As a general and rigid mathematical tool, wavelet theory has found many applications and is constantly developing. This article reviews the development history of wavelet theory, from the construction method to the discussion of wavelet properties. Then it focuses on the design and expansion of wavelet transform. The main models and algorithms of wavelet transform are discussed. The construction of rational wavelet transform (RWT) is provided by examples emphasizing the advantages of RWT over traditional wavelet transform through a review of the literature. The combination of wavelet theory and neural networks is one of the key points of the review. The review covers the evolution of Wavelet Neural Network (WNN), the system architecture and algorithm implementation. The review of the literature indicates the advantages and a clear trend of fast development in WNN that can be combined with existing neural network algorithms. This article also introduces the categories of wavelet-based applications. The advantages of wavelet analysis are summarized in terms of application scenarios with a comparison of results. Through the review, new research challenges and gaps have been clarified, which will serve as a guide for potential wavelet-based applications and new system designs.

https://ieeexplore.ieee.org/ielx7/6287639/6514899/09785993.pdf

A Review of Wavelet Analysis and Its Applications: Challenges and Opportunities

As a general and rigid mathematical tool, wavelet theory has found many applications and is constantly developing. This article reviews the development history of wavelet theory, from the construction method to the discussion of wavelet properties. Then it focuses on the design and expansion of wavelet transform. The main models and algorithms of wavelet transform are discussed. The construction of rational wavelet transform (RWT) is provided by examples emphasizing the advantages of RWT over traditional wavelet transform through a review of the literature. The combination of wavelet theory and neural networks is one of the key points of the review. The review covers the evolution of Wavelet Neural Network (WNN), the system architecture and algorithm implementation. The review of the literature indicates the advantages and a clear trend of fast development inWNNthat can be combined with existing neural network algorithms. This article also introduces the categories of wavelet-based applications. The advantages of wavelet analysis are summarized in terms of application scenarios with a comparison of results. Through the review, new research challenges and gaps have been clarified, which will serve as a guide for potential wavelet-based applications and new system designs. 

in this hybrid model we proposed Hybrid technique combination of sundry compression techniques. Image compression is reduce the number of bits required to represent an image without degrading the quality of the image to an unacceptable level. The reduction in file size allows more images to be stored in a given amount of disk or memory space and reduces the time required for images to be sent via the Internet. Storage capacity and the speed of transmission are the two important factors that arise during the heavy duty of multimedia over Internet. The best image quality at a given bit-rate (or compression rate) is the main goal of image compression. we implement lossless technique so our PSNR and MSE will go better than the old algorithms and due to DCT and DWT we will get good level of compression. Hence overall result of hybrid compression technique is good.

/pdf/image-compression-using-discrete-cosine-transform-and-pjmog18ug0.pdf

Image Compression Using Discrete Cosine Transform and Discrete Wavelet Transform

Here in this hybrid model we are going to proposed a Nobel technique which is the combination of several compression techniques. Image compression is minimizing the size in bytes of a graphics file without degrading the quality of the image to an unacceptable level. The reduction in file size allows more images to be stored in a given amount of disk or memory space. It also reduces the time required for images to be sent over the Internet or downloaded from Web pages.JPEG and JPEG 2000 are two important techniques used for image compression. First we implement DWT and DCT on the original image because these are the lossy techniques and in the last we introduce Huffman Coding technique which is a lossless technique. In the end, we implement lossless technique so our PSNR and MSE will go better than the old algorithms and due to DWT and DCT we will get good level of compression. Hence overall result of hybrid compression technique is good.

http://www.ijarcsee.org/index.php/IJARCSEE/article/download/175/166

Hybrid Image Compression Using DWT, DCT and Huffman Coding Techniques

Digital image and video image require large amount of capacity to store. Image compression means reducing the size of image, without losing its quality. Depending on the reconstructed image, to be exactly same as the original or some unidentified loss may be incurred, two techniques for compression exist. Two techniques are: lossy techniques and lossless techniques. Digital imaging play an important role in image processing therefore it is necessary to develop a system that produces high degree of compression while preserving critical image. In this paper we present hybrid model which is the combination of several compression techniques. This paper presents DWT and DCT implementation because these are the lossy techniques and also introduce Huffman encoding technique which is lossless. On several medical, Lena images simulation has been carried out. At last implement lossless technique so our PSNR and MSE will go better, and due to DWT and DCT we will get good level of compression without losing any image. When compared to standalone DCT and DWT algorithms,the proposed hybrid algorithm gives better result in term of peak-signal-tonoise ratio with a higher compression ratio.

Comparison and improvement of image compression using dct, dwt & huffman encoding techniques

An image compression method based on adaptive segment and adaptive quantified is presented in this paper. The image is divided into smooth and detail areas using the multi-threshold-segmentation method based on the potential function. The quantization table varied with the different image. The 2-D DCT is decomposed into 1-D fast DCT based on base-2 FFT. The Compression-to-PSNR Rate can evaluate the image compression result more effectively than that of the compression rate or PSNR respectively. The experiment shows that the algorithm gives the superior performance compared with traditional JPEG.

The Image Compression Method Based on Adaptive Segment and Adaptive Quantified

The biorthogonal wavelets families are usedwidely because they have compact support, complete symmetry and linear phase. According to Bezout’s theorem,the biorthogonal wavelets available now are only some particular examples of total solutions. The quantity of solutions is decided jointly by the scaling function vanishingmoment N and dual vanishing moment N. The relationship of N, N and solutions’ quantity is discussed in detail.According to the constraint conditions which the compactbiorthogonal wavelets satisfy, a number of biorthogonalwavelets are constructed in which the global convergenthomotopy method is used for diﬀerent N and N. The ﬁlter coeﬃcients and plots of scaling function, dual scalingfunction, wavelet function and dual wavelet function aregiven.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/cje.2015.10.018

Biorthogonal Wavelet Construction Using Homotopy Method

The biorthogonal wavelet families are used widely in image compression, but the properties were not discussed in detail. In this paper, four types of biorthogonal wavelets and their duals are discussed whose vanish moment are different. Their filters supports, centers and linear phase are given. As example, the wavelets, including spline 5/3 and CDF9/7, are given. The waveform, magnitude and phase spectrum are plotted respectively. These wavelets are used in image compression and JPEG2000 standard.

Shufang Zhang

Papers

The Image Compression Method Based on Adaptive Segment and Adaptive Quantified

Biorthogonal Wavelet Construction Using Homotopy Method

Biorthogonal wavelets in image compression