Introduction

Image compression is fundamental to the efficient and cost-effective use of digital medical imaging technology and applications. There are two methods of image compression: lossless compression enables an exact reproduction of the original image from the compressed file. However, this scheme achieves relatively low compression rates of about 3:1. The second, lossy compression eliminates the redundant and high frequency data from an image, which is usually outside the range of human visual perception. This results in much higher compression ratios, typically 20:1 or greater, but with some data loss [₈].

There are a number of techniques or compression algorithms for producing lossy or lossless images, it is quite important that the method used is based on an adopted medical imaging standard. Standards ensure simplified and long-term interoperability with other imaging devices; they also minimize the risk of diagnostic data being rendered obsolete over time [₃]. Digital Imaging and Communications in Medicine (DICOM) is a medical imaging standard for all imaging modalities. The DICOM standard supports RLE (Run Length Encoding) lossless compression, and JPEG lossy compression for both static and dynamic clips. RLE lossless compression is good for static images, typically achieving ratios of 3:1 for grayscale images [₅]. A variety of lossy compression techniques are available, some of them standardized e.g., JPEG has the advantage of being available as commercial products, but also has the disadvantage of creating block artifacts at respectable compression ratios, i.e., over 10:1. This is a consequence of its 8 x 8 discrete cosine transform (DCT) coding scheme [₇].

Most current research efforts in lossy compression that appear promising involve the discrete wavelet transform (DWT), after the pioneering work by Dubieties [₂]. The reasons for this are that the DWT operates on the whole image as a single block thereby avoiding blocking artifacts typical in JPEG, while dynamically adjusting its spatial/frequency resolution to the appropriate level in various regions of the image. Wavelet compression methods appear to perform better than JPEG, particularly for large-matrix images such as radiographs using the dual pathology approach, compression ratios as high as 80:1[₁]. The goal of this paper is to compare Wavelet and JPEG lossy compression methods applied to a set of CT images using Wavelet Compression Engine (standard edition 2.5) available at [₁₀], and JPEG wizard version (1.1.7) available at [₆]. The size of each image before compression is 512x512 x 8 bit.

Implementation

Techniques commonly employed for image compression result in some degradation of the reconstructed image. A widely used measure of reconstructed image fidelity for an N x M size image is the mean square error (MSE) is given by [₉].

Figure 1

Where f (i, j) is the original image data and is the compressed image value. Signal-to-Noise Ratio (SNR) is widely used in the signal processing literature (since it is related to the signal power and noise power), and is perhaps more meaningful because it gives 0 dB for equal signal and noise power. SNR is used more commonly in the image-coding field. So, the SNR that is used corresponding to the above error is defined as

Figure 2

Another quantitative measure is the peak signal-to-noise ratio (PSNR), based on the root mean square error of the reconstructed image. The formula for PSNR is given by

Figure 3

where RMSE, is calculated as

Figure 4

Values for these quantities were obtained using LuraWave Smart Compression software (version 1.7.1) available at [₄].

Materials and Methods

By using the formulas in the previous section, some parameters were calculated for JPEG and Wavelet respectively. Signal-to-Noise-Ratio (SNR) measures are estimates of the quality of a reconstructed image compared with the original image. Mean square error (MSE) is the cumulative squared error between original and compressed image. Lower value of MSE means lesser error, and these values give higher peak signal-to-noise ratio (PSNR). Peak signal-to-noise ratio (PSNR) is another qualitative measure based on the root-mean-square-error of the reconstructed image. In our study we calculate the compression ratio, MSE, SNR, and PSNR for various sets of CT images: - 18,20,17 image sequence for brain, chest and abdomen respectively.

Results and Discussion

Figure 1 shows three different CT images, which are brain, chest, and abdomen. Tables 1, and 2, represent the results for compression ratio (CR), MSE, SNR, and PSNR for CT-brain by using JPEG and Wavelet compression. This result was also plotted in Fig. 2, 3, and 4. The results for chest and abdomen images are given in Tables 3 - 6 respectively. This result was also plotted in Fig. 5 - 10. The comparisons between the results are given in Table 7.

Figure 5

Figure 1: (A) CT-brain image, (B) CT- chest image, and (C) CT-abdomen image

Figure 6

Table 1: Analysis of CT-brain images by using JPEG

Figure 7

Figure 8

Table 2: Analysis of CT-brain images by using Wavelet compression

Figure 9

Figure 2: Compression ratio against CT-brain image sequence for JPEG and Wavelet compression

Figure 10

Figure 3: MSE against CT-brain image sequence for JPEG and Wavelet compression

Figure 11

Figure 4: SNR against CT-brain image sequence for JPEG and Wavelet compression

Figure 12

Table 3: Analysis of CT-chest images by using JPEG

Figure 13

Table 4: Analysis of CT-chest images by using Wavelet compression

Figure 14

Figure 5: Compression ratio against CT-chest image sequence for JPEG and Wavelet compression

Figure 15

Figure 6: MSE against CT-chest image sequence for JPEG and Wavelet compression

Figure 16

Figure 7: SNR against CT-chest image sequence for JPEG and Wavelet compression

Figure 17

Table 5: Analysis of CT-abdomen images by using JPEG

Figure 18

Figure 19

Table 6. Analysis of CT-abdomen images by using Wavelet compression

Figure 20

Figure 21

Figure 8: Compression ratio against CT-abdomen image sequence for JPEG and Wavelet compression

Figure 22

Figure 9: MSE against CT-abdomen image sequence for JPEG and Wavelet compression

Figure 23

Figure 10: SNR against CT-abdomen image sequence for JPEG and Wavelet compression

Figure 24

Table 7: Comparison between different CT image sequence (brain, chest, and abdomen) by using JPEG and Wavelet compression

Conclusion

From the results of this study we conclude that the Wavelet compression can be used at higher compression ratios before information loss than JPEG for CT images. The Wavelet algorithm introduces less image errors, which yields higher PSNR for low bit rate. We have shown that in terms of image quality, the Wavelet algorithm is either equivalent or better than JPEG for these images.

Our results illustrate that we can achieve higher compression ratios for brain than chest and abdomen images and that the anatomical structure and its complexity have an effect on image compression. Furthermore we also observe that by using JPEG, for chest and abdomen images the PSNR values obtained were higher than those achieved by using Wavelet compression. For a lower compression ratio, JPEG yielded higher quality image than Wavelet compression. From the numerical values obtained we observe that for chest and abdomen images the PSNR is equal to 24dB for compression ratio up to 31:1by using JPEG, whereas for brain image the PSNR is equal to 22 to 34 dB for compression ratio between 52 to 240:1 by using Wavelet compression.

The degree of compression is dependent on anatomic structures and complexity of diagnostic information in the image so careful consideration must be given to the level of compression ratio before archiving clinical images otherwise essential information will be lost.