How to identify the binary compression type from the content?

I am trying to restore files which are stored in MS SQL database (used by third party application which has stopped their support) as an image data type(byte arrays). So what I do is to write those rows of byte arrays to file to convert for know file extensions. However some of them are not known which I believe they are compressed. Since I get "CC_Compress" string and random characters in the file after conversion. I was wondering if it is possible to find out which compression method were used and how can I decompress it before I convert them.

Thanks in advance,