Abstract <p>A method for compressing multidimensional discrete arrays is studied. Based on the reduction of the extremum of post-extrapolation residuals, the method can be used to handle video and image arrays. The compression algorithm calculates post-extrapolation residuals for all samples of an initial multidimensional discrete array and then roughens these residuals to reduce the required capacity of a storage system and raise the data transmission rate. The method allows more reliable control of discrepancy between the original multidimensional discrete array and its unpacked version by reducing the extremum of roughened post-extrapolation residuals. Computer simulations validate that the use of the reduction of the extremum of post-extrapolation residuals increases the efficiency of the multidimensional data compression algorithm. The experiments also demonstrate the approach to be more efficient than other popular algorithms used for the compression of multidimensional discrete-data arrays.</p>