Profile-Splitting Linearized Bregman Iterations for Trend Break Detection Applications

Abstract

Trend break detection is a fundamental problem that materializes in many areas of applied science, where being able to identify correctly, and in a timely manner, trend breaks in a noisy signal plays a central role in the success of the application. The linearized Bregman iterations algorithm is one of the methodologies that can solve such a problem in practical computation times with a high level of accuracy and precision. In applications such as fault detection in optical fibers, the length N of the dataset to be processed by the algorithm, however, may render the total processing time impracticable, since there is a quadratic increase on the latter with respect to N. To overcome this problem, the herewith proposed profile-splitting methodology enables blocks of data to be processed simultaneously, with significant gains in processing time and comparable performance. A thorough analysis of the efficiency of the proposed methodology stipulates optimized parameters for individual hardware units implementing the profile-splitting. These results pave the way for high performance linearized Bregman iteration algorithm hardware implementations capable of efficiently dealing with large datasets.Electronics 2020, 9, 423 2 of 18 quadratic with respect to the dataset length N-which is demonstrated in Section 2-and the timing necessary for the algorithm to converge becomes eventually impracticable. Even though the TBD problem has a broad presence across different scientific fields, the application focus, in this document, will be given to fault detection in optical fiber profiles, in which trend breaks are associated with such faults [13,14]. In such an application, timely trend break detection results are sought so that mobile repair units can be quickly deployed and the downtime of the network can be kept as small as possible so as not to affect the network users greatly [15,16]. Simultaneously, datasets produced by optical fiber monitoring devices can contain several thousands of points [11].In this work, a new methodology to deal with high-dimensional TBD problems within the LBI framework is proposed. This is the profile-splitting method, where, instead of analyzing the profile as a single N-dimensional vector, the algorithm evaluates multiple M-dimensional vectors that, together, compose the original data. In Section 2, the combined 1 / 2 minimization cast as a TBD problem is presented, as well as the structure of the profile-splitting method. Even though the gain in timing arising from this approach can be easily demonstrated, two fundamental issues arise.The first issue regards the performance of the algorithm, which must be maintained in order for the method to be valid; otherwise, the method would be equivalent to sacrificing estimation performance for faster results, which could be achieved with different algorithms for even faster processing times [14]. Upholding the unmatched trend break detection prowess of the LBI [11,12] is, therefore, a crucial goal of the profile-splitting method, and the discussion and r...

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