Optimized measurements for kernel compressive sensing

Certain classes of signals can be well approximated using a few principal components in the feature space, that is obtained by a non-linear transformation of the input signal space. Compressive sensing of such signals with random measurements can be performed using the kernel trick. In this paper, we propose a procedure to compute optimized measurement vectors for kernel compressive sensing. We show that the optimized measurements correspond to the data samples that have the highest energy when projected onto the kernel principal components. Simulation results obtained with handwritten digits and the sculpted faces dataset show that the proposed measurement system results in a substantially better recovery when compared to using the same number of random measurements.