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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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This article introduces novel image processing techniques due to improve the images under examine based on Chebyshev wavelet filter. The technique enabling to obtain Chebyshev wavelet transform using four kinds of Chebyshev wavelet operation matrix of integration, which conduct to enhance the images quality under examine. After comparing the results with standard waves that have a large role in the image processing, it was concluded that the second type of proposed wavelets is the most efficient of the three types, all this work was done using the MatLab program. The obtained results indicate decreasing of MSE= 1.777910-29, increasing both PSNR=340.2918, BPP=0.0078125 and compression ratio CR=0.03% reveal the effectiveness and accuracy of the suggested technique. The results can be utilized in various areas such as science treatment, medicine, noise removal and compression images.

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