Recursive two dimensional spectral estimation based on an AR model excited by a T-distribution process using QR decomposition approach

In this paper a robust two dimensional spectral estimation based on an AR model is proposed. The robustness of the method is obtained by assuming that the output or the residual signal has an independently and identically distribution with a t probability density function. By doing so, the effect of large amplitude residuals can be reduced. To reduce the calculation burden, the optimal solution is recursively calculated by incorporating the QR-decomposition method. The simulation results show that the obtained spectral estimate after 100 by 100 pixels iterations by using small α; i.e. α=3; is more accurate than that obtained by using large α; i.e. α=∞. The plots of the mean square error (MSE) to the iteration number show that by using small α we can obtain a smaller MSE than that by using large α