Adaptive Compressive Sensing for Reconstruction and Denoising with Sparsity-Measure-Driven Sampling

This study proposes a compressive sensing-based approach for adaptive reconstruction and denoising of wireless signals. By employing a dynamic sampling strategy, the approach adjusts the sampling rate according to the complexity of the signal region, as determined by the $\ell_{1}$-norm - more samples are used to reconstruct occupied regions while less samples are used for the less occupied ones. Applied to multiple, overlapping frequency hopping spread spectrum signals corrupted by Gaussian noise, this approach not only recover the signal but also helps in noise reduction, leading to an improvement in the signal-to-noise ratio. Results highlight its potential for interference mitigation and adaptive spectrum management in wireless systems.