Regularization approaches based on spectral filtering can be highly effective in solving ill-posed inverse problems. These methods, however, require computing the singular value decomposition (SVD) and choosing appropriate regularization parameters. These tasks can be prohibitively expensive for large-scale problems. In this paper, we present a framework that uses operator approximations to eff...

We examine several zero-range potentials in non-relativistic quantum mechanics. The study of such potentials requires regularization and renormalization. We contrast physical results obtained using dimensional regularization and cutoff schemes and show explicitly that in certain cases dimensional regularization fails to reproduce the results obtained using cutoff regularization. First we consid...

The area of mathematical inverse problems is quite broad and involves the qualitative and quantitative analysis of a wide variety of physical models. Applications include, for example, the problem of inverse heat conduction, image reconstruction, tomography, the inverse scattering problem, and the determination of unknown coefficients or boundary parameters appearing in partial differential equ...

Instead of the Tikhonov regularization method which with a scalar being the regularization parameter, Liu et al. [1] have proposed a novel regularization method with a vector as being the regularization parameter. As a continuation we further propose an optimally scaled vector regularization method (OSVRM) to solve the ill-posed linear problems, which is better than the Tikhonov regularization ...

The effectiveness of regularization to improve SNR in parallel imaging techniques has been reported in previous works [1-2], but how to optimize the regularization parameter remains a problem. The regularization parameter controls the degree of regularization and thereby determines the compromise between SNR and artifacts. Over-regularization causes high level of artifact, while under-regulariz...

آگاهی از میزان تاج‌پوشش درختان در مناطق شهری به‌علت تأثیرات آن کاهش آلودگی‌‌های هوا، آلودگی صوتی، جلوگیری باد، ذخیرة نزولات آسمانی، و کنترل رواناب‌های بسیار ضروری است. ازآن‌جا‌که استخراج با روش‌های دستی وقت‌گیر پرهزینه است، تکنیک‌های سنجش دور می‌توانند ابزار مناسبی برای تأمین این داده‌ها باشند. طبقه‌بندی شیء‌پایه، انتخاب پارامترهای بهینة قطعه‌بندی، به‌ویژه پارامتر مقیاس، اهمیت بسیاری دارد معمول...

We discuss the framework of Transductive Support Vector Machine (TSVM) from the perspective of the regularization strength induced by the unlabeled data. In this framework, SVM and TSVM can be regarded as a learning machine without regularization and one with full regularization from the unlabeled data, respectively. Therefore, to supplement this framework of the regularization strength, it is ...

In learning theory, the convergence issues of the regression problem are investigated with the least square Tikhonov regularization schemes in both the RKHS-norm and the L -norm. We consider the multi-penalized least square regularization scheme under the general source condition with the polynomial decay of the eigenvalues of the integral operator. One of the motivation for this work is to dis...