Direction-Adaptive Discrete Wavelet Transform for Image Compression

Abstract

Abstract-We propose a direction-adaptive DWT (DA-DWT) that locally adapts the filtering directions to image content based on directional lifting. With the adaptive transform, energy compaction is improved for sharp image features. A mathematical analysis based on an anisotropic statistical image model is presented to quantify the theoretical gain achieved by adapting the filtering directions. The analysis indicates that the proposed DA-DWT is more effective than other lifting-based approaches. Experimental results report a gain of up to 2.5 dB in PSNR over the conventional DWT for typical test images. Subjectively, the reconstruction from the DA-DWT better represents the structure in the image and is visually more pleasing.

Image Compression using ANFIS in Wavelet Domain

“…Discrete wavelet transform is a linear transform operates on a data vector whose length is an integer power of two transforming it into numerically different vector of same length [10].Data can be separated into different frequency components, further this data studies each component with resolution matched to its scale. Using wavelet analysis, perfect reconstruction filter bank could be formed with coefficients sequences aL(k) and aH(k) as shown in figure 1 below.…”

Multidimensional Filter Banks and Multiscale Geometric Representations

“…(The situations for the other two channels can be inferred by symmetry.) After the 3D hourglass filter (H 1 (ξ)), we sequentially decompose the signal by a concatenation of two 2D filter banks, with the first one, denoted as FB ( ) 12 , operating along the (n 1 ,n 2 )-plane and the second one, FB ( ) 13 , along the (n 1 ,n 3 )-plane.…”

“…The two filter banks FB ( ) 12 and FB ( ) 13 have exactly the same structure, and hence we will only focus on FB ( ) 12 . As shown in Figure 6.11(b), the analysis part of FB ( ) 12 is constructed as an -level binary tree, with an appropriate resampling matrix U ( ) k (0 ≤ k < 2 ) attached to each of the 2 output channels of the tree.…”

“…Well-known examples include bandelets [78], edge-adapted multiscale transform [17], wedgelets [32,101], wavelet footprints [35], best tree-based representations [43,85], directionlets [96], motion-adaptive transform for videos [81], adaptive directional lifting [13,26], and grouplets [66]. We omit further discussions on these adaptive signal representations and refer readers to the references cited above for more details.…”

Sparse Image Representation by Directionlets

“…This scheme is exploited by Gerek and Ç etin (2006), where transform directions are adapted pixel-wise throughout images. A similar adaptation is used by Ding et al (2004) and Chang and Girod (2007), but with more (9 and 11, respectively) different directions. In addition, the method proposed by Ding et al (2004) Taubman (2006), where a wavelet packet decomposition is applied.…”