The fusion technique involves integrating or combining the two or more level information together to obtain more accurate information. Here in our proposed method before fusing two MRI images, the process of reducing the noise elements in the source images is done using Weiner Filter and then two-level fusion is performed. Discrete wavelet transforms (DWT) and curvelet transforms (CT) (Candes & Donoho 2000) are used for hybrid fusion. Fusion of images is done using co-efficient developed. DWT Coefficients will be of two levels; detailed and approximate coefficient. Approximate coefficients are applied further to Curvelet Transform and detailed coefficient is directly assigned to fusion rule. Resulted coefficients are combined with detailed coefficients developed by DWT(Candes & Donoho 2005) using fusion rule.
Curvelet(Starck et al., 2002) will develop low-low, low-high, high-low and high-high bands with the information of the image. Among all four low-low band consists of highest information of the coefficient. Ignoring rest three bands fusion rules are applied only on the low-low band. Once the fusion rule is applied coefficients are to be converted back to their original spatial domain. Inverse transforms are applied on fused values to rebuilt spatial domain values that can be analyzed easily. The final fused image represents the image with the information integrating into it of both two input images.
In numerical analysis and functional analysis, a discrete wavelet transform (DWT)(Sruthy et al., 2013) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures other frequency and location information (location in time). The Figure 1 shows how to extract the approximate coefficients and detailed coefficients and these information are further fused using simple average fusion rule respectively for both the coefficient to extract features of fused coefficients of information.
Fusion using feature extraction
Robust Principal Component Analysis (RPCA)(Wright et al., 2009) is a modification of the widely used statistical procedure of Principle Component Analysis (PCA) which works well with respect to grossly corrupted observations. A number of different approaches exist for Robust PCA, including an idealized version of Robust PCA, which aims to recover a low-rank matrix L0 from highly corrupted measurements M = L0 +S0. This decomposition in low-rank and sparse matrices can be achieved by techniques such as Principal Component Pursuit method (PCP),Stable PCP, Quantized PCP, Block based PCP and Local PCP Then, optimization methods are used such as the Augmented Language Multiplier, Alternating Detection Method (ADM), Fast Alternating Minimization (FAM) or Iteratively Reweighted Least Squares (IRLS).