Stockwell Transform Based Medical Image Compression
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Date
2017-11
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Addis Ababa University
Abstract
Image compression is achieved by reducing the redundant and irrelevant data so that the number of bits to represent each image pixel array is reduced. This could be achieved by using transform coding. Images can be transformed from one domain to a different type of representation using some well-known transform. Different types of linear transforms exist in this regard. The Fourier transform and cosine transform are few examples. Multiresolution analysis is becoming important in image analysis and signal processing as it gives resolution on both frequency and time domains, which is not the case in the Fourier and cosine transforms. Wavelet Transform (WT) is the earlies multiresolution member and was proposed on various image processing fields, JPEG2000 image compression tool uses WT. But due to the lack of the absolutely referenced frequency and phase information and sensitivity to noise the application area of WT is limited. The Stockwell transform (S-Transform) is another proposed multiresolution transform that offers the absolutely-referenced frequency and phase information. There exists a very direct relationship between the S-transform and the natural Fourier transform and the S-transform is always invertible. Such advantages of the S-transform inspired many researchers to navigate very useful applications of the transform in different disciplines. But S-transform redundantly doubles the dimension of the original data set making computation expensive and hence the Discrete Orthonormal Stockwell Transform (DOST) was proposed. DOST is a pared-down version of the fully redundant S-transform which reduces the computational cost without changing its multiresolution nature and the absolutely-referenced frequency and phase information.
The proposed image compression scheme in this thesis uses JPEG 2000 image compression scheme as a bench mark. As S-transform outperforms the WT in some useful aspects, WT that is used in the JPEG2000 scheme is replaced by the DOST and a new algorithm has been developed. Compression Ratio (CR), Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index (SSIM) were used to quantify the performance of the proposed compression scheme. Results showed that the DOST allows effective and efficient image compression and outperforms other transform-based approaches including those that makes use of the discrete cosine as well as wavelet transforms. The proposed algorithm has been tested on images acquired from freely available research database and offered an average PSNR, CR, MSE and SSIM of 47.0099, 50.6031, 8.0097 and 0.9295 respectively. In comparison, WT offered an average PSNR, CR, MSE and SSIM of 42.9151, 49.8519, 8.2633 and 0.9108 respectively.
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Keywords
Medical Image, Stockwell, Compression