Note: This article pertains to ArcGIS versions 8.x and 9.x. Later versions of ArcGIS may contain different functionality, as well as different names and locations for menus, commands and geoprocessing tools.
Yes, it is possible to project MrSID and JPEG images in ArcGIS; see Related Information, below, for methods to do this.
However, these images are special cases of rasters. While it is possible to convert these rasters to another format and project it, returning these rasters to the original format would further degrade the data. Recall that these formats use lossy compression schemes, so subsequent iterations of the process introduce larger and larger errors into the data.
If the original source data--before MrSID or JPEG compression has been applied--can be obtained, project that data before applying the compression. This allows the data to be in the desired coordinate system while minimizing the loss of data quality.