Methods and apparatus for decompressing a bit stream of compressed data representing a plurality of image blocks. This includes multi-step processing of data codes, e.g. DC and AC codes. For example, with respect to the processing of AC codes, a plurality of bits of compressed input data relating to the AC codes are first retrieved from the bit stream. A first decoding operation is then executed based on the obtained compressed input data in order to generate first output data. It is then determined the first coding operation was sufficiently correct. If it is determined that the first coding operation was sufficiently correct, the first output data is outputted. On the other hand, if it is determined that the first coding operation was not sufficiently correct, an alternate second decoding operation in executed in order to generate second output data.