Convergence and Optimality of Adaptive Regularization for Ill-posed Deconvolution Problems in Infinite Spaces

The adaptive regularization method is first proposed by Ryzhikov et al. in [6] for the deconvolution in elimination of multiples which appear frequently in geoscience and remote sensing. They have done experiments to show that this method is very effective. This method is better than the Tikhonov regularization in the sense that it is adaptive, i.e., it automatically eliminates the small eigenvalues of the operator when the operator is near singular. In this paper, we give theoretical analysis about the adaptive regularization. We introduce an a priori strategy and an a posteriori strategy for choosing the regularization parameter, and prove regularities of the adaptive regularization for both strategies. For the former, we show that the order of the convergence rate can approach O（｜｜n｜｜^4v/4v＋1） for some 0 〈 v 〈 1, while for the latter, the order of the convergence rate can be at most O（｜｜n｜｜^2v/2v＋1） for some 0 〈 v 〈 1.

Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization for Hyperspectral Image Classification

Low-Rank and Sparse Representation(LRSR)method has gained popularity in Hyperspectral Image(HSI)processing.However,existing LRSR models rarely exploited spectral-spatial classification of HSI.In this paper,we proposed a novel Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization(LRSR-ANR)method for HSI classification.In the proposed method,we first represent the hyperspectral data via LRSR since it combines both sparsity and low-rankness to maintain global and local data structures simultaneously.The LRSR is optimized by using a mixed Gauss-Seidel and Jacobian Alternating Direction Method of Multipliers(M-ADMM),which converges faster than ADMM.Then to incorporate the spatial information,an ANR scheme is designed by combining Euclidean and Cosine distance metrics to reduce the mixed pixels within a neighborhood.Lastly,the predicted labels are determined by jointly considering the homogeneous pixels in the classification rule of the minimum reconstruction error.Experimental results based on three popular hyperspectral images demonstrate that the proposed method outperforms other related methods in terms of classification accuracy and generalization performance.

Magnetotelluric extremum boundary inversion based on different stabilizers and its application in a high radioactive waste repository site selection

Geophysical inversion under different stabilizers has different descriptions of the target body boundary,especially in complex geological structures.In this paper,we present an extremum boundary inversion algorithm based on different stabilizers for electrical interface recognition.Firstly,we use the smoothest and minimum-support stabilizing functional to study the applicability of adaptive regularization inversion algorithm.Then,an electrical interface recognition method based on different stabilizers is developed by introducing extremum boundary inversion algorithm.The testing shows that the adaptive regularization inversion method does work for different stabilizers and has a low dependence on the initial models.The ratio of the smooth and focusing upper and lower boundaries obtained using the extremum boundary inversion algorithm can clearly demarcate electrical interfaces.We apply the inversion algorithm to the magnetotelluric(MT)data collected from a preselected area of a high-level-waste clay-rock repository site in the Tamusu area.We recognized regional structures with smooth inversion and the local details with focusing inversion and determined the thickness of the target layer combined with the geological and drilling information,which meets the requirement for the site of the high-level waste clay-rock repository.

Ultrasound liver tumor segmentation using adaptively regularized kernel-based fuzzy C means with enhanced level set algorithm

Purpose-The purpose of this study is to develop a hybrid algorithm for segmenting tumor from ultrasound images of the liver.Design/methodology/approach-After collecting the ultrasound images,contrast-limited adaptive histogram equalization approach(CLAHE)is applied as preprocessing,in order to enhance the visual quality of the images that helps in better segmentation.Then,adaptively regularized kernel-based fuzzy C means(ARKFCM)is used to segment tumor from the enhanced image along with local ternary pattern combined with selective level set approaches.Findings-The proposed segmentation algorithm precisely segments the tumor portions from the enhanced images with lower computation cost.The proposed segmentation algorithm is compared with the existing algorithms and ground truth values in terms of Jaccard coefficient,dice coefficient,precision,Matthews correlation coefficient,f-score and accuracy.The experimental analysis shows that the proposed algorithm achieved 99.18% of accuracy and 92.17% of f-score value,which is better than the existing algorithms.Practical implications-From the experimental analysis,the proposed ARKFCM with enhanced level set algorithm obtained better performance in ultrasound liver tumor segmentation related to graph-based algorithm.However,the proposed algorithm showed 3.11% improvement in dice coefficient compared to graph-based algorithm.Originality/value-The image preprocessing is carried out using CLAHE algorithm.The preprocessed image is segmented by employing selective level set model and Local Ternary Pattern in ARKFCM algorithm.In this research,the proposed algorithm has advantages such as independence of clustering parameters,robustness in preserving the image details and optimal in finding the threshold value that effectively reduces the computational cost.