Optimized sampling distribution based on nonparametric learning for improved compressive sensing performance

In this work, an optimized nonparametric learning approach for obtaining the data-guided sampling distribution is proposed, where a probability density function (pdf) is learned in a nonparametric manner based on past measurements from similar types of signals. This learned sampling distribution is then used to better optimize the sampling process based on the underlying signal characteristics. A realization of this stochastic learning approach for compressive sensing of imaging data is introduced via a stochastic Monte Carlo optimization strategy to learn a nonparametric sampling distribution based on visual saliency. Experiments were performed using different types of signals such as fluorescence microscopy images and laser range measurements. Results show that the proposed optimized sampling method which is based on nonparametric stochastic learning outperforms significantly the previously proposed approach. The proposed method is achieves higher reconstruction signal to noise ratios at the same compression rates across all tested types of signals.