Gaussian Hermite polynomial based lossless medical image compression
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Gaussian Hermite polynomial based lossless medical image compression S. N. Kumar1 · A. Ahilan2 · Ajay Kumar Haridhas3 · Jins Sebastian1 Received: 4 April 2020 / Accepted: 25 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The role of compression is inevitable in the storage and transmission of medical images. The polynomial based image compression is proposed in this work for the compression of abdomen CT medical images. The input images are preprocessed by min–max normalization; the pixels are scanned and subjected to polynomial approximation. The polynomial approximated coefficients are subjected to llyods quantization and encoded by arithmetic coder. The medical image compression using Gaussian Hermite polynomial gives superior results when compared with the legendre polynomial based image compression and JPEG lossless compression techniques in terms of Peak to signal noise ratio (PSNR), Mean square Error (MSE) and other picture quality metrics. The algorithms are tested on real-time DICOM abdomen CT image and can be used for data transfer in teleradiology application. Keywords Image compression · Legendre Polynomial · Hermite polynomial · JPEG lossless compression
1 Introduction Image compression is a technique by which large images are represented in compressed form by less number of bits and the original image is generated during the decoding process. The key feature of an image compression algorithm is to minimize the redundancies thereby lowering the storage requirements and cost of communication [1, 2]. The reduction in storage requirement improves the storage capacity of media and thereby the bandwidth of the data transmission increases. The image compression techniques are broadly classified into two categories: lossy and lossless models. In the lossless model, Communicated by Y. Zhang. * S. N. Kumar [email protected] A. Ahilan [email protected] Ajay Kumar Haridhas [email protected] 1
Amal Jyothi College of Engineering, Kanjirappally, Kerala, India
2
Infant Jesus College of Engineering, Tirunelveli, India
3
Mar Ephraem College of Engineering and Technology, Elavuvilai, India
the reconstructed image has superior quality since there is no loss of information, where as in lossy compression technique, the reconstructed image has loss of information. In [3], a detailed survey has been done on the applications of discrete legendre polynomials for engineering applications. The discrete Legendre polynomials {Pm(k, n)}, where m = 0, 1, 2, ..., n is the degree of the polynomial, at discrete interval k = 0, 1, 2, ..., n; is defined as follows N ∑
Pm(K, N)Pi(K, N) = 0 for m = 0
(1)
k=0
The polynomial representation of images gains importance in the interpolation, geometric transformation and spatial features extraction. The coefficients are obtained by applying separable linear transform and the coefficients are estimated from the inversion of two Vandermonde matrixes [4]. The 2D autoregressive model was employed for the linear p
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