Medical Image Based On Discrete Cosine Transform Biology Essay

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As we know, medical imaging needs storage area of large quantities of digitized clinical data. Because of the constrained bandwidth and storage capacity, a medical image should be compressed before transmission and storage. Hence, this research proposes to utilize DCT as compression method. This method operates with the values of DCT coefficients of 8x8 pixels block of an image and was proposed based on different quantization values. For each DCT coefficient of the block allows the energy compaction between original and reconstructed images. The quality of medical images are also validated based on MSE and PSNR using different quantization values.

Image compression plays a critical role in telematics applications especially in telemedicine. It is desired that either single images or sequences of images can be transmitted over computer networks at large distances so as that they could be used in a multitude of purposes. For instance, it is necessary that medical images to be transmitted are reliable, improved and fast medical diagnosis that need to be performed by many centres could be facilitated. For the purpose, image compression is an important study. On the other hand, in several applications reside on the fact that, while high compression rates are desired, the applicability of the reconstructed images rely on if some significant characteristics of the original images are conserved after the compression process is completed.

In this paper, it is aimed to implement DCT as a method for compression. The Discrete Cosine Transform (DCT) is a mathematical function that transforms digital image data from the spatial domain to the frequency domain [7] [12]. JPEG process is a widely used form of lossy image compression that centres on the DCT. DCT convert images from time-domain to frequency domain to de-correlate pixels. The DCT transformation is reversible. The general equation for a two- dimension transformation of DCT and IDCT is defined by the following equation;




Where for were Defined as;

Besides that, f (x,y) defined a pixel value in the spatial domain and C (u,v) defined as the DCT coefficients in the frequency domain.

The DCT works by separating images into parts of differing frequencies. During a step called quantization, where part of compression actually occurs, the less important frequencies are discarded, hence the use of the term "lossy". Then, only the most important frequencies that remain are used retrieve the image in the decompression process. The goals of this research are to validate the effectiveness of DCT for image compression via the different quantization values compared with the normal DCT. MATLAB programming will be used to develop the algorithm.


A. Medical Image Compression by Sampling DCT Coefficients

Today many researchers tried to improve compression of the medical images. In previous studies, Wu [2] used subjective and objective measurement for assessing compression algorithm in his research. Wu used an adaptive algorithm of sampling by calculating the difference between right places and has previously said a decision on the significant coefficients. Transmission of the significant coefficients achieved the goal of compression technique. On the decoder side, a linear is employed to reconstruct the coefficients between two sequent significant coefficients. This method is found to maintain information fidelity while reducing the amount of data. Wu states that PSNR has been used widely for quality measure in image compression.

B. Image Compression Using Discrete Cosine Transform

Nageswara Rao Thota and Srinivasa Kumar Devireddy [7] implement the basic JPEG compression using only basic MATLAB functions. In this paper, the lossy compression techniques have been used where data loss cannot affect the image clarity in this area. Image compression addresses the problem of reducing the amount of data required to represent a digital image. It also reduces the storage area to load an image. For this goal, they used JPEG. JPEG is a still frame compression standard, which is based on, the Discrete Cosine Transform and it is also enough for most compression applications.

C. DCT Quantization Noise in Compressed Images

Mark A. Robertson and Robert L. Stevenson [16] provide a spatial domain model of the quantization error based on a statistical noise model of the error introduced when quantizing the DCT coefficients. The resulting theoretically derived spatial domain quantization noise model shows that in general the compression noise in the spatial domain are both correlated and spatially varying. More importantly, the proposed noise model can be incorporated in a post-processing algorithm that correctly incorporates the spatial correction of the quantize error.


Figure 3.1: Normal DCT

Figure 3.1 shows the process of normal DCT that compressed using full rows that separated from full columns. As a result in normal DCT (50%) provides almost identical reconstruction in all images and the reconstructed block will still be the same as the original block. Hence, we shall soon see, these levels of distortion can be adjusted with adding the quantization values during the DCT compression stage.

Figure 3.3: Methodology of Project

The detailed process can be described in Figure 3.3. In this part, for efficiency analysis of the compression, a set of six medical images with same pixel size (256x256) pixels have been used. The six medical images were to 256 x256 pixels as shown in Figure 3.4.

Figure 3.4: Medical Images were used

After that, the medical images will be compressed for DCT compression. The DCT coefficients located in the upper left positions contain most of the information of the image block. The highest intensity of the images indicates as the most significant information. Then, these DCT coefficients were applied to represent the features of the block. Besides that, a scale function was used to quantize and adjusted these DCT coefficients. The scale function is defined as below;


Where 0 ≤ 1, j ≤ 7, and α is the position number

The parameter α is used to quantize the significant DCT coefficients. The different α value will used to compare the quality when used a different quantization values. We can obtained a new reconstructed DCT coefficient matrix C′′ (i, j) by adopting the above scale function. Finally, DCT transformation was used to transform each adjusted DCT block into 8Ã-8 pixels.


In this section, results and discussions are presented to demonstrate the proposed method. The simulation was carried out on a MATLAB program.

A block of 8 x 8 (Figure6)

The DCT coefficients (Figure6)

(c) The adjusted DCT coefficients (Figure6)

Figure 4.1: DCT and the adjusted DCT coefficients examples

Figure 4.1 (a) shows a block of 8 x8 pixels extracted from a real image. The small variations from sample to sample indicate the domination of low spatial frequencies. Figure 4.1 (b) shows the resulting DCT coefficients. Except for a few of the lowest frequency coefficients, the amplitudes are quite small. After that, the scale function was used to adjust ten of the significant DCT coefficients. The quantization value, α= 2. The adjusted DCT coefficients are as shown in Figure 4.1 (c).

Figure 4.2: The Reconstructed Images after DCT with quantization values, α=2, 4, 6 and 8 (Figure6).

Figure 4.2 showed the reconstructed images after DCT with quantization values α=2, 4, 6 and 8. Thus, from the Figure 4.1, when the value of α was increased, the extracted features will be able to survive under high JPEG lossy compression. Nevertheless, the image quality of the compression medical images will be decreased at the same time. As given in Equation 3, this is because the increased of quantization value, α will enlarge the variety of the DCT coefficients. Besides that, when quantization value, α was decreased, then the quality of images of the compression medical images will be increased.

The MSE values and PSNR for these images also were calculated and compared. The PSNR and MSE most commonly used distortion measures in image compression. The Peak Signal to Noise Rate (PSNR) is used to evaluate the image quality, and the following equation defined the PSNR computation as followed;


Where the 255 is the peak image amplitude and Mean Square Error (MSE) for an NÃ-N gray-level image is;


Here denotes an original pixel value, and denotes the corresponding decoded pixel value. Here x means the original image size while means the compressed image size. MSE is one of the techniques to quantify the difference between original images and reconstructed image and to measure the average of the errors that occurred in image. The MSE and PSNR in the reconstructed image were calculated and compared for each case.

Table 4.1: The MSE of the reconstructed images for normal DCT (50%) and MSE of the reconstructed images with the different quantization values α=2, 4, 6and 8

Table 4.1showed the value of Mean Square Error (MSE) for normal DCT based on 50% compression rate and the value of Mean Square Error (MSE) for each reconstructed images with the different quantization values α=2, 4, 6 and 8. The best image for normal DCT (50%) and proposed method is Figure 6 because this image has lower MSE. At the proposed method, the errors will increase when the value of α is increased.

Figure 4.4: MSE versus Quantization Values

Then, the graph was obtained from the Mean Square Error (MSE) versus the Quantization Values to show the best quantization values were used. Besides that, MSE represents the power of noise or the difference between original and compression images. The graph Figure 4.4 below shows the increasing of error value when it quantized at α=8. The higher value of α affected the increasing of error in reconstructed images.

Table 4.2: The PSNR of the reconstructed images for DCT normal (50%) and The PSNR of the reconstructed images with the different quantization values α=2, 4, 6and 8

Table 4.2 shows the value of Peak Signal to Noise Ratio (PSNR) for normal DCT based on 50% compression rate and the PSNR for the reconstructed images with the different quantization values α=2, 4, 6 and 8. The best image for normal DCT (50%) and the proposed method is Figure6. Besides that, the quantization value, α=2 is the best quantization value because consists the higher value of PSNR. It can conclude that the PSNR of the normal DCT is lower than the PSNR of proposed method.

Figure 4.5: PSNR versus Quantization Values

Then, the Figure 4.5 obtained from the PSNR versus the different quantization values to shows which one medical image has the better images quality. Figure 6 shows the best quality of image rather than others image because it has the largest value of PNSR. The best quality of image consists the higher value of PNSR and this value will increase when the value of α is reduced. It can conclude that, the larger PSNR is the better the image quality.

Figure 4.6: Correlated images using different quantization values

The energy compaction shown too analysed where the intensities are very high. Figure 4.6 showed the energy compaction for image (Figure6) using different alpha, α. Figure 4.6 (a) and 4.6 (b) shows the top left corner where the intensities are very high. This low frequency, which is the high intensities coefficients carry the most important coefficient in the frequency matrices and carry most information about the original image. So, the energy of the correlated image was packed into the low frequency region. Figure 4.6 (c) and 4.6 (d) shows the images with increasing high frequency and spatial content. Therefore, the transform coefficients are spread over low and high frequencies.


From these results, it can be concluded that the medical images based on the normal DCT method usually affect the quality of the decompressed images. So, with different quantization values it will show which images with better image quality. The best quality of image consists the higher value of PNSR and this value will increase when the value of α is reduced. The best quality of image contained the higher value of PNSR. Experimental results showed that the qualities of the recovered images have been significantly improved. Thus, it can say that the proposed method is indeed feasible and efficient.