FPGA-embedded Linearized Bregman Iteration algorithm for trend break detection

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.