Optimal Recovery Algorithms Research Articles

Efficient Metadata Management in Block-Level CDP System for Cyber Security

Continuous Data Protection (CDP) is an emerging scheme of data backup and recovery for Cyber Security. Compared with traditional data protection techniques, it can provide much higher reliability and allow the data state to be reverted to any point-in-time in the past. CDP continuously captures and logs every disk update, producing large amount of information, thus desperately requires an efficient mechanism of organizing such information (about the disk I/Os) in order to guarantee the performance to be acceptable. However, there are few works which address the organization of history data to improve the recovery efficiency in case of the disaster occurrences. In this paper, three methods of metadata management for Cyber Security are presented, of which two are simple implementations based on MySQL database (named DIR_MySQL and OPT_MySQL respectively) and the other one is designed with consideration of its characteristics. Experimental results show that META_CDP method is far more efficient than the other two and its performance is reasonably acceptable. Furthermore, we discuss in-depth two recovery algorithms, which are full-recovery and incremental recovery. Users can choose the optimal recovery algorithm based on the required recovery time point.

Data Assimilation in Reduced Modeling

This paper considers the problem of optimal recovery of an element u of a Hilbert spaceH from measurements of the form ‘j(u), j = 1;:::;m, where the ‘j are known linear functionals on H. Problems of this type are well studied [18] and usually are carried out under an assumption that u belongs to a prescribed model class, typically a known compact subset ofH. Motivated by reduced modeling for solving parametric partial dierential equations, this paper considers another setting where the additional information about u is in the form of how well u can be approximated by a certain known subspaceVn ofH of dimensionn, or more generally, in the form of how well u can be approximated by each of a sequence of nested subspaces V0 V1 Vn with each Vk of dimension k. A recovery algorithm for the one-space formulation was proposed in [16]. Their algorithm is proven, in the present paper, to be optimal. It is also shown how the recovery problem for the one-space problem, has a simple formulation, if certain favorable bases are chosen to represent Vn and the measurements. The major contribution of the present paper is to analyze the multi-space case. It is shown that, in this multi-space case, the set of all u that satisfy the given information can be described as the intersection of a family of known ellipsoids in H. It follows that a near optimal recovery algorithm in the multi-space problem is provided by identifying any point in this intersection. It is easy to see that the accuracy of recovery of u in the multi-space setting can be much better than in the one-space problems. Two iterative algorithms based on alternating projections are proposed for recovery in the multi-space problem and one of them is analyzed in detail. This analysis includes an a posteriori estimate for the performance of the iterates. These a posteriori estimates can serve both as a stopping criteria in the algorithm and also as a method to derive convergence rates. Since the limit of the algorithm is a point in the intersection of the aforementioned ellipsoids, it provides a near optimal recovery for u.

Joint Spectra of Toeplitz Operators and Optimal Recovery of Analytic Functions

We consider optimal recovery problems in weighted Bergman spaces in the unit ball of ℂ k . It is shown that if corresponding measures are Carleson and not compactly supported, the optimal recovery algorithm is a limit of optimal recovery algorithms corresponding to truncated problems with compactly supported measures. We also express the Lagrange equation for the dual problem in terms of joint spectra of Toeplitz operators induced by information measures and use this expression for proving that the regularity condition in the dual problem is stable. Examples in the last section illustrate our results.

Super-resolution using neural networks based on the optimal recovery theory

An optimal recovery based neural-network super resolution algorithm is developed. The proposed method is computationally less expensive and outputs images with high subjective quality, compared with previous neural-network or optimal recovery algorithms. It is evaluated on classical SR test images with both generic and specialized training sets, and compared with other state-of-the-art methods. Results show that our algorithm is among the state-of-the-art, both in quality and efficiency.

Systems of equations fo zonal wavefront recovery in adaptive optics

The basic results obtained in the present work may be stated as follows: 1) a method of obtaining the analytical solution of the systems of difference equations arising in problems of zonal wavefront recovery is described; the expressions obtained may be used for a noniterative algorithm of solution of the given systems; 2) the possibility of choosing an optimal recovery algorithm in accordance with the system characteristics of the adaptive instrument and the phase fluctuations of the detectable field is shown; 3) analytical expressions are obtained for the recovery error due to measurement noise, depending on the dimension of the mass of recovered phase values; the agreement between Eqs. (24), (26), and (28) and the results of numerical solution of the given systems in [10, 11] is complete.