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This paper is intended to present a lossless image compression method based on multiple-tables arithmetic coding (MTAC) method to encode a gray-level image

With the rapid development of image processing and Internet technologies, a great number of digital images are being created every moment. Therefore, it is necessary to develop an effective image-compression method to reduce the storage space required to hold image data and to speed the image transmission over the Internet [

Image compression reduces the amount of data required to describe a digital image by removing the redundant data in the image. Lossless image compression deals with reducing coding redundancy and spatial redundancy. Coding redundancy consists in using variable-length codewords selected to match the statistics of the original source. The gray levels of some pixels in an image are more common than those of others–-that is, different gray levels occur with different probabilities–-so coding redundancy reduction uses shorter codewords for the more common gray levels and longer codewords for the less common gray levels. We call this process variable-length coding. This type of coding is always reversible and is usually implemented using look-up tables. Examples of image coding schemes that explore coding redundancy are the Huffman coding [

There exists a significant correlation among the neighbor pixels in an image, which may result spatial redundancy in data. Spatial redundancy reduction exploits the fact that the gray levels of the pixels in an image region are usually the same or almost the same. Methods, such as the LZ77, LZ88, and LZW methods, exploit the spatial redundancy in several ways, one of which is to predict the gray level of a pixel through the gray levels of its neighboring pixels [

To encode an image effectively, a statistical-model-based compression method needs precisely to predict the occurrence probabilities of the data patterns in the image. This paper proposes a lossless image compression method based on multiple-tables arithmetic coding (MTAC) method to encode a gray-level image.

A statistical-model-based compression method generally creates a code table to hold the probabilities of occurrence of all data patterns. The type of data pattern significantly affects the encoding efficiency when minimizing storage space. When the data come from different sources, it is difficult to find an appropriate code table to describe all the data. Therefore, this MTAC method categorizes the data and adopts distinct code tables that record the frequencies which the data patterns occur in different clusters.

The proposed MTAC method contains three approaches: median edge detector (MED) processing, base-switching transformation, and statistical-model-based compressing. This section introduces these three approaches.

Shannon's entropy equation can estimate the average minimum number of bits needed to encode a data pattern based on the frequency which the data pattern occurs in a data set [

It is impossible to encode the data set, in a lossless manner, with a bit rate higher than or equal to

Let

The scanning order of the MED in an image represented by

Part of the pixels in an image.

For

Let

The estimated error

Figure

Two gray-level images, Airplane and Baboon

Airplane

Baboon

According to formula (

The difference images and their histograms of Airplane and Baboon

Airplane

Baboon

Figure

The sign bit images of the images Airplane and Baboon.

Airplane

Baboon

The pixel values of

Figure

The MSB images of Airplane and Baboon.

Airplane

Baboon

The difference images and color histograms of Airplane and Baboon.

Airplane

Baboon

The gray level of a pixel in a gray-level image is generally represented by an 8-bit memory space. However, it is uneconomical if the gray levels of the pixels in a gray-level image are similar. Hence, the MTAC method adopts the base-switching transformation (BST) algorithm [

The BST algorithm partitions a difference image into small nonoverlapping image blocks, each consisting of

For each image block, the BST algorithm needs to hold only

An image block of

After the MED processing approach, image

The arithmetic coding algorithm [

Next, the MTAC method concatenates the gray-level differences of all the image blocks into a binary string

After the statistical-model-based compressing approach has been employed, the MTAC method concatenates

In the decompression phrase, the MTAC method first draws

The purpose of this section is to investigate the performance of the MTAC method by experiments. In these experiments, ten

Entropies of ten original images and their error images.

Image | Entropy rate of original image | Entropy rate of error image |
---|---|---|

Airplane | 6.529 | 3.567 |

Baboon | 7.224 | 5.091 |

Lena | 7.432 | 3.681 |

Toy | 6.748 | 3.123 |

Gold | 7.452 | 3.853 |

Sailboat | 7.248 | 4.126 |

Boat | 6.975 | 3.595 |

Barb | 7.647 | 4.557 |

Pepper | 7.570 | 3.535 |

Girl | 7.260 | 3.935 |

The testing images.

Airplane

Lena

Baboon

Gold

Sailboat

Boat

Toy

Barb

Pepper

Girl

In experiment 2, the arithmetic coding method is used to encode the sign bit images of the ten test images, where the bit length of each data pattern is 8 bits. Table

The size of the sign bit images and their compression data.

Image | Size of original image (bytes) | Size of compression data (bytes) |
---|---|---|

Airplane | 8192 | 8069 |

Baboon | 8192 | 8256 |

Lena | 8192 | 8187 |

Toy | 8192 | 8135 |

Gold | 8192 | 8169 |

Sailboat | 8192 | 8310 |

Boat | 8192 | 8152 |

Barb | 8192 | 8222 |

Pepper | 8192 | 8201 |

Girl | 8192 | 8296 |

Entropy rates of the difference images.

Image | Entropy rate |
---|---|

Airplane | 4.368 |

Baboon | 6.048 |

Lena | 4.527 |

Toy | 3.900 |

Gold | 4.742 |

Sailboat | 4.997 |

Boat | 4.396 |

Barb | 5.442 |

Pepper | 4.390 |

Girl | 4.801 |

The last experiment compares the performance of the MTAC method with that of the lossless JPEG2000 [

Bit rates (bits/pixel) obtained by the MTAC and lossless JPEG 2000.

Image | Method | |

MTAC | Lossless JPEG2000 | |

Airplane | 4.14 | 4.35 |

Lena | 4.20 | 4.25 |

Baboon | 6.10 | 6.11 |

Gold | 4.71 | 4.90 |

Sailboat | 4.88 | 5.10 |

Boat | 4.24 | 4.44 |

Toy | 3.90 | 4.16 |

Barb | 5.14 | |

Pepper | 4.34 | 4.43 |

Girl | 4.63 | 4.73 |

The difference image of Barb and its partial image.

This paper proposes the MTAC method to encode a gray-level image

The experimental results reveal that the MTAC method usually gives a better bit rate than the lossless JPEG2000 does, particularly for the images with small gray-level variations among adjacent pixels. However, when the gray-level variations among adjacent pixels in an image are very large, the MTAC method performs worse in terms of bit rate.