Nonlinear Compressed Sensing Based on Kernel Sparse Representation

The validity of the compressed sensing (CS) is premised on the sparsity of the signals. In general, a signal is sparse if it can be linearly represented by few column combinations of a certain basis matrix. However, when signals exhibit some complex structure, or in other words, are difficult or inconvenient to be linearly represented, existing many CS methods may suffer from poor performance. In this paper, by introducing a sample set and the widely used kernel trick to CS, we investigate a sample based nonlinear compressed sensing (SNCS) model. In particular, with the help of kernel trick, our SNCS model can capture the nonlinear sparse structure of signals, and hence leads to a better performance than that of the traditional CS. On the other hand, due to the introduction of sample set, our SNCS model performs again better than a recent emerged kernel trick compressed sensing (KTCS) model. What's more, the optimization problem induced by our SNCS model still keeps concise and is easily solved by traditional CS methods.