Research on Wavelet Transform Image Compression Mode

Summary

In today's society where information flow is common, the demand for video is increasing, and the digitization of video is an inevitable trend. However, the amount of data in digitalized images is quite large, and it is inconvenient in transmission and processing. Compressing data is the best method. Now there is a new model, which has good performance in both compression and reduction. It has not yet had a standard format, so it has not been popularized in applications. But in the near future, its potential is limitless. There is an inseparable relationship between images in printing. Therefore, this article introduces the historical sources of WAVELET transformation. The basic principle of wavelet transformation. The impact of today's development on the printing industry. The future development of video compression.

Preface

As science and technology advance with each passing day, printing has moved from traditional printing to digital printing. In the process of digitization, the image data has always been a problem of excessive files, and the memory is too much, which makes the data transmission and processing time-consuming. Nowadays, individuals own True Color video cards and 24-bit data. Full-color printers and scanners are no longer a fantasy, and the user's requirements for image graphics must not only be multi-colored, real and natural, but must be combined with multimedia or animation. However, the relatively high quality of visual enjoyment, the price to be paid is a large amount of storage space, users often can only watch the large volume of graphics files occupy the hard disk, tape and optical disc space; beautiful image files in It's a natural thing to have a good relationship between friends and family, but it takes more than 3 minutes to use the Internet to send a 640480 True Color image. People often yawn. Everyone can't help but doubt that the image file can't be compressed even smaller. Are you? The newspaper industry can also be faster when it is published. Therefore, a good compression format is indispensable, making the memory occupied by the image smaller and easier to handle. However, the compression mode currently used in the market is not ideal in terms of compression ratio and loses the meaning of compression. Otherwise, the compression ratio is so large that it causes image distortion. Even if mathematicians and information theoreticians take turns around the clock and try their best to find a faster and more exciting algorithm for the lossless coding method, it is inevitable that the image compression rate will be reduced. Still not good enough. In addition, the images used to print cause blurred images or jagged images. Both will cause print output problems. Is video compression really a dead end? Please believe that the potential of mankind to solve problems is limitless. Since the old coding method was not adequate, the scientists turned their attention to the WAVELET conversion method, and the results not only found a satisfactory answer, but also opened up a bright and smooth way. Wavelet analysis is a mathematical theory developed in recent years. Wavelet analysis, whether it is a continuous wavelet transform as a mathematical theory, or a discrete wavelet transform as an analytical tool or method, still has many places that can be studied. It is a major breakthrough in tools and methods in recent years. Wavelet analysis is an important development of Fourier analysis. He retains the advantages of Fourier theory and overcomes its shortcomings. Complete distortion can be achieved, and the compression ratio is also acceptable. As its mathematical theory was proposed as early as the middle of the 1960s, it has only been applied to the reality in the past. Its theory still has considerable room for development, and its practical application is just starting. Its subsequent development can be It is limitless. Therefore, the study's motivation is born.

The historical origins of è´°, WAVELET

WAVELET originated from Joseph Fourier's thermodynamic formula. The Fourier equation was proposed by Joseph Fourier (1768-1830) in the early 19th century, laying the foundation for modern signal analysis. In the 19th to 20th century, basic mathematics research also occupied a very important position. Fourier proposed that any equation, even an equation that draws a discontinuous pattern, can be represented by a simple analytical formula. Wavelet analysis is an extension of the mathematical theory developed in recent years to the Fourier equation.

The wavelet analysis method can be traced back to the wavelet norm base proposed by Haar in 1910. Later, in 1984, when French geophysicist J. Morlet analyzed the local nature of seismic waves, he found that traditional Fourier transforms were difficult to meet their requirements. Therefore, wavelet concepts were introduced in signal analysis to decompose signals. Then the theoretical physicist A. Grossman made this signal to Morlet according to the expansion of a certain function, the translation system {a -1/2 Ψ[(xb)/a] ;a,b?R,a≠0} The feasibility of the study was carried out and opened the way for the formation of wavelet analysis.

In 1986, Y. Meyer constructed a attenuated smooth function Ψj,k(x), whose binary scaling and translation system {Ψj,k(x)=√2jΨ(2jx-k);j,k?Z} The orthonormal basis of L2(R). In 1987, Mallat intelligently introduced the idea of ​​multi-resolution analysis into wavelet analysis, constructed the construction of wavelet functions and the decomposition and reconstruction of signals by wavelet transformation. In 1988, Daubechies constructed a wavelet with Orthonormal and Compactly Supported and only a non-zero wave in a limited area. Thus, the system theory of wavelet analysis was initially established.

Third, WAVELET image compression introduction and introduction of basic theory

First, WAVELET compression concept

WAVELET is based on three main basic theories, namely pyramid coding, filter bank theory, and subband coding. It can be said that the wavelet transform integrates this. Three technologies. Wavelet transform can decompose various intertwined signals with different frequencies into signals with different frequencies, so it can be effectively applied to encoding, decoding, detecting edges, compressing data, and linearizing nonlinear problems. A good analysis of the local time-domain and frequency-domain signals compensates for the absence of Fourier transforms, and therefore wavelet transforms are hailed as mathematical microscopy.

WAVELET does not retain all of the original data, but instead selectively retains the necessary parts so that the original data can be derived from mathematical formulas. This may not be very complete, but it can be very close to the original data. As far as the image is concerned, it must be preserved, what should be discarded, and the size of the energy stored (depending on wavelength and frequency). Replacing the original data with less data to achieve the purpose of compressing data, this approach of achieving a compressed target through the choice of data is a breakthrough in the modern digital video coding technology. That is, the concept of WAVELET is introduced into coding technology.

WAVELET conversion is considered a rookie in digital image conversion technology. However, space science and technology have long since passed. Imaging satellites and Hubble telescopes transmit images back to Earth and medical fiber optic images have long been compressed/restored using the WAVELET principle. Image data, and the excellent compression ratio and the effect of the original video reproduction.

In the past, the lossless encoding method only emphasized the performance of the compression algorithm, and sent the digitized image data to the compression without any leaks. Therefore, the restored data and the original data are not different from each other, but the compression ratio of this compression method is not good. Convert digital image data into data types that are conducive to coding, control the quality of decoded images, select appropriate coding methods, and, when capturing graphic data, first help data “lose weight”. This is the main concept of the WAVELET coding method.

Second, the image compression process

Raw graphics data → Color mode conversion → DCT conversion → Quantizer → Encoder → End of encoding

Third, there are three basic elements of coding

(a) A compression/reduction conversion can be performed on an image.

(b) The conversion coefficient is quantifiable.

(iii) The quantized coefficients can be coded using functions.

Fourth, the main part of the existing WAVELET image compression tools

(A) Wavelet Transform (WAVELET conversion): The graphic is divided into any size, at least one-half compression.

(B) Filters: This section contains Wavelet Transform, and some famous compression methods.

(iii) Quantizers: Contains two forms of quantification, one is the average quantification and the other is the interpolative quantification, which has a certain influence on the coding architecture.

(D) Entropy Coding: There are two formats, one is to reduce it, and the other is to interpolate.

(5) Arithmetic Coder (mathematical formula): This is based on the Alistair Moffat`s linear time coding histogram.

(6) Bit Allocation (Data Distribution): This process uses efficient division to efficiently allocate any kind of quantification.

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