IOSR Journal of VLSI and Signal Processing (IOSR-JVSP) Volume 5, Issue 6, Ver. II (Nov -Dec. 2015), PP 16-24 e-ISSN: 2319 – 4200, p-ISSN No. : 2319 – 4197 www.iosrjournals.org DOI: 10.9790/4200-05621624 www.iosrjournals.org 16 | Page Single image super resolution with improved wavelet interpolation and iterative back-projection Boniface M. Ngocho, Elijah Mwangi School of Engineering, University of Nairobi. PO BOX 30197 Nairobi 00100, Kenya Abstract : Spatial resolution of digital images is limited by practical considerations of digital imaging systems. Single image super resolution is therefore required to create images that allow better identification and interpretation of details. A number of investigations have been carried out on image super resolution using the discrete wavelet transform. In this paper, a comparative study is made of different interpolation based methods for the estimation of high frequency sub-bands for the super resolution image. An investigation of the effect of different parameters in bicubic interpolation kernel is also carried out. Based on the result, a new algorithm is proposed for single image super resolution using the discrete wavelet transform and incorporating iterative back-projection. The proposed method is tested against other approaches and found to give superior results in terms of peak signal to noise ratio and structural similarity index measure. Keywords: Super resolution, wavelets, bicubic interpolation, iterative back-projection I. INTRODUCTION Digital imaging systems have a wide variety of applications for commercial, medical and recreational purposes. In many of these applications, a high quality image is required to allow human interpretation or machine perception. However, the spatial resolution of digital images is sometimes limited by technical considerations of the imaging system or the environmental conditions in which the image is captured. This has led to the need for signal processing techniques to create a higher resolution image that will allow better identification and interpretation of details. The aim of single image super resolution is to create a high resolution image from a single instance of a low resolution image of the original scene. Among the popular methods are direct interpolation, estimation of the missing data using statistical methods, use of wavelets and example based procedures. In spatial domain interpolation, the pixel values of a low resolution image are extrapolated to fit a high resolution grid using an interpolation kernel. Commonly used interpolation kernels are nearest neighbour, bilinear interpolation, bicubic interpolation and windowed sinc functions [1], [2], [3], [4]. The cubic B-spline is another interpolation method that has been found to produce better results than most other interpolation kernels. The kernel however does not directly interpolate the pixels of the low resolution image. The implementation of B-spline interpolation therefore requires a two-step process which leads to an increase in computation time. This has resulted in bicubic interpolation getting more widespread application than cubic B-spline interpolation [1]. In wavelet based super resolution, the available LR image is assumed to be the low frequency sub- band, LL, of a high resolution image. The resolution task is to estimate the high resolution sub-bands in order to complete the image. Tsai and Acharya proposed to use the Stationary Wavelet Transform (SWT) of the LR image to provide the high resolution sub-bands [5]. Since the SWT is not decimated, the LH, HL and HH sub- bands will have the same size as the LR image. Implementing Inverse Discrete Wavelet Transform (IDWT) will therefore result in image with twice the number of rows and columns. Temizel and Vlachos used a similar approach in which high resolution sub-bands are derived from un-decimated SWT coefficients [6]. Other approaches combined SWT and Discrete Wavelet Transform (DWT) to achieve higher Peak Signal to Noise Ratio (PSNR) than SWT alone [7], [8], [9], [10]. In [8], DWT decomposition is carried out on bicubic interpolated LR image. In [7] and [9], high frequency sub-bands are obtained through bicubic interpolation of DWT sub-bands of the LR image. Bicubic interpolation followed by DWT without combination with SWT is applied in [11] and [12]. A number of investigations have proposed the incorporation of edge enhancement in the reconstruction of high frequency sub-bands [13], [14], [15]. Carey et al [13] used multiple levels of DWT decomposition to identify strong edges. The rate of decay of the edges was then used to estimate the unknown high frequency sub-bands. Kwon and Park [16] propose a support vector machine to synthesize the high frequency sub-bands from the DWT decomposed low resolution image without use of interpolation. Single image super resolution is an ill-defined inverse problem without a unique solution. Application of additional constraints in the process can limit the number of possible outcomes and achieve results that are closer to the ground truth. One such process is Iterative Back-Projection (IBP), first proposed for application in image super resolution by Irani and Peleg [17]. This has been subsequently applied in other investigations. Dai