal super-resolution mapping (STSRM) fuses fine-spatial-coarse-temporal remote sensing data with coarse-spatial-fine-temporal data, allowing for urban impervious surface mapping at both fine-spatial and fine-temporal resolutions. The STSRM involves two main steps: unmixing the coarse-spatial-fine-temporal remote sensing data to class fraction images, and downscaling the fraction images to sub-pixel land cover maps. Yet, challenges exist in each step when applying STSRM in mapping impervious surfaces. First, the impervious surfaces have high spectral variability (i.e., high intra-class and low inter-class variability), which impacts the accurate extraction of sub-pixel scale impervious surface fractions. Second, downscaling the fraction images to sub-pixel land cover maps is an ill-posed problem and would bring great uncertainty and error in the predictions. This paper proposed a new Spatiotemporal Continuous Impervious Surface Mapping (STCISM) method to deal with these challenges in fusing Landsat and Google Earth imagery. The STCISM used the Multiple Endmember Spectral Mixture Analysis and the Fisher Discriminant Analysis to minimize the within-class variability and maximize the between-class variability to reduce the spectral unmixing uncertainty. In addition, the STCISM adopted a new temporal consistency check model to incorporate temporal contextual information to reduce the uncertainty in the time-series impervious surface prediction maps. Unlike the traditional temporal consistency check model that assumed the impervious-to-pervious conversion is unlikely to happen, the new model allowed the bidirectional conversions between pervious and impervious surfaces. The temporal consistency check was used as a post-procession method to correct the errors in the prediction maps. The proposed STCISM method was used to predict time-series impervious surface maps at 5 m resolution of Google Earth image at the Landsat frequency. The results showed that the proposed STCISM outperformed the STSRM model without using the temporal consistency check and the STSRM model using the temporal consistency check based on the unidirectional pervious-to-impervious surface conversion rule. Full article