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Incomplete data is an important problem in the data analysis of all areas. There have been a number of applications related to inpainting problem which are intriguing. In these papers mathematical theory of shearlet and wavelet transforms related to inpainting problem are studied and numerical application results are compared, and several inpainting methods are applied to images with vertical, square and random masking. In one of these studies the suggested undone problems includes applying circular masking. In this paper following this suggestion, firstly circular masking with arbitrary radius is developed and applied to images, then shearlet and wavelet transforms are applied to images with circular masking to recover the images. Numerical results show that shearlets are able to inpaint larger gaps than wavelets in the circular masking case.

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