In this chapter, the effect of transform features (shift sensitivity and directional selectivity) has been examined by implementing the homomorphic and non-homomorphic speckle suppressors in three alternative wavelet domains-DWT, RDWT and CWT. The experimental results demonstrate that performance of DWT is worst on all type of images whereas the performance of RDWT and DT-CWT is comparable. On certain types of images (images dominated by uniform areas), RDWT performs better while on others (textured images), DT-CWT-based methods are the best. This shows that the shift-dependence of a transform causes a significant degradation in performance of a despeckling technique and good directional selectivity is essential for representing the textured images optimally. From these investigations, it is concluded that both DT-CWT and RDWT are equally good for designing wavelet-based de-noising applications. However, the low computational complexity of DT-CWT and the textured nature of medical US images, favours the use of DT-CWT in comparison to RDWT for despeckling applications. More work is required to develop shorter length filters for the DTCWT (e.g. analogous to Haar wavelet) in order to further improve the despeckling performance of the US images.

Chapter Contents:

• 9.1 Introduction
• 9.2 Discrete wavelet transform
• 9.3 Limitations of DWT and its improvements in de-noising
• 9.4 Dual tree-complex wavelet transform
• 9.5 DT-CWT and shift-invariance
• 9.6 CWT and directional selectivity
• 9.7 Filter implementation of DT-CWT
• 9.8 Practical algorithm
• 9.9 Results and discussions
• 9.10 Conclusions
• References

Inspec keywords: image denoising; trees (mathematics); medical image processing; image texture; biomedical ultrasonics; discrete wavelet transforms; image filtering

Other keywords: wavelet-based denoising applications; dual tree-complex wavelet transform; transform features; redundant discrete wavelet transform; medical ultrasound images; RDWT; shorter length filters; shift sensitivity; despeckling technique; wavelet domains; computational complexity; DT-CWT; homomorphic speckle sup- pressors; textured images; DWT; directional selectivity

Subjects: Sonic and ultrasonic applications; Computer vision and image processing techniques; Sonic and ultrasonic radiation (biomedical imaging/measurement); Combinatorial mathematics; Combinatorial mathematics; Integral transforms; Biology and medical computing; Integral transforms; Patient diagnostic methods and instrumentation; Algebra, set theory, and graph theory; Sonic and ultrasonic radiation (medical uses); Function theory, analysis; Optical, image and video signal processing