Wavelet Based Hybrid Coding of Images

Recently, several wavelet transform based image coding techniques are reported in literature. Though these schemes yield very low bit rates, they suffer from the drawback of computational complexity. There is always a need for simple, fast and easy to implement image coding techniques that yield good subjective quality at low bitrates. To obtain good data compression, the wavelet transform coefficients are encoded using the scalar or vector quantization. Scalar quantization techniques are simple and fast. Therefore an attempt has been made to derive hybrid coding algorithms by combining the discrete wavelet transform with Modified Block Truncation Coding and New Block Truncation Coding techniques. The performance analysis of these algorithms in terms of subjective quality and quantitative measures such as mean square error, peak signal to noise ratio, compression ratio and bitrate have been carried out on two images viz., Lena & Pepper and the results are found to be encouraging. Indexing terms: Wavelet transform, Modified Block Truncation Coding, Scalar quantization INTRODUCTION Sampling and quantization of a 2-D light intensity function to generate a digital image results in enormous amount of data. The volume of data generated may result in huge storage, large processing time and large video transmission bandwidth. Image data compression deals with the problem of reducing the volume of data required to represent a digital image. Image compression plays an important role in many fields such as tele-videoconferencing, remote sensing, document and medical imaging, Facsimile transmission (FAX) and military applications. In image processing, wavelet analysis has been mainly used for solving problems such as data compression and noise removal. Recently, the Discrete Wavelet Transform (DWT) has emerged as a powerful tool for decomposing images into various multiresolution approximations (Mallat,1989). The pyramidal algorithm for computing DWT is proposed in (Mallat,1989). Multiresolution decomposition schemes are known for yielding high quality images at low bitrates (Sri Ram et.al.,1995) . In references (Villasenor et.al.,1995) and (Wang et.al.,1996) different filter banks that can be used in wavelet compression are proposed. As the application of DWT does not result in significant reduction in the bitrate, it has to be combined with scalar and vector quantization techniques for reducing the bitrate further. In references (Wang et.al.,1996) and (Weterink.et.al.,1988) wavelet-based image coding techniques using vector quantization are proposed. Vector quantization techniques are computationally complex and time consuming. On the other hand, scalar quantization techniques discussed in (Gonzalez et.al.,1993) and (Udpikar et.al.,1985) are simple and efficient. Hence the scalar quantization techniques of (Gonzalez et.al.,1993) and (Udpikar et.al.,1985) can be combined with the wavelet transform. In this paper, two hybrid image coding algorithms using wavelet transform and the scalar quantization schemes of (Gonzalez et.al.,1993) are proposed and their performance is compared in terms of mean square error, PSNR, CR, bitrate and subjective quality. II. DISCRETE WAVELET TRANSFORM AN OVERVIEW The pyramidal algorithm (Mallat et.al.,1989) is used for wavelet decomposition and reconstruction. In order to apply wavelet decomposition to images, a separable DWT is employed in which emphasis is given to the horizontal and vertical directions. Fig.1 shows the basic pyramidal structure for 2-D wavelet decomposition. At each step, the image Am(f) is decomposed into a coarse approximation Am+1(f) and three detail sub-images D 1 m+1(f),D 2 m+1(f) and D 3 m+1(f). The rows of Am(f) are first convolved with a one-dimensional filter and every other column is retained. Next the columns of the resulting signals are convolved with another one-dimensional filter and every other row is retained. The filters used in this decomposition are the quadrature mirror filters h and g. Fig.2 shows the disposition of Am+1(f) D 1 m+1(f),D 2 m+1(f) and D 3 m+1(f) obtained after wavelet decomposition. For reconstruction at each level, the image Am[f] is reconstructed from Am+1[f], D 1 m+1[f], D 2 m+1[f] and D 3 m+1[f] . This algorithm is illustrated in Fig.3. Between each column of the sub images Kavitha Srinivasan, Dr.N.M.Nandhitha, Dr.T.Ravi, Dr.E.Logashsnmugam / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 2,Mar-Apr 2012, pp.1274-1277 1275 | P a g e Am+1[f], D 1 m+1[f], D 2 m+1[f] and D 3 m+1[f] a column of zeros is added and the rows are convolved with a one-dimensional filter. A row of zeros is added between each row of the resulting image and the columns are convolved with another onedimensional filter. The filters used in this reconstruction are the quadrature mirror filters h and g. In this paper, in the implementation of the pyramidal algorithm for wavelet transform, the convolution operations are performed using Fast Fourier transform. The impulse response of the filters h and h are referenced from Wang et.al,1996. After wavelet decomposition or reconstruction, any pixel value found greater than 255 is limited to 255 and any pixel value less than zero is limited to zero. Figs.4 and 5 show the original Lena image of size 256*256, the one-level wavelet decomposition of and reconstructed image after performing WTMBTC and WT-NBTC compression technique on Lena image respectively. The detailed sub-images are ignored for simplicity, as they do not contain significant energy. With these approximations, the bitrate is 128 * 128 * 8 bits per pixel (bpp) = 256 * 256 = 2 bpp. Fig 1. Pyramidal Algorithm for 2D Wavelet Decomposition Fig 2. Wavelet Decomposed Sub Images III. PROPOSED ALGORITHMS In this section, two wavelet based hybrid imagecoding algorithms are proposed in order to reduce the bitrate further. The algorithms considered together with the Wavelet Transform (WT) are 1. Discrete Wavelet Transform with Modified Block Truncation Coding (DWTMBTC) algorithm. 2. Discrete Wavelet Transform with New Block Truncation Coding (DWTNBTC) algorithm. The aforementioned algorithms are applied on the approximation sub image obtained after one-level wavelet decomposition of the original image. The proposed algorithms are discussed below.