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.

Detection of level shifts in a noisy signal, or trend break detection, is a problem that appears in several research fields, from biophysics to optics and economics. Although many algorithms have been developed to deal with such a problem, accurate and low-complexity trend break detection is still an active topic of research. The Linearized Bregman Iterations have been recently presented as a low-complexity and computationally efficient algorithm to tackle this problem, with a formidable structure that could benefit immensely from hardware implementation. In this work, a hardware architecture of the Linearized Bregman Iteration algorithm is presented and tested on a Field Programmable Gate Array (FPGA). The hardware is synthesized in different-sized FPGAs, and the percentage of used hardware, as well as the maximum frequency enabled by the design, indicate that an approximately 100 gain factor in processing time, concerning the software implementation, can be achieved. This represents a tremendous advantage in using a dedicated unit for trend break detection applications. The proposed architecture is compared with a state-of-the-art hardware structure for sparse estimation, and the results indicate that its performance concerning trend break detection is much more pronounced while, at the same time, being the indicated solution for long datasets.

Supervision of the physical layer of optical networks is an extremely relevant subject. To detect fiber faults, single-ended solutions, such as the optical time-domain reflectometry (OTDR), allow for precise measurements of fault profiles. Combining the OTDR with a signal processing approach for high-dimensional sparse parameter estimation allows for automated and reliable results in reduced time. In this paper, a measurement system composed of a photon-counting OTDR data acquisition unit and a processing unit based on a linearized Bregman iterations' algorithm for automatic fault finding is proposed. An in-depth comparative study of the proposed algorithm's fault-finding prowess in the presence of noise is presented. Characteristics, such as sensitivity, specificity, processing time, and complexity, are analyzed in simulated environments. Real-life measurements that are conducted using the photon-counting OTDR subsystem for data acquisition and the linearized Bregman-based processing unit for automated data analysis demonstrated accurate results. It is concluded that the proposed measurement system is particularly well-suited to the task of fault finding. The natural characteristic of the algorithm fosters embedding the solution in digital hardware, allowing for reduced costs and processing time.