The colored image has a large array of numbers that take up a lot of space, creating a problem with transportation and storage, which needs to be urgently solved. It’s essential to find a mathematical tool that shrinks this space when transferring and storing the colored image over the years. Continuous waves such as Fourier and discrete waves such as Haar Symlet 2, coiflet 2, and daubecheis 2 were founded by shrinkage and expansion and characterized with the help of s and r parameters. With the help of the MATLAB program, these basic wavelets installed supplication and image compression, analysis, and lifting procedures. In this study, new waves based on polynomials were discovered, relying on the parent function and through many calculations, clarifying many theories and important features that this wave possesses, such as the orthogonal feature and approach that qualifies these new waves in image processing such as squeeze, jam, and analyze images by searching for a filter. It is suitable and new for carrying out the analysis and reconstruction process with high-pass and low-pass filters resulting from the scaling and wavelet function. Four samples of color images are shown. The compression process was carried out with the help of MATLAB. The use of new waves is Multi Discrete Laguerre Wavelet Transfer, where the standard criteria resulting from the compression process were calculated and the most efficient results were obtained without losing the original information of the image, compared to the standard waves’ tables, which will demonstrate the efficiency of these new wavelets in Multi Discrete Laguerre Wavelet transform.

In this work the new operations matrix was derived for Multi Discrete Laguerre Wavelets Transform (MDLWT) with the dimension  and this matrix was derived by the integrals of the functions that obtained from the mother function or the mother wave. This matrix is the coefficients matrix of the developed multi wavelet and this wavelet was applied in image processing using the Matlab program, where a new program was built that applies to many of the images and examples the proposed wave efficiency. In addition, MSE and PSNR were calculated and good results were compared to the previous methods.