Variable-density complex discrete wavelet transform based on perfect translation invariance

2008 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Variable Density ◽  
Discrete Wavelet ◽  
Translation Invariance

PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM

2013 ◽  
Vol 11 (04) ◽  
pp. 1360003 ◽  
Author(s):  
HIROSHI TODA ◽  
ZHONG ZHANG ◽  
TAKASHI IMAMURA
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Frequency Domain ◽  
Wavelet Transforms ◽  
Wavelet Packet ◽  
Variable Density ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Translation Invariant ◽  
High Degree

The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain.

scholarly journals Fast Compressed Sensing MRI Based on Complex Double-Density Dual-Tree Discrete Wavelet Transform

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Shanshan Chen ◽  
Bensheng Qiu ◽  
Feng Zhao ◽  
Chao Li ◽  
Hongwei Du
Keyword(s):  
Wavelet Transform ◽  
Compressed Sensing ◽  
Discrete Wavelet Transform ◽  
Signal To Noise Ratio ◽  
Similarity Index ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Signal To Noise ◽  
Reconstruction Methods ◽  
Noise Ratio

Compressed sensing (CS) has been applied to accelerate magnetic resonance imaging (MRI) for many years. Due to the lack of translation invariance of the wavelet basis, undersampled MRI reconstruction based on discrete wavelet transform may result in serious artifacts. In this paper, we propose a CS-based reconstruction scheme, which combines complex double-density dual-tree discrete wavelet transform (CDDDT-DWT) with fast iterative shrinkage/soft thresholding algorithm (FISTA) to efficiently reduce such visual artifacts. The CDDDT-DWT has the characteristics of shift invariance, high degree, and a good directional selectivity. In addition, FISTA has an excellent convergence rate, and the design of FISTA is simple. Compared with conventional CS-based reconstruction methods, the experimental results demonstrate that this novel approach achieves higher peak signal-to-noise ratio (PSNR), larger signal-to-noise ratio (SNR), better structural similarity index (SSIM), and lower relative error.

scholarly journals Image Forgery Recognition using SWT Method

2019 ◽  
Vol 8 (6) ◽  
pp. 293-296
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Digital Image ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Feature Transformation ◽  
Scale Invariant ◽  
Image Forgery ◽  
Invariant Feature ◽  
Scale Invariant Feature

Using SWT (Stationary Wavelet Change) & SIFT (Scale Invariant Feature Transformation) we attempted to increase the number of features recognized & matched with digital image for forgery identification. Digital image received preferable match for forged area. We collected the forgery area using SIFT& SURF for identification of forgery. We used DWT (Discrete Wavelet Transform) w.r.t. SIFT & SW to subdue absence of translation invariance..

Multi-Resolution Transforms Based Robust Image Enhancement for High Frequency Colour Images

2014 ◽  
Vol 933 ◽  
pp. 762-767
Author(s):  
T. Menakadevi ◽  
J. Arivudainambi ◽  
M. Sulochana
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
High Frequency ◽  
Resolution Enhancement ◽  
Input Image ◽  
Image Resolution ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Stationary Wavelet Transform ◽  
Colour Image

An Image Resolution Enhancement Technique based on Interpolation of the high frequency sub-band of colour images obtained by Discrete Wavelet Transform and the input colour image is proposed in this paper. Interpolation determines the intermediate values on the basis of observed values. One of the commonly used interpolation technique is Bicubic Interpolation. The edges are enhanced by introducing an intermediate stage by using Stationary Wavelet Transform. It is designed to overcome the lack of Translation-Invariance of Discrete Wavelet Transform. This is widely used in Signal Denoising and Pattern Recognition. Discrete Wavelet Transform is applied in order to decompose an input colour image into different sub-bands. Then the high frequency sub-bands as well as the input colour image are interpolated separately. The interpolated high frequency sub-bands and the Stationary Wavelet Transform high frequency sub-bands have the same size which means they can be added with each other. The new corrected high frequency sub-bands can be interpolated further for higher enlargement. Then all these sub-bands are combined with interpolated input image for new high resolution image by using Inverse Discrete Wavelet Transform. This has been done by MATLAB. The Peak Signal-Noise Ratio was obtained upto 5dB greater than the conventional and state-of-art image resolution enhancement techniques.

Practical design of perfect-translation-invariant real-valued discrete wavelet transform

2014 ◽  
Vol 12 (04) ◽  
pp. 1460005 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang ◽  
Takashi Imamura
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Irrational Number ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Wavelet Frame ◽  
Reconstruction Algorithms ◽  
The Real ◽  
Practical Design ◽  
Tight Wavelet Frame

The real-valued tight wavelet frame having perfect translation invariance (PTI) has already proposed. However, due to the irrational-number distances between wavelets, its calculation amount is very large. In this paper, based on the real-valued tight wavelet frame, a practical design of a real-valued discrete wavelet transform (DWT) having PTI is proposed. In this transform, all the distances between wavelets are multiples of 1/4, and its transform and inverse transform are calculated fast by decomposition and reconstruction algorithms at the sacrifice of a tight wavelet frame. However, the real-valued DWT achieves an approximate tight wavelet frame.

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