wavelet

The Wavelet Series is just a sampled version of Continuous Wavelet Transform (CWT) and its computation may consume a significant amount of time and resources, depending on the resolution required. The Discrete Wavelet Transform (DWT), which is based on sub-band coding is found to yield a fast computation of Wavelet Transform. It is easy to implement and reduces the computation time and resources required (BANOTH 2007) . A two-dimensional scaling function, , and three two-dimensional wavelet , and are critical elements for wavelet transforms in two dimensions. Given separable 2-D scaling and wavelet functions, 2-D DWT can be defined. First, we define the scaled and translated or shifted basis functions are defined as follows (Gonzalez and Woods 2008):                 Where i = directional wavelet index. Therefore, 2-D DWT of  an image  of size is given by (Gonzalez and Woods 2008):     Where Arbitrary starting scale  Approximation coefficients for at scale  Horizontal, vertical and diagonal details coefficients at scales    ,   Then the two-dimensional DWT can be implemented using digital filters and downsamplers . The block diagram in Fig. 2 shows the process of taking the one-dimensional FWT of the rows of and the subsequent one-dimensional FWT of the resulting columns. Three sets of detail coefficients including the horizontal, vertical, and diagonal details are produced.     The proposed work has examined, Haar discrete wavelet transform based, 7th  level decomposition of the breast cancer histopathology images . The discrete wavelet transform named Haar, have originally been designed by (Haar 1911). At first level of decomposition, breast cancer histopathology images  are being divided into four equal size sub-images, namely LL1 (approximation coefficients), LH1 (horizontal coefficients), HL1 (vertical coefficient) and HH1 (diagonal coefficient). Subsequently at the second level of decomposition LL1 (approximation coefficient) sub-image is further decomposed into four equal size sub-images LL2, LH2, HL2 and HH2. Continuously until we reach the seventh level of decomposition. In this manner 28 sub-images have been formed from the every channel (red, green & blue) thus, we get 28 x 3 sub-images have been established from the original image. Then we calculated nine of traditional statistical features (Mean, Standard deviation, Skewness, kurtosis, Entropy, Energy, Root mean square, Mean Absolute Deviation, Median Absolute Deviation). Overall, nine statistical features have been acquired from each sub-images; and 756 features for each of the breast cancer histopathology image samples.