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An optimized medical image compression algorithm based on wavelet transform and improved vector quantization is introduced. The goal of the proposed method is to maintain the diagnostic-related information of the medical image at a high compression ratio. Wavelet transformation was first applied to the image. For the lowest-frequency subband of wavelet coefficients, a lossless compression method was exploited; for each of the high-frequency subbands, an optimized vector quantization with variable block size was implemented. In the novel vector quantization method, local fractal dimension (LFD) was used to analyze the local complexity of each wavelet coefficients, subband. Then an optimal quadtree method was employed to partition each wavelet coefficients, subband into several sizes of subblocks. After that, a modified

With the rapid development of modern medical industry, medical images play an important role in accurate diagnosis by physicians. However, the large amount of images put forward a high demand on the capacity of the storage devices. Besides, telemedicine is a development trend of medical industry, while narrow transmission bandwidth limits the development of this project. To solve the problems mentioned above, a large number of researches have been carried out into medical image compression.

Medical image compression approaches can simply be divided into two kinds: lossless compression and lossy compression. Lossless compression can reconstruct the original image completely identical. Lossy compression takes advantage of the human weak psychovisual effects to optimize compression results but loses certain image information [

VQ is an efficient information source coding method. The principle of it is constructing a vector based on several scalar data group, so the vector quantization coding is superior to scalar quantization coding. LBG algorithm was named after its proposers Linde et al. and afterwards there were many other improved methods [

This paper introduces a novel approach for medical image compression based on wavelet transformation and vector quantization, which could provide an efficient compression performance with good visual quality. In our scheme, as most energy of the original image concentrates in the lowest-frequency subband, we decompose the original image into one low frequency subimage and several high-frequency subimages using wavelet transformation The low-frequency subimage is manipulated with the Huffman coding as its information is very sensitive to human’s eyes. Information in high-pass octave bands is always the details or edges. According to the human visual system (HVS), the loss of this part will not be perceived. So, we process the high-frequency subimages with our proposed vector quantization approach.

In our scheme, an original image is first decomposed into multiresolution subimages through the wavelet transform; then, coefficients in the low-pass octave bands are encoded by the Huffman coding method while coefficients in each of the high-pass octave bands are encoded by the proposed novel vector quantization with variable block. The diagram of the proposed algorithm is shown in Figure

The diagram of the proposed algorithm.

The Huffman coding method is a common method in the field of image compression, so the introduction of this part is ignored. The optimized vector quantization with variable block size includes two steps. The first step is dividing the subimage into series of sub-blocks. The smooth areas of the coefficient matrix are divided into sub-blocks with a relatively large size, while those containing many details are divided into small-size sub-blocks. The metric of complexity is based on the value of local fractal dimension (LFD). In order to classify the local fractal dimension into predetermined classes, a method of discriminant analysis is applied [

Fractal dimension (FD) is a statistical quantity that gives an indication of how completely a fractal object appears to fill space. The value of FD has a strong relevance with the human judgment of surface roughness. In this sense, FD is an excellent tool in the field of image processing. The fractal dimension measurement cannot be derived exactly but must be estimated. In this paper, the blanket method [

where

while the surface area is measured as

On the other side, the area of a fractal surface behaves according to

Therefore, the

After the local complexity analysis of the subimage, a LFD mapping image is obtained. In the LFD mapping image, the pixel value of each point is the local fractal dimension of the corresponding pixel in the original subimage. According to the local fractal dimension, the image is divided into sub-blocks of different sizes. Because all the LFD values of the subimage are being decimal in the range of

In this paper, an optimized quadtree method is performed to decompose the subimage into several sizes of blocks. In order to understand the optimized quadtree method, the quadtree algorithm is first explained as follows.

Quadtree is a tree data structure which was named by Finkel and Bentley in 1974 [

During the process of variable block division, what sizes of block a pixel will be contained is not only depending on the priority of itself, but also on the priority of its surrounding pixels. So we can draw a conclusion that adjacency relationship is very important to each pixel. As for the whole sub-band, if we can find a good adjacency relationship for all pixels, the proportion of different sizes of image blocks will be changed and the quality of decoded subimage will also be changed. The purpose of the optimized quadtree is to select an excellent initial position to split the subimage, which will improve the compression ratio or boost the image quality at the same bit ratio.

In conventional quadtree method, the image is first divided into many initial sizes of sub-blocks from the first row to the last, from the first column to the last column, then the initial sub-blocks will continue to split. In the proposed technique, the initial split position will change regularly and then the best initial split position is chosen to process the initial division of the image. The novel method consists of two steps: statistics step and selection step. The schematic diagram of the optimized quadtree method is shown in Figure

Schematic diagram of the optimized quadtree method.

Assume that the size of the initial sub-block is denoted as

At each of the initial positions, variable block division is performed. And in this process, the numbers of different sizes of image blocks will be counted and the structural similarity (SSIM) between the division image and the LFD mapping image will be calculated. After that, the best initial position, which will lead to the largest summation of the structure similarity (SSIM) and the number of the smallest sub-blocks, will be chosen as the final initial split position to segment the subimage. The structure similarity will be introduced in detail in the following part. Structure similarity is a numerical in the interval of ^{5} before the operation mentioned above. The way to choose the best initial split position is defined by

Here,

The SSIM [

The SSIM separates the task of similarity measurement into three comparisons: luminance, contrast and structure. The SSIM between two images is defined by

where

In order to simplify the expression, we set

One disadvantage of the

A common used method to initialize codebook is the Forgy and Random Partition [

In this paper, we introduce a new method to set initial code vectors of the codebook, which is based on the energy of each sub-block. In the proposed method, we first calculate the energy of each sub-block. The energy function is defined as

To validate the performance of the proposed medical image compression algorithm, 30-pair liver CT digital imaging and communications in medicine (DICOM) images and brain CT DICOM images from a 64 row CT machine in a domestic large hospital were tested. The resolution of all the images is

After that, the LFD value of each high-frequency subband will be classified into three categories by the discriminant analysis approach, and then each sub-band is divided into

Liver CT images and brain CT images are used to test the proposed method. Figure

Comparison of the decoded images of the energy codebook and the random codebook at compression ratio around 10.

Original liver image

Decoded images encoded by the energy codebook

Decoded images encoded by the random codebook

Original brain image

Decoded images encoded by the energy codebook

Decoded images encoded by the random codebook

As shown in Figure

Average SSIM for liver images against compression ratio.

Average SSIM for head images against compression ratio.

As shown in Figures

In order to verify the effectiveness of our proposed algorithm, we compare our algorithm with several recent and conventional compression methods, such as DCT, Fisher’s fractal coding, JPEG, and JPEG2000. The corresponding contrast results are shown in Figure

Contrast of compression results at a compression ratio of 25.

Original image

Result of DCT

Result of JPEG

Result of JPEG2000

Result of Fisher’s fractal coding

Result of our proposed algorithm

As shown in Figure

We take peak signal-to-noise ratio (PSNR), mean squared error (MSE), the running time, and normalized cross-correlation (NCC) as four evaluation indexes to compare our proposed algorithm with the contrast methods. When the compression ratio is fixed to 25, the value of the above evaluation index is shown in Table

Evaluation index value of our proposed algorithm and some contrast algorithms with compression ratio of 25.

PSNR (dB) | Time (s) | MSE | NCC | |
---|---|---|---|---|

DCT | 27.24 | 13.22 | 37.12 | 0.9945 |

JPEG | 28.11 | 14.65 | 35.65 | 0.9950 |

JPEG2000 | 34.16 | 12.20 | 24.94 | 0.9988 |

Fisher’s method | 31.54 | 10.50 | 33.66 | 0.9968 |

The proposed method | 37.5 | 2.34 | 11.70 | 0.9996 |

As shown in Table

In this paper, we propose an optimized medical image compression algorithm based on wavelet transform and vector quantization with variable block size. We, respectively, manipulate the low-frequency components and high-frequency components with the Huffman coding and improved VQ by the aids of wavelet transformation. Although the implement of the proposed algorithm is more complex than some traditional medical image compression algorithms, it can compress an image with good visual quality with high compression ratio. Besides, in contrast with some traditional and current medical image compression algorithm, the proposed algorithm owns better performance through the evaluation index of PSNR, running time, MSE, and NCC.

This research is supported by the National Nature Science Foundation of China (no. 61272176, no. 60973071) and the Fundamental Research Funds for the Central Universities (no. 110718001).