Auto-Regressive (AR) modeling has a broad range of applications in signal processing. An auto-regressive operator utilizes the time history of a signal to extract important information hidden in the signal. It has been widely utilized in the area of spectrum estimation, as well as signal filtering.<br>One of the main applications of AR modeling is signal prediction. Spitz (1991) and Porsani (1999) used AR modeling to interpolate the regularly sampled seismic records in the spatial direction. Also, Naghizadeh and Sacchi (2007a) introduced the Multi-Step Auto-Regressive (MSAR) algorithm in order to reconstruct nonuniformly sampled data in the spatial direction. The latter is a novel way of applying AR operation with jumping steps in the low frequency portion of the data in an attempt to extract AR operators for the high frequency portion. The extracted Prediction Filter (PF) for each frequency is then used as a regularization term to reconstruct the missing spatial samples.<br>In this paper we investigate the performance of MSAR algorithm for more than one spatial direction. First, in the theory section, an optimality proof of multidimensional (MD) MSAR algorithm is discussed. Then a practical implementation of MSAR using simple flowcharts is discussed. Finally, synthetic and real data examples of application of MSAR are shown.


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