We propose a stable reconstruction method for polynomial splines from compressive samples based on the maximum a
posteriori (MAP) estimation. The polynomial splines are one of the most powerful tools for modeling signals in real
applications. Since such signals are not band-limited, the classical sampling theorem cannot be applied to them. However,
splines can be regarded as signals with finite rate of innovation and therefore be perfectly reconstructed from noiseless
samples acquired at, approximately, the rate of innovation. In noisy case, the conventional approach exploits Cadzow
denoising. Our approach based on the MAP estimation reconstructs the signals more stably than not only the conventional
approach but also a maximum likelihood estimation. We show the effectiveness of the proposed method by applying it to
compressive sampling of vehicular signals.