The continuous fractional wavelet transform on a generalized Sobolev space

2016 ◽  
Vol 14 (06) ◽  
pp. 1650046 ◽  
Author(s):  
Akhilesh Prasad ◽  
Praveen Kumar
Keyword(s):  
Wavelet Transform ◽  
Sobolev Space ◽  
Approximation Properties ◽  
Fractional Wavelet Transform

The main goal of this paper is to study continuous fractional wavelet transform (CFrWT) on generalized Sobolev space [Formula: see text] and its approximation properties. Convergence of convolution for [Formula: see text] in [Formula: see text] is also discussed.

Logarithmic uncertainty principle, convolution theorem related to continuous fractional wavelet transform and its properties on a generalized Sobolev space

2017 ◽  
Vol 15 (05) ◽  
pp. 1750050 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Sobolev Space ◽  
Inversion Formula ◽  
Uncertainty Relation ◽  
Fractional Fourier Transform ◽  
Convolution Theorem ◽  
Inner Product ◽  
Fractional Wavelet Transform ◽  
Product Relation

The continuous fractional wavelet transform (CFrWT) is a nontrivial generalization of the classical wavelet transform (WT) in the fractional Fourier transform (FrFT) domain. Firstly, the Riemann–Lebesgue lemma for the FrFT is derived, and secondly, the CFrWT in terms of the FrFT is introduced. Based on the CFrWT, a different proof of the inner product relation and the inversion formula of the CFrWT are provided. Thereafter, a logarithmic uncertainty relation for the CFrWT is investigated and the convolution theorem related to the CFrWT is established using the convolution of the FrFT. The CFrWT on a generalized Sobolev space is introduced and its important properties are presented.

Image encryption based on Fractional wavelet transform, Arnold transform with the double random phases in HSV color domain

2020 ◽  
Vol 13 ◽  
Author(s):  
Aarushi Shrivastava ◽  
Janki Ballabh Sharma ◽  
Sunil Dutt Purohit
Keyword(s):  
Wavelet Transform ◽  
Image Encryption ◽  
Fractional Fourier Transform ◽  
Color Image ◽  
Random Phase ◽  
Arnold Transform ◽  
Time Frequency ◽  
Key Space ◽  
Secret Keys ◽  
Fractional Wavelet Transform

Objective: In the recent multimedia technology images play an integral role in communication. Here in this paper, we propose a new color image encryption method using FWT (Fractional Wavelet transform), double random phases and Arnold transform in HSV color domain. Methods: Firstly the image is changed into the HSV domain and the encoding is done using the FWT which is the combination of the fractional Fourier transform with wavelet transform and the two random phase masks are used in the double random phase encoding. In this one inverse DWT is taken at the end in order to obtain the encrypted image. To scramble the matrices the Arnold transform is used with different iterative values. The fractional order of FRFT, the wavelet family and the iterative numbers of Arnold transform are used as various secret keys in order to enhance the level of security of the proposed method. Results: The performance of the scheme is analyzed through its PSNR and SSIM values, key space, entropy, statistical analysis which demonstrates its effectiveness and feasibility of the proposed technique. Stimulation result verifies its robustness in comparison to nearby schemes. Conclusion: This method develops the better security, enlarged and sensitive key space with improved PSNR and SSIM. FWT reflecting time frequency information adds on to its flexibility with additional variables and making it more suitable for secure transmission.

Quaternionic fractional wavelet transform

2018 ◽  
Vol 26 (2) ◽  
pp. 313-322
Author(s):  
R. Roopkumar
Keyword(s):  
Wavelet Transform ◽  
Fractional Wavelet Transform

scholarly journals Certain properties of continuous fractional wavelet transform on Hardy space and Morrey space

2021 ◽  
Vol 41 (5) ◽  
pp. 701-723
Author(s):  
Amit K. Verma ◽  
Bivek Gupta
Keyword(s):  
Wavelet Transform ◽  
Hardy Space ◽  
Morrey Space ◽  
New Class ◽  
Fractional Wavelet Transform

In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space and Morrey space. The theory developed generalize and complement some of already existing results.

Region-Based Fractional Wavelet Transform Using Post Processing Artifact Reduction

2012 ◽  
Vol 8 (8) ◽  
pp. 45-53
Author(s):  
Jassim Abdul-Jabbar ◽  
Alyaa Taqi
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Low Cost ◽  
Image Features ◽  
Artifact Reduction ◽  
Digital Cameras ◽  
Wireless Multimedia ◽  
Wavelet Filters ◽  
Fractional Wavelet Transform ◽  
Memory Resources

Wavelet-based algorithms are increasingly used in the source coding of remote sensing, satellite and other geospatial imagery. At the same time, wavelet-based coding applications are also increased in robust communication and network transmission of images. Although wireless multimedia sensors are widely used to deliver multimedia content due to the availability of inexpensive CMOS cameras, their computational and memory resources are still typically very limited. It is known that allowing a low-cost camera sensor node with limited RAM size to perform a multi-level wavelet transform, will in return limit the size of the acquired image. Recently, fractional wavelet filter technique became an interesting solution to reduce communication energy and wireless bandwidth, for resource-constrained devices (e.g. digital cameras). The reduction in the required memory in these fractional wavelet transforms is achieved at the expense of the image quality. In this paper, an adaptive fractional artifacts reduction approach is proposed for efficient filtering operations according to the desired compromise between the effectiveness of artifact reduction and algorithm simplicity using some local image features to reduce boundaries artifacts caused by fractional wavelet. Applying such technique on different types of images with different sizes using CDF 9/7 wavelet filters results in a good performance.

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