Cardinality Constraint Non-Uniform Sampling for Maximizing Reconstruction Accuracy of Time-Varying Signals

Non-uniform sampling selects samples at irregular intervals for concise signal representation. Prior works on non-uniform sampling predominantly focused on maximizing reconstruction accuracy or optimizing sample size. However, a trade-off exists between the two factors, as increasing the sample size can improve the reconstruction accuracy, but it decreases the bandwidth efficiency. The reverse is true for under-sampling. Thus, it is important to balance the two factors. This motivates us to consider CAISOS, a CArdinalIty conStraint nOn-uniform Sampling problem that aims to select at most k sample points of a given time-varying signal such that the regenerated signal has the maximum reconstruction accuracy. Applications of CAISOS include fixed-rate sampling and signal compression in the time domain, such as in robotics and fixed-rate speech encoders. It proposes an integer linear programming model to address CAISOS and shows that the time complexity of the same increases exponentially with increasing signal size. It further proves that CAISOS is an NP-complete problem by showing that it is both NP and NP-hard by using a polynomial-time reduction from the 0/1 knapsack problem. Thus, the paper proposes a polynomial time heuristic based on the least-cost branch-and-bound approximation to solve CAISOS. Finally, it demonstrates the effectiveness of the proposed approaches through simulation by comparing them with the existing counterparts using various time-varying signals available in multiple databases.