DNA microarrays are one of the fastest-growing new technologies in the field of genetic research, and DNA microarray images continue to grow in number and size. Since analysis techniques are under active and ongoing development, storage, transmission and sharing of DNA microarray images need be addressed, with compression playing a significant role. However, existing lossless coding algorithms yield only limited compression performance (compression ratios below 2:1), whereas lossy coding methods may introduce unacceptable distortions in the analysis process. This work introduces a novel Relative Quantizer (RQ), which employs non-uniform quantization intervals designed for improved compression while bounding the impact on the DNA microarray analysis. This quantizer constrains the maximum relative error introduced into quantized imagery, devoting higher precision to pixels critical to the analysis process. For suitable parameter choices, the resulting variations in the DNA microarray analysis are less than half of those inherent to the experimental variability. Experimental results reveal that appropriate analysis can still be performed for average compression ratios exceeding 4.5:1.