A Novel Approach to Sparse Histogram Image Lossless Compression Using Jpeg2000

Abstract

In this paper a novel approach to the compression of sparse histogram images is proposed. First, we define a sparsity index which gives hints on the relationship between the mathematical concept of matrix sparsity and the visual information of pixel distribution. We use this index to better understand the scope of our approach and its preferred field of applicability, and to evaluate the performance. We present two algorithms which modify one of the coding steps of the JPEG2000 standard for lossless image compression. A theoretical study of the gain referring to the standard is given. Experimental results on well standardized images of the literature confirm the expectations, especially for high sparse images.

Two-Layer Lossless HDR Coding Using Histogram Packing Technique with Backward Compatibility to JPEG

“…For image signals having such sparseness, it is well known that the histogram packing technique improves lossless compression performance [24][25][26][27][28][29]. In Refs.…”

“…In Refs. [11,12,[22][23][24][25][26][27][28][29][30], the sparseness of a histogram of an image is used for efficient compression. 'Sparse' histogram means that not all the bins in a histogram are utilized.…”

Lossy compression of sparse histogram image

“…Even though this lossless mapping does not reduce the 1st order entropy itself, it does reduce data volume of sparse images when it is combined with a lossless coding as illustrated in Fig.2 [4,5]. However it has been limited to 'lossless', and therefore the bit rate can't be controlled.…”

“…8 bit per pixel which is equivalent to 2 8 available tones for a pixel). In this case, the sparseness in histogram has been becoming a new point of view to be considered [3][4][5]. Due to huge variety of available tone slots, not all the bins in a histogram are utilized in general.…”

“…It maps a set of original values into another set so that the sparse histogram becomes dense. It contributes to reduce data volume in combination with a lossless coding based a transform or a prediction [4,5]. However, it has been limited to 'lossless', so far.…”