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.