Example use:
$im = new Imagick("mypicture.jpg");
$ctype = $im->getImageCompression();
if($ctype == Imagick::COMPRESSION_ZIP) echo "PNG file!";
if($ctype == Imagick::COMPRESSION_JPEG) echo "JPG file!";
if($ctype == Imagick::COMPRESSION_LZW) echo "GIF file!";
All options:
COMPRESSION_UNDEFINED
COMPRESSION_NO
COMPRESSION_BZIP
COMPRESSION_FAX
COMPRESSION_GROUP4
COMPRESSION_JPEG
COMPRESSION_JPEG2000
COMPRESSION_LOSSLESSJPEG
COMPRESSION_LZW
COMPRESSION_RLE
COMPRESSION_ZIP
COMPRESSION_DXT1
COMPRESSION_DXT3
COMPRESSION_DXT5
COMPRESSION_ZIPS
COMPRESSION_PIZ
COMPRESSION_PXR24
COMPRESSION_B44
COMPRESSION_B44A
COMPRESSION_LZMA
COMPRESSION_JBIG1
COMPRESSION_JBIG2
The numbers for which those constants stand differ by version. So always use the constants.