The Internet has turned the entire world into a small village;this is because it has made it possible to share millions of images and videos. However, sending and receiving a huge amount of data is considered to be a main challenge. To address this issue, a new algorithm is required to reduce image bits and represent the data in a compressed form. Nevertheless, image compression is an important application for transferring large files and images. This requires appropriate and efficient transfers in this field to achieve the task and reach the best results. In this work, we propose a new algorithm based on discrete Hermite wavelets transformation (DHWT) that shows the efficiency and quality of the color images. By compressing the color image, this method analyzes it and divides it into approximate coefficients and detail coefficients after adding the wavelets into MATLAB. With Multi-Resolution Analyses (MRA), the appropriate filter is derived, and the mathematical aspects prove to be validated by testing a new filter and performing its operation. After the decomposition of the rows and upon the process of the reconstruction, taking the inverse of the filter and dealing with the columns of the matrix, the original matrix is improved by measuring the parameters of the image to achieve the best quality of the resulting image, such as the peak signal-to-noise ratio (PSNR), compression ratio (CR), bits per pixel (BPP), and mean square error (MSE).

翻译：互联网将整个世界变成了一个小村庄，这是因为其使得数百万张图像和视频的共享成为可能。然而，海量数据的发送和接收仍被视为一项主要挑战。为解决此问题，需要一种新算法来减少图像比特数并以压缩形式表示数据。尽管如此，图像压缩仍是传输大文件和图像的重要应用。这需要在该领域进行适当且高效的传输，以完成任务并达到最佳效果。本文提出了一种基于离散埃尔米特小波变换（DHWT）的新算法，该算法展示了彩色图像的效率和保真度。通过压缩彩色图像，该方法在将小波引入MATLAB后，对其进行分析并将其分解为近似系数和细节系数。利用多分辨率分析（MRA），推导出合适的滤波器，并通过测试新滤波器并执行其运算来验证数学方面的有效性。在行分解后，于重建过程中，通过取滤波器的逆并处理矩阵的列，利用测量图像参数（如峰值信噪比（PSNR）、压缩比（CR）、每像素比特数（BPP）和均方误差（MSE））来改进原始矩阵，以获得最佳输出图像质量。