First-order Stationary Markov Research Articles

Modified slant and modified slant Haar transforms for image data compression

Transform image processing is done in nonoverlapping blocks and a block of (4 × 4) or a (8 × 8) subpicture size is reasonable in terms of both mean-square error and subjective picture quality. It is therefore desirable to search for a fast transform which is efficient for data of small sequence length. This paper presents a modified slant and a modified slant Haar transform. Computational operations are increased by 2 additions and 4 multiplications only as compared to conventional slant and slant Haar transforms. Performance evaluation based on a first-order stationary Markov process signal such as variance distribution, mean-square error estimate due to scalar Wiener filtering of signal corrupted by white noise and decorrelation property establish the superiority of the transforms. Comparative study of results on a monochrome picture are encouraging.

More on least squares estimation of the transition matrix in a stationary first-order markov process from sample proportions data

Miller suggested ordinary least squares estimation of a constant transition matrix; Madansky proposed a relatively more efficient weighted least squares estimator which corrects for heteroscedasticity. In this paper an efficient generalized least squares estimator is derived which utilizes the entire covariance matrix of the distrubances. This estimator satisfies the condition that each row of the transition matrix must sum to unity. Madansky noted that estimates of the variances could be negative; a method for obtaining consistent non-negative estimates of the variances is suggested in this paper. The technique is applied to the hypothetical sample data used by Miller and Madansky.