Restoration of uncertain blurs using an error in variables criterion

In image-restoration problems involving a known blur, set-theoretic estimation provides an effective framework for incorporation of both noise statistics and a priori information. However, the sets formulated for use with known blurs are not suitable for situations involving unknown stochastic blurs. In this paper, new sets based on an error in variables criterion are developed, which are more appropriate for restoration of uncertain blurs. The conditions for convexity of these sets are rigorously established. Through 1-D simulations, the set-theoretic restoration scheme utilizing these sets is compared with the stochastic MMSE filter and with set-theoretic schemes for stochastic blurs developed earlier.