For the archiving of mammograms, the FDA requires lossless image compression. Using near-lossless compressors for temporary examination of medical images could be advantageous “if the interpreting physician deems that acceptable”. However, the FDA [1] states, “we do not believe there is consensus on what loss of information is acceptable”. To address this concern, we present a new near-lossless compression algorithm for grayscale medical images that guarantees a minimum PSNR value.

For secure and efficient transmission or storage, data files are commonly compressed and encrypted. In this work, we introduce a cost-effective encryption method of files as a built-in component of a lossless compression algorithm, thus avoiding the added cost of employing two separate processes. We have shown in earlier studies that preprocessing data with Burrows-Wheeler Transformation followed by Inversion Ranking transformation in advance of the utilization of an entropy coder resulted in an extremely effective general-purpose lossless compression technique [1], [2]. During the compression process, we encrypt the frequency vector of the Inversion Ranking transformation and transmit it along with the compressed data. Since the frequency vector is required for decompression, no further encryption is necessary to secure the compressed file, see Figure 1.

This work introduces a new technique for lossless compression of color images. The technique is composed of first transforming an RGB image into luminance and chrominance domain (Y CuCv). Then, the luminance channel Y is compressed with a context-based, adaptive, lossless image coding technique (CALIC). After processing the chrominance channels with a hierarchical prediction technique that was introduced by Kim and Cho, Burrows-Wheeler Inversion Coder (BWIC) or JPEG 2000 is used to compress of the chrominance channels Cu and Cv. It is demonstrated that, on a wide variety of images, particularly on medical images, the technique achieves substantial compression gains over other well-known compression schemes such as CALIC, JPEG 2000, LOCO-I, BPG(HEVC), and the previously proposed hierarchical prediction and context adaptive coding technique LCIC.

DNA microarray images are used to identify and monitor gene activity, or expression. In this study, we investigate the performance of the inversion coding technique in lossless compression of DNA microarray images. We show that inversion coding outperforms commonly used entropy coders and generic image compressors.

In this work, we propose a new method, a modified pseudo-distance technique, for color-mapped image compression. There are several techniques that yield better compression results than GIF and PNG; however, some algorithms require two passes on the image data, while some do not run in linear time. Unlike these methods, the pseudo-distance technique requires one pass and runs in linear time.

Summary form only given. We expand the theoretical foundations of LPSA (lexical permutation sorting algorithm) (see Arnavut, Z., and Magliveras, S.S., The Computer Journal, vol.40, no.5, pp.292-5, 1997) from permutations to multiset permutations (data strings) and give the general theory behind the BWT combinatorially. We then show the information theoretic relationship between interval ranks and canonical sorting permutations. Finally, we explore the relationship between inversion ranks and recency ranks and present improved compression results over other BSC (binary symmetric channel) coders, such as Bzip and Szip.

Motivated by the move-to-front (MTF) coder's (recency ranking) utilization of small size permutations which are restricted to the data source's alphabet size, we investigate compression of data files by using the canonical sorting permutations from the set of {0,...,n}, where n is the size of a data source, followed by inversion coding. We show that the inversion coding (ranking) technique introduced yields better compression gain than the recency ranking (MTF coder) for almost all the test data files. Furthermore, we investigate replacement of MTF coder in the block sorting schemes and show that when inversion coding is used after the BWT transformation, it yields better compression gains on average than the well-known block sorting techniques such as Bzip, Bks98 and Szip-b.

[Summary form only given]. Introduced by Bentley et al (1986), move-to-front (MTF) coding is an adaptive, self-organizing list (permutation) technique. Motivated with the MTF coder's utilization of small size permutations which are restricted to the data source's alphabet size, we investigate compression of data files by using the canonical sorting permutations followed by permutation based inversion coding (PBIC) from the set of {0, ..., n-1}, where n is the size of the data source. The technique introduced yields better compression gain than the MTF coder and improves the compression gain in block sorting techniques.

Summary form only given. The Block Sorting Lossless Data Compression Algorithm (BSLDCA) described by Burrows and Wheeler (1994) has received considerable attention. BSLDCA achieves compression ratio closer to PPM, but with a faster execution speed than PPM. Arnavut and Magliveras (1997) described the theoretical basis for block sorting schemes in the case of permutations and introduced the Lexical Permutation Sorting Algorithm (LPSA). This paper, generalizes the theoretical foundations of block sorting schemes to the multiset permutations (data strings). By expanding the theoretical foundations of LPSA from permutations to multiset permutations (data strings), we introduce a different block transformation, linear order transformation (LOT), and delineate its relationship to the Burrows Wheeler transformation (BWT). We show that LOT is faster than BWT, and for certain data types, such as pseudo-color images, LOT transformation followed by the MTF coder, yields the same amount of compression.

Multispectral images, such as Thematic Mapper (TM) images, have high spectral correlation among some bands. These bands also have different dynamic ranges. Hence, when linear predictive techniques employed to exploit the spectral and spatial correlation among the bands of a TM image, the variance of the prediction errors becomes greater. Markas and Reif (1993), have used histogram equalization (modification) techniques for lossy compression of multispectral images. In general, histogram equalization techniques are not reversible. However, by defining a monotonically increasing transformation, so that two adjacent gray values will not map to the same gray value of the transformed image, and selecting a target image with a wider probability density function than the source image, one can define a reversible mapping. We introduce a distinct reversible remapping scheme which utilizes sorting permutations. This technique differs from histogram equalization. It is a reversible transformation. We show that, by utilizing the remapping technique introduced and employing linear predictive techniques on a pair of bands, one can achieve better lossless compression than the results reported previously.

The block sorting lossless data compression algorithm (BSLDCA) described by Burrows and Wheeler (1994) has received considerable attention. It achieves as good compression rates as context-based methods, such as PPM, but at execution speeds closer to Ziv-Lempel techniques. This paper, describes the lexical permutation sorting algorithm (LPSA), its theoretical basis, and delineates its relationship to the BSLDCA. In particular we describe how the BSLDCA can be reduced to the LPSA and show how the LPSA could give better results than the BSLDCA when transmitting permutations. We also introduce a new technique, inversion frequencies, and show that it does as well as move-to-front (MTF) coding when there is locality of reference in the data.

Summary form only given. Linear prediction schemes, such as JPEG or BJPEG, are simple and normally result in a significant reduction in source entropy. Occasionally the entropy of the prediction error becomes greater than that of the original image. Such situations frequently occur when the image data has discrete gray-levels located within certain intervals. To alleviate this problem, various authors have suggested different methods. However, the techniques reported require two-pass algorithms. In this paper, we give a one-pass algorithm based on inversions of a multiset permutation. We obtain comparable results when we applied JPEG and even better results when we applied BJPEG on preprocessed image, which is treated as a multiset permutation. Lehmer [1964] describes a relatively short method for recovering a permutation /spl pi/ from its inversion vector. Lehmer-type inversion methods may create more compact data (which has a lower dynamic range, with respect to the original data). We extend the definition of Lehmer-type inversions from permutations to multiset permutations in a similar manner. We give algorithms that generate inversion vectors of multiset permutations and then methods for recovering a multiset permutation from a corresponding inversion vector [Arnavut, 1995]. Results obtained from some images (green band) of the USC-database are shown.