Learning Dynamic Compressive Sensing Models

Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming probability when incoming data can be sparsely represented with a fixed number of components, which is one of the drawbacks of CS frameworks because the signal sparsity in many dynamic systems changes over time. We present a new CS framework that handles signals without the fixed sparsity assumption by incorporating the distribution of signal sparsity. We show that the signal recovery success in our beta distribution modeling is more accurate than the success probability analysis in the CS framework. Alternatively, the success or failure of signal recovery can be relaxed, and the numbers of components included in signal recoveries can be represented with a probability distribution. We show this distribution is skewed to the right and naturally represented by the gamma distribution. Experimental results confirm the accuracy of our modeling in the context of dynamic signal sparsity.