小波变换的理论是近年来兴起的新的数学分支，素有“数学显微镜”的美称。它

The theory of wavelet transform is a new branch of mathematics that has emerged in recent years and is known as "mathematical microscope". It is another milestone field after Fourier proposed Fourier transform in 1822, and solved many difficult problems that Fourier transform could not solve. Wavelet transform can simultaneously process the low-frequency long-term characteristics and high-frequency short-term characteristics of the signal, has good localization properties, can effectively overcome the limitations of the Fourier transform when processing non-stationary and complex signals, and has a very strong Adaptive, so it has excellent application value in image processing. This design mainly analyzes the image decomposition and image compression technology based on wavelet transform, and uses Matlab software to decompose the image, and then extract the low-frequency information similar to the original image to achieve the purpose of compressing the image. Make the first layer decomposition and the second layer decomposition separately, and compare the effect of image compression. <br><br>Keywords: wavelet transform; Matlab; image decomposition; image compression

The theory of wavelet transformation is a new branch of mathematics that has emerged in recent years, and is known as the "mathematical microscope". It is another landmark field after Fourier proposed the four-way transformation in 1822, solving many difficult problems that Fourier transformation cannot solve. Wavelet transformation can make the low frequency long-time characteristic steam and high frequency short-term characteristics of the signal be processed at the same time, have good localized properties, can effectively overcome the limitations of Fu's transformation in dealing with non-stable complex signals, has a strong adaptability, so it has excellent application value in image processing. This design mainly analyzes the image decomposition and image compression technology based on wavelet transformation, and uses Matlab software to decompose the image, and then extracts the low-frequency information similar to the original image, so as to achieve the purpose of compressing the image. The first layer decomposition and the second layer decomposition are made, and the effect of image compression is compared.<br><br>Keywords: Waveshift; Matlab; Image Decomposition; Image Compression

The theory of wavelet transform is a new branch of mathematics rising in recent years, known as "mathematical microscope". It is another milestone field after Fourier transform was put forward in 1822. It has solved many difficult problems that cannot be solved by Fourier transform. Wavelet transform can make the low-frequency long-time characteristics and high-frequency short-time characteristics of the signal be processed at the same time. It has good localization property, can effectively overcome the limitations of Fourier transform in processing non-stationary complex signals, and has strong adaptability. Therefore, it has excellent application value in image processing. This design mainly analyzes the image decomposition and image compression technology based on wavelet transform, and uses MATLAB software to decompose the image, and then extracts the low-frequency information similar to the original image to achieve the purpose of image compression. The first level decomposition and the second level decomposition are made respectively, and the effect of image compression is compared.<br>Keywords: wavelet transform; MATLAB; image decomposition; image compression<br>