Source Recovery of Underdetermined Blind Source Separation Based on Modified Shortest Path Algorithm

Shortest path algorithm is a simple algorithm used for source recovery of underdetermined blind source separation (UBSS), but this algorithm is only applicable to the case where the number of sensors is two. However, in most real-life scenarios, the number of sensors is more than two. Then we proposed a smoothing method to improve the shortest path algorithm. The main thought is as follows: assume the number of sensors ism, select two adjacent observed signals to form a combination each time, then m — 1 kinds of combination are generated. As to each combination, recover their source signals by using the traditional shortest path algorithm, and m —1 groups of recovered source signals are derived, and then average the sum of all the corresponding signal values of m —1 groups. To verify the modified shortest path algorithm, simulations are performed when source signals are sufficiently sparse and insufficiently sparse respectively, and results show that the modified algorithm proposed in this paper is applicable when the number of sensors is two or more. The modified method enriches the tools that can be utilized for underdetermined source signal recovery.