The confidential access to medical images becomes significant in recent years. In this paper, we propose two types of region-based selective encryption schemes to achieve secure access for medical images. The first scheme randomly flips a subset of the bits belonging to the coefficients in a Region of Interest inside of several wavelet sub-bands, which is performed in compression domain but only incurs little loss on compression efficiency. The second scheme employs AES to encrypt a certain region's data in the code-stream. The size of encrypted bit-stream is not changed and there is no compression overhead generated in the second scheme. Moreover, both of two schemes support backward compatibility so that an encryption-unaware format-compliant player can play the encrypted bit-stream directly without any crash.