This article describes a new image processing method in order to enhance the images under testing based on discrete Hermite wavelet filter. Discrete Hermite Wavelet Transform, which was used in image processing, including compression and noise removal was used after a number of theories proved to be mathematically ready for use in image processing. Through Discrete Hermite Wavelet Transform at different levels by finding a new filter and using it to find peak-to-noise ratio values (PSNR), compression ratio, mean square error (MSE) and bits per pixel found. Achieving a high compression ratio is acquired by using a new image decomposition algorithm. Bit reduction per pixel is obtained at the second level when increasing the level of decomposition to obtain compression ratio while PSNR is decreased with the basic wavelets, due to the features that characterize Discrete Hermite Wavelet Transform. A new filter was discovered more efficient and effective in reducing the error significantly in rebuilding, MSE and bits per pixel, the samples image is used show efficient intermittent wavelets that were built in this work. This method enabling to extract the integration matrices using Hermite wavelet operation matrix of integration that leads to improve the quality of images under testing. The obtained results for decreasing of and increasing of confirm the accuracy and effectiveness of the proposed method. These results can be used in many fields such as medicine, science treatment, compression, and noise removal images.
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