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In the case of astronomical observations from the surface of the Earth, it is difficult to obtain high resolution images due to the distorting influence of the atmosphere. There are two groups of methods for mitigating this influence. The first group does not interfere with the process of image formation and is related to the processing of already recorded images. The methods from the second group involve constructing special observational instruments. Placing the instrument outside the atmosphere may also be considered a method from this group. In this case, there is no atmospheric influence, and acquisition of images with diffraction-limited resolution is assumed to be possible without additional effort. The factors that may lead to phase distortions during observations with an orbital multimirror telescope are discussed. The total phase accumulation method is proposed for removing the distortions. The method is designed for compensating for the distortion of Fourier component phases caused by the Earth's atmosphere. Assumptions as to the statistics of phase distortions used in its development are quite general and do not interfere with its application to space observations. Computer modeling is used to demonstrate the technique effectiveness and study its capabilities in processing images from a multimirror space telescope. The use of modeling as an instrument for research is motivated by the high cost and complexity of the real experiment and the necessity of having a true image of an object for evaluating the method error. The aperture configuration of the upcoming James Webb Telescope is used for modeling. The modeling was used to explain the different behavior of phase distortions between space observations and observations from the Earth's surface. It is demonstrated that, in case of space observations, the total phase accumulation is required instead of the main phase values' accumulation. It is found that the dependence of the reconstruction error on the number of accumulated images is nonmonotonic. [ABSTRACT FROM AUTHOR]