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The JPEG compression method is one of the most popular compression schemes. There are many hardware and software systems based on the JPEG compression standard.This is an indication that the format is still very important before these systems become outdate. This paper presents an adaptive regression method applied to the standard JPEG compression for archiving higher compression ratios. Besides,an interesting coding scheme, Golomb-Rice coding, is introduced also for improve the JPEG standard. Since the coding scheme is not based on frequency analysis from certain of images to gain a codebook, the decoded images that are encoded with this scheme are assured in average quality. The standard JPEG compression scheme can import these two for higher compression rates or wider application fields.