Compressive Pattern Matching on Multispectral Data

We introduce a new constrained minimization problem that performs template and pattern detection on a multispectral image in a compressive sensing context. We use an original minimization problem from Guo and Osher that uses L₁ minimization techniques to perform template detection in a multispectral image. We first adapt this minimization problem to work with compressive sensing data. Then, we extend it to perform pattern detection using a formal transform called the specialization along a pattern. That extension brings out the problem of measurement reconstruction. We introduce shifted measurements that allow us to reconstruct all measurement with a small overhead, and we give an optimality constraint for simple patterns. We present numerical results showing the performances of the original minimization problem and the compressed ones with different measurement rates and applied on remotely sensed data.