Rudra Pratap Singh Chauhan / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 1, Jan-Feb 2012, pp. 464-470 464 | P a g e A Novel Approach to Overcome the Intertwined Shortcomings of DWT For Image Processing and De-noising Rudra Pratap Singh Chauhan (Deptt.-ECE, Uttaranchal Institute of Technology, Dehradun, Uttarakhand, India ABSTRACT Shift variance, poor directional selectivity, oscillations and aliasing are four fundamental, intertwined shortcomings of the DWT that undermines its application for certain image processing tasks. The initial motivation behind the work to use advanced CWT which will overcome the limitations of standard DWT. In this paper, we demonstrate that excellent shift-invariance properties and directional selectivity with transform-domain redundancy in 2D. We achieve this by projecting the wavelet coefficients from Selesnick’s almost shift-invariant, double-density wavelet transform so as to separate approximately the positive and negative frequencies, thereby increasing directionality. Subsequent decimation and a novel inverse projection maintain the low redundancy while ensuring perfect reconstruction. Although the advanced CWT generates complex-valued coefficients allowing processing capabilities that are impossible with real-valued coefficients. The proposed method is highly efficient and useful for image processing applications and also outperforms the method proposed by the previous authors for image de-noising with significant improvement in the value of PSNR over RMSE as given by the other classical methods. KEYWORDS- Complex DWT, De-noising, 1-D DWT, 2-D DWT, Redundant CWT. 1. INTRODUCTION Many scientific experiments results in a datasets corrupted with noise, either because of the inadequate data acquisition process, or because of environmental effects. A first preprocessing step in analyzing such datasets is de-noising, that is, removing the unknown signal of interest from the available noisy images. There are several approaches to de- noise images. Despite similar visual effects, there are subtle differences between de-noising, de-blurring, smoothing and restoration. It has been observed that standard DWT and its extensions suffer from two or more serious limitations. The initial motivation behind the earlier development of complex- valued DWT was the third limitation that is the „absence of phase information‟. Complex Wavelets Transforms(CWT) use complex-valued filtering(analytic filter) that decomposes the real/complex signals into real and imaginary parts in transform domain. The real and imaginary coefficients are used to compute amplitude and phase information, just the type of information needed to accurately described the energy localization of oscillating functions(wavelet basis). Edges and other singularities in signal processing applications manifest themselves as oscillating coefficients in the wavelet domain. The amplitude of these coefficients describes the strength of the singularity while the phase indicates the location of singularity. In order to determine the correct value of localized envelop and phase of an oscillating function, „analytic‟ or „quadrature‟ representation of the signal is used. This representation can be obtained from the Hilbert transform of the signal. Thus, the complex orthogonal wavelet may prove to be a good choice, since it will allow processing of both magnitude and phase simultaneously. This paper presents the concept of DT-DWT versions of RCWT have limited redundancy with very good properties of shift-invariance, improved directionality and availability of phase information, which are not present in standard DWT. RCWT has a huge potential in signal/image de-noising.. The paper is organize as follows: Section 2 involves Separable DWT. The Complex Dual Tree DWT is discussed in Section 3 & Section 4 deals with bivariate shrinkage functions. Section 5 gives the general method involves in image de-noising. Section 6 deals with results & discussions & the conclusion are given in Section 7. 2. Separable DWT 2.1 1-D Discrete Wavelet Transform In separable DWT the analysis filter bank decomposes the input signal x(n) into two sub band signals, c(n) and d(n). The signal c(n) represents the low frequency part of x(n), while the signal d(n) represents the high frequency part of x(n). We denote the low pass filter by af1(analysis filter 1) and the high pass filter by af2(synthesis filter 2). As depicted in figure(1), the output of each filter is then down sampled by 2 to obtain the two sub band signals c(n) & d(n). c(n) x(n) y(n) d(n) Fig.(1): Separable DWT(Analysis) & (Synthesis) Filter Bank af af sf sf