During the past ten years Genetics and especially molecular Genetics have been the subject of many transformations. The advent of microarray technology is one of the causes of these improvements. Microarray is a powerful tool for analysis and study of the behavior of thousands of genes in a concurrent manner. Furthermore, microarray has had a great role in discovery of many diseases and finding of treatment for these diseases. The outcome a microarray experiment is a large image with a size of 2000x5000 pixels. The high cost of experimentations and the need to share these images in data bases have exacerbated the importance of compression of these images. Due to specific characteristics of microarray images usual compression techniques do not show good performance in compressing these images. A number of software and hardware techniques have been proposed for compression of microarray images. These techniques have applied both lossless and lossy methods. In this thesis three techniques are proposed which are capable of controlling the loss level and consequently control the compression ratio of the algorithms. All three algorithms segment an image into spots and background regions. The spots regions are compressed in a lossless manner while background is compressed by lossy methods. In the first proposed method the compression is performed without considering spatial correlations among image pixels through quantization of histogram bins. The second method uses a trellis to exploit spatial correlation among neighboring pixels for better compression of an image. The third proposed algorithm improves the strategy of the second algorithm and obtains better results.