1 Jyoti Sharma and Parveen Lehana, “Investigations of image compression using polynomial fitting of singular values,” International Journal of Scientific and Technical Advancements, Volume 1, Issue 4, pp. 1-5, 2015. International Journal of Scientific and Technical Advancements ISSN: 2454-1532 Investigations of Image Compression using Polynomial Fitting of the Singular Values Jyoti Sharma 1 , Parveen Lehana 2 1 Department of Computer Applications, Govt. College for Women, Gandhi Nagar, Jammu, J&K, India-180004 2 Department of Electronics, University of Jammu, Jammu, J & K, India-180006 Email address: 1 jyoti.vashisth@gmail.com Abstract— An image, though it appears simple, needs numerous pixel values to represent it. If the image may be represented using lesser number of parameters, the image may be easily processed, stored, and transmitted. There are several techniques for compression. For example, singular value decomposition (SVD), Eigen values based analysis, discrete cosine transform, wavelet based transform, etc. Although each of these techniques has been used extensively in literature, SVD has been shown more advantageous. In the present research, the variation of singular values is approximated by a polynomial and at the time of synthesis, singular values are computed from the polynomial whose coefficients are estimated at the time of analysis. The objective is to explore the use of polynomial fitting for representing the whole set of singular values. Because the polynomial equation may be represented using smaller number of coefficients, it may be expected that the proposed technique would reduce the size of the image leading to better compression ratio. Keywords— Digital images; eigen values; enhancement; principle component analysis; singular value decomposition. I. INTRODUCTION mages convey more information as compared to phrases used in textual or verbal communication[1]. An image is a function of two real variables, represented as f(x,y). Here, f is the intensity at (x,y) coordinate position, called the pixel [2]. When x, y and intensity values of f are finite discrete values, then the image is called as digital image [3]. The increasing use of images in medicine, education, remote sensing, and entertainment has led to vast image archives that requires effective management and retrieval strategies [4]. Image processing is carried out to enhance an image by applying some mathematical transformation for deriving desired parameters. Input image may be obtained from a still camera, frame of a video clip, or scanned photograph. Usually, image processing systems acquire two dimensional images and apply a specific processing method to enhance it [5]. The use of image processing techniques may improve or distort an image [6]. Image processing may be carried out on geometric figures and surfaces textures using the same technique [7]. Image processing involves several overlapping fields in computer engineering, image denoising, enhancement, and image compression being the mostly employed. Generally, the images contain noise because of defective devices, inefficient data gathering process, or natural disturbances. All these factors lower the quality of acquired image. Thus, the first step is to denoise the image. An improperly selected method for denoising may further degrade the image by introducing blurring of the image. In the recent years, a good amount of research has been carried out on image denoising using wavelet as it provides an efficient mechanism of denoising [8]. Image enhancement is the process of improving the image parameters so that better input can be provided to the image processing systems. It is used in a wide variety of fields including medical imaging, art studies, forensics, and atmospheric sciences. There are several methods to enhance a digital image without degrading its image quality. These techniques may generally be grouped into two classes: spatial domain methods and frequency domain methods. In spatial domain methods, the pixel values are manipulated to get desired processed image. In frequency domain, all the operations of image enhancement are executed on the Fourier transform of the image. After that, the inverse Fourier transform is performed to obtain the processed image. Wavelet based methods have also been investigated and these methods provide better results as compared to Fourier transform [9]. The enhancement operations may modify the image in terms of brightness, contrast, or the distribution of the grey levels [10]. The enhancement procedure makes pixel values more noticeable. As a result different objects can be easily identified in an image [11]. Image compression is a method to transform and organize the information stored in an image in such a way that it can be easily transmitted with lesser memory and bandwidth [12]. It is performed to represent an image using lesser number of pixels while retaining the picture quality of the image. Image compression process requires two algorithms – the image compression algorithm and the image reconstruction algorithm [13]. There are several techniques for compression. For example, principal component analysis (PCA), singular value decomposition (SVD), Eigen values based analysis, discrete cosine transform, wavelet based transform, etc. Although each of these techniques has been used extensively in literature, PCA and SVD have been more advantageous. Image compression techniques view image as a matrix and then operations are performed on the image matrix. Image compression reduces the redundant pixel values, storage space requirement, while maintaining the quality of image [14]. Most image compression algorithms typically divide an image I