## 3 Compression Standards
### Image Compression Standards  
In our experiments we have tested the performance of standard image compression schemes as well. As in [PERSON]'s work, we have evaluated lossless JPEG2000, JBIG and JPEG-LS. In addition, we have examined results for CALIC and different modes for lossless JPEG2000. While [PERSON] _et al_. tested only the JJ2000 implementation using the default parameter selections of DWT, with 5 decomposition levels and 33 quality layers, we have also evaluated the performance with 0 to 5 decomposition levels and the same number of quality layers with both the JJ2000 and Kakadu implementations. We show in Table 6 an updated version of the data that we have previously provided [49]. As in the case of the general compression schemes, results are obtained by dividing the total number of bits of the compressed images by the total number of pixels of the original images. \begin{table}
\begin{tabular}{l c c c} \hline
**Image set** & **Images** & **Size (px)** & **Average entropy (bpp)** \\ MicroZip & 3 & \(>1,800\times 1,900\) & 9.831 \\ Yeast & 109 & \(1,024\times 1,024\) & 6.628 \\ ApoA1 & 32 & \(1,044\times 1,041\) & 11.033 \\ ISREC & 14 & \(1,000\times 1,000\) & 10.435 \\ Stanford & 20 & \(>2,000\times 2,000\) & 8.293 \\ Arizona & 6 & \(4,400\times 13,800\) & 9.306 \\ \hline \end{tabular}
\end{table} 
Table 4: Image sets used in the literature and in this work. All images are 16 bpp. \begin{table}
\begin{tabular}{l c c c c c c} \hline
**Algorithm** & **MicroZip** & **Yeast** & **ApoA1** & **ISREC** & **Stanford** & **Arizona** \\ \hline Gzip (LZ77) & **11.426** & 7.548 & **12.711** & **12.462** & **9.813** & **11.032** \\ AC (16-bit symbols) & 11.011 & **7.688** & 12.531 & 12.011 & 9.564 & 10.398 \\ XZ (LZMA2) & 9.696 & 6.385 & 11.321 & 11.015 & 8.163 & 9.284 \\ Bzip2 & **9.394** & **6.075** & **11.067** & **10.921** & **7.867** & **8.944** \\ \hline \end{tabular}
\end{table} 
Table 5: Lossless compression results in bpp for general (not image compressors nor microarray-specific) entropy coders and individual image compression, using the best compression invocation parameters, obtained by the authors. All images are 16 bpp. Best results are highlighted in **green** and worst results in **red**. We have obtained essentially identical results as in [PERSON] _et al._'s work for the cases on which they have reported. Very similar results for all sets are obtained when using the Kakadu implementation with the same parameter choices used for JJ2000. In general, increasing the number of wavelet decomposition levels improves compression performance by approximately \(0.5\) bpp. The only exception is the Yeast set, where using 0 decomposition levels yields \(32.33\%\) better results than using 5 decomposition levels. A possible explanation is that the original images from the Yeast set contain less than \(6\%\) of all the possible intensities for a \(16\) bpp image, but applying one level of DWT produces three times as many different coefficient values and increases the entropy by more than 2 bits. CALIC and JPEG-LS prediction-based schemes perform better than all the other non-specific schemes on all image sets except for the Yeast set, where JPEG2000 with 0 decomposition levels and JBIG significantly outperform CALIC in more than \(23\%\). The best image compressor for each set is between \(2.86\%\) and \(5.25\%\) better than Bzip2, the best generic compressor. [PERSON]'s algorithm performs \(12.81\%\), \(10.45\%\) and \(11.85\%\) better than the best non-microarray-specific technique for the MicroZip, ApoA1 and ISREC sets, respectively.