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The detection, identification, and adaptation method based on data snooping (DIA-datasnooping) is commonly used to deal with outliers in the Gauss–Markov model. However, the application of DIA-datasnooping might be limited in case of multiple outliers. In this contribution, the Maximum a posteriori (MAP) estimate is applied to the DIA framework, and a DIA method based on MAP (DIA-MAP) is proposed. Based on the prior distribution of gross errors, DIA-MAP chooses the hypothesis with the maximum posterior probability to conduct the detection and identification of outliers. To this end, a hyperparameter determination method based on supervised learning is proposed to find suitable priors for gross errors. With the priors of gross error, DIA-MAP provides a unified DIA process for both single and multiple outliers. Also, the prior can be flexibly adjusted rather than fixed to be uniform, so that the DIA method can be adapted to different application cases. Finally, a set of new evaluation indices for the DIA method with multiple outliers is defined, including True Positive Rate (TPR) which describes the detectability for outliers and True Negative Rate (TNR) which denotes the acceptance ability for inliers. Experimental results of GNSS positioning examples verified that the performance of the proposed DIA-MAP method is superior to the conventional used methods when dealing with multiple outliers. [ABSTRACT FROM AUTHOR]

In this paper, a simultaneous MAP-based video denoising and rate-distortion optimized video encoding algorithm is proposed. We begin with formulating the denoising problem as a maximum a posteriori (MAP) estimate problem. Then, according to the Bayes rule, we show that the MAP estimate is determined by two terms: noise conditional density model and priori conditional density model. Based on the assumptions that the noise satisfies Gaussian distribution and the priori model is measured by the bit-rate, the MAP estimate can be expressed as a rate distortion optimization problem. With this, we are able to simultaneously perform MAP-based video denoising and rate-distortion optimized video encoding under some assumptions. Moreover, we describe in details how to select suitable coding parameters, i.e., quantization parameter, mode, motion vector, reference index, and regularization parameter. Finally, we conduct several experiments to verify our proposed algorithm. [ABSTRACT FROM AUTHOR]