## 2 State of the Art of DNA Microarray Image Compression
### Entropy Coding
#### 2.4.1 Segmentation Based Coding  
DNA microarray images are usually segmented into spot and background pixels as part of the preprocessing stage to exploit their different statistical properties. Segmentation is always performed when extracting genetic information. Particular specific segmentation proposals have been discussed in Section 2.1. Several techniques that exploit this segmentation in their coding stage are presented next. In 2002 and in 2003 [PERSON] _et al_. [13,29] presented a lossy-to-lossless compression scheme called SLOCO, a version of the LOCO-I algorithm, the basis of the JPEG-LS standard. After griding and segmentation, the image is divided into multiple rectangular subblocks, one for each spot. In this way, each spot can be accessed and sent independently and with different quality. For each spot subblock, two subimages are created: one where the background has been set to the spot mean value (the spot subimage), and another where the foreground has been set to the estimation of the background value so that the subimages have more homogeneous pixel intensities. Then each of the images is processed with SLOCO, which uses prediction in the spatial domain [31]. An important contribution of SLOCO is the use of an adaptive quantizer (UQ-adjust instead of UQ) that permits variable error per pixel \(\delta\) so that spot pixels with higher intensities can be expressed with lower precision. [PERSON] _et al_. proposed both a scalar and a L1-norm vector quantizer (L1 VQ), whose errors can be bitplane-encoded to obtain progressive lossy-to-lossless compression. In 2003, [PERSON] _et al_. presented a prediction-based lossless compression technique [12]. The image is gridded in rectangular subblocks, and spot centers are then estimated. For each of the subblocks, a spiral path is created to transform the 2D sequence into a 1D one. A linear prediction scheme that uses neighbor pixel intensities and their distances to the spot center is then applied on the 1D sequence. Differences between consecutive prediction errors form a sequence that is adaptive Huffman coded after being split on the index that minimizes the expected length of the coded sequences. In 2004, [PERSON] _et al_. presented microarray BASICA software [15] and proposed a progressive lossy-to-lossless compression scheme. In their work, they first grid and segment the image. After that, they separate each of the subblocks into foreground and background and then code them with a modified version of the EBCOT algorithm, the basis of the JPEG2000 standard [32]. The main modification to EBCOT is an adaptation of the original context modeling, which allows a better handling of the irregular shapes of the foreground and background subimages. Bit shifts are also performed when coding the foreground so that the most relevant information is sent first in this progressive scheme. Also in 2004, [PERSON] and [PERSON] presented their MicroZip software [14], which offers both lossless and lossy compression. In their work, the image is first gridded and segmented into foreground and background. Then each of the \(16\)-bit streams is divided into two 8-bit substreams comprising the most and least significant bytes. The four resulting substreams are losslessly coded except for the LSB of the background, which can be compressed either losslessly or with loss. Lossless coding is done usingthe Burrows-Wheeler Transform [26], originally designed for text compression, which reduces the total entropy by computing all permutations of a given channel and then sorting them lexicographically. Lossy coding is done with the SPIHT algorithm [33]. In 2006, [PERSON] _et al_. presented their lossless compression MACE (Micro Array Compression and Extraction) software [17]. In their work, high and low intensity pixels are separated using a simple threshold-based method to exploit the fact that intensity distribution in microarray images is very skewed. One image is generated for the low intensity pixels, and another for the high intensity ones.