Image Denoising With 2D Scale-Mixing Complex Wavelet Transforms

2014 ◽  
Vol 23 (12) ◽  
pp. 5165-5174 ◽  
Author(s):  
Norbert Remenyi ◽  
Orietta Nicolis ◽  
Guy Nason ◽  
Brani Vidakovic
Keyword(s):  
Image Denoising ◽  
Wavelet Transforms ◽  
Complex Wavelet

DAUBECHIES COMPLEX WAVELET TRANSFORM BASED TECHNIQUE FOR DENOISING OF MEDICAL IMAGES

2007 ◽  
Vol 07 (04) ◽  
pp. 663-687 ◽  
Author(s):  
ASHISH KHARE ◽  
UMA SHANKER TIWARY
Keyword(s):  
Wavelet Transform ◽  
Image Denoising ◽  
Medical Image ◽  
Medical Images ◽  
Universal Method ◽  
Complex Wavelet Transform ◽  
Shrinkage Function ◽  
Daubechies Complex Wavelet Transform ◽  
Complex Wavelet

Wavelet based denoising is an effective way to improve the quality of images. Various methods have been proposed for denoising using real-valued wavelet transform. Complex valued wavelets exist but are rarely used. The complex wavelet transform provides phase information and it is shift invariant in nature. In medical image denoising, both removal of phase incoherency as well as maintaining the phase coherency are needed. This paper is an attempt to explore and apply the complex Daubechies wavelet transform for medical image denoising. We have proposed a method to compute a complex threshold, which does not depend on any assumed model of noise. In this sense this is a "universal" method. The proposed complex-domain shrinkage function depends on mean, variance and median of wavelet coefficients. To test the effectiveness of the proposed method, we have computed the input and output SNR and PSNR of various types of medical images. The method gives an improvement for Gaussian additive, Speckle and Salt-&-Pepper noise as well as for the mixture of these noise types for a range of noisy images with 15 db to 30 db noise levels and outperforms other real-valued wavelet transform based methods. The application of the proposed method to Ultrasound, X-ray and MRI images is demonstrated in the experiments.

Signal quantitative analysis using customizable perfect-translation-invariant complex wavelet functions

2014 ◽  
Vol 12 (04) ◽  
pp. 1460010 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Quantitative Analysis ◽  
Frequency Band ◽  
Wavelet Transforms ◽  
Wavelet Coefficient ◽  
Discrete Wavelet ◽  
Digital Signals ◽  
Orthonormal Wavelet ◽  
Translation Invariant ◽  
Fast Calculation ◽  
Complex Wavelet

In this paper, we introduce several methods of signal quantitative analysis using the perfect-translation-invariant complex wavelet functions (PTI complex wavelet functions), which are used in our proposed perfect-translation-invariant complex discrete wavelet transforms (PTI CDWTs) and can be designed by customization. First, using PTI complex wavelet functions, we define the continuous wavelet coefficient (CWC). Next, using orthonormal wavelet functions in the classical Hardy space, we analyze the CWC, and show that, using a CWC, we can measure the energy of a customizable frequency band, and additionally, using numbers of CWCs, we can measure the energy of the whole frequency band. Next, we introduce the fast calculation method of CWCs and show the applicability of the PTI CDWTs to digital signals. Based on them, we introduce some examples of signal quantitative analysis, including the methods to obtain instantaneous amplitude, instantaneous phase and instantaneous frequency. Additionally, we introduce the energy measurement of the whole frequency band using the PTI DT-CDWT, which is one of our proposed PTI CDWTs.

Sign in / Sign up

Export Citation Format

Share Document