Stochastic Formulation of (a,b,c,d)-Bandlimited Signal Reconstruction

Many reconstruction algorithms for bandlimited signals associated with linear canonical transform have been proposed. However, these reconstruction algorithms have assumed a deterministic signal with no noise. This assumption is almost never satisfied in real applications. Deterministic formulations do not accurately describe the random nature of the reconstruction problem when the signal is best considered as a random process, possibly corrupted by noise. In this paper, we formulate the reconstruction problem of bandlimited signal associated with linear canonical transform within a stochastic framework. A stochastic, minimum mean squared error reconstruction algorithm from noisy observations is proposed, from which four commonly used reconstruction algorithms for different stochastic models are derived. By the derived algorithms, the relationship between the theories for the stochastic and deterministic cases is clarified. The relationship between the theories for the noise-free and noisy cases is also clarified.