A note on discrete wave packet frames in ℂN

2021 ◽  
pp. 2150006
Author(s):  
Deepshikha ◽  
Jyoti
Keyword(s):  
Wave Packet ◽  
Nonzero Vector ◽  
Discrete Wavelet ◽  
Unitary Space ◽  
Vector Formula ◽  
Wave Packet System

We show that for every nonzero vector [Formula: see text] in [Formula: see text], the discrete wave packet system [Formula: see text] constitutes a frame for the unitary space [Formula: see text]. An application of this result is given, where frame conditions cannot be derived from discrete wavelet systems in [Formula: see text]. The canonical dual of discrete wave packet frame is also discussed.

Improving Space Localization Properties of the Discrete Wavelet Transform

Informatica ◽  
2013 ◽  
Vol 24 (4) ◽  
pp. 657-675
Author(s):  
Jonas Valantinas ◽  
Deividas Kančelkis ◽  
Rokas Valantinas ◽  
Gintarė Viščiūtė
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Discrete Wavelet ◽  
Space Localization

An Adaptive Binarization Method for Cost-efficient Document Image System in Wavelet Domain

2020 ◽  
Vol 64 (3) ◽  
pp. 30401-1-30401-14 ◽  
Author(s):  
Chih-Hsien Hsia ◽  
Ting-Yu Lin ◽  
Jen-Shiun Chiang
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Document Image ◽  
Background Information ◽  
Raspberry Pi ◽  
Discrete Wavelet ◽  
Image System ◽  
Low Frequencies ◽  
Cost Efficient ◽  
Binarization Method

Abstract In recent years, the preservation of handwritten historical documents and scripts archived by digitized images has been gradually emphasized. However, the selection of different thicknesses of the paper for printing or writing is likely to make the content of the back page seep into the front page. In order to solve this, a cost-efficient document image system is proposed. In this system, the authors use Adaptive Directional Lifting-Based Discrete Wavelet Transform to transform image data from spatial domain to frequency domain and perform on high and low frequencies, respectively. For low frequencies, the authors use local threshold to remove most background information. For high frequencies, they use modified Least Mean Square training algorithm to produce a unique weighted mask and perform convolution on original frequency, respectively. Afterward, Inverse Adaptive Directional Lifting-Based Discrete Wavelet Transform is performed to reconstruct the four subband images to a resulting image with original size. Finally, a global binarization method, Otsu’s method, is applied to transform a gray scale image to a binary image as the output result. The results show that the difference in operation time of this work between a personal computer (PC) and Raspberry Pi is little. Therefore, the proposed cost-efficient document image system which performed on Raspberry Pi embedded platform has the same performance and obtains the same results as those performed on a PC.

Evaluvation of Multiresolution Watermarking Algorithm

2017 ◽  
Vol 7 (8) ◽  
pp. 85
Author(s):  
S. Thabasu Kannan ◽  
S. Azhagu Senthil
Keyword(s):  
Digital Watermarking ◽  
Wavelet Transformation ◽  
Signal To Noise Ratio ◽  
Rapid Development ◽  
Threshold Value ◽  
Discrete Wavelet ◽  
Digital Production ◽  
Common Framework ◽  
Sampling Operation ◽  
Watermarking Scheme

Now-a-days watermarking plays a pivotal role in most of the industries for providing security to their own as well as hired or leased data. This paper its main aim is to study the multiresolution watermarking algorithms and also choosing the effective and efficient one for improving the resistance in data compression. Computational savings from such a multiresolution watermarking framework is obvious. The multiresolutional property makes our watermarking scheme robust to image/video down sampling operation by a power of two in either space or time. There is no common framework for multiresolutional digital watermarking of both images and video. A multiresolution watermarking based on the wavelet transformation is selected in each frequency band of the Discrete Wavelet Transform (DWT) domain and therefore it can resist the destruction of image processing.   The rapid development of Internet introduces a new set of challenging problems regarding security. One of the most significant problems is to prevent unauthorized copying of digital production from distribution. Digital watermarking has provided a powerful way to claim intellectual protection. We proposed an idea for enhancing the robustness of extracted watermarks. Watermark can be treated as a transmitted signal, while the destruction from attackers is regarded as a noisy distortion in channel.  For the implementation, we have used minimum nine coordinate positions. The watermarking algorithms to be taken for this study are Corvi algorithm and Wang algorithm. In all graph, we have plotted X axis as peak signal to noise ratio (PSNR) and y axis as Correlation with original watermark. The threshold value ά is set to 5. The result is smaller than the threshold value then it is feasible, otherwise it is not.

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