In this paper, new methods to eliminate boundary artifacts for overlapping trigonometric bases used in image compression are introduced. By applying overlapping cosine-sine-II bases to images instead of non-overlapping cosine-II bases used in the JPEG algorithm, block artifacts can be reduced. In contrast to non-overlapping transforms, an extension of the signal at the signal bounds is necessary. To prevent boundary artifacts in the reconstructed image, the symmetric periodic extension is preferred in image coding. The cosine-II and sine-II basis functions are symmetric, but nevertheless a conventional symmetric periodic extension is not possible, because different basis functions are used in adjacent intervals. In this paper, we derive weighting functions to make the symmetric periodic extension for these bases possible. We show, that compared to the periodic extension, no visible artifacts appear in the reconstructed image if our new approach is used. In addition, we show that the adaptation of the basis functions at the signal boundaries leads to a better quality of the reconstructed signal.