A lossy compression algorithm for data basis images based on DCT decomposition and diffuse representation

In this manuscript, we present a novel approach for compressing a database of images. Initially, we introduce a new representation that effectively reduces the data required to represent the image, enhancing the efficiency of subsequent compression steps. We apply the Discrete Cosine Transform (DCT) to the new representation and perform thresholding at different levels for a selected image. The DCT is known for concentrating image energy into a few coefficients, making it ideal for compression. By calculating the Peak Signal-to-Noise Ratio (PSNR) variation of the reconstructed image and evaluating the percentage of non-zero coefficients after thresholding, we plot the corresponding curve. These calculations provide insights into the quality of the reconstructed image, ensuring minimal degradation from compression. We repeat the steps with the Discrete Wavelet Transform (DWT), known for its multi-resolution analysis, to compare its performance against the DCT. The curves help us observe which process allows for image reconstruction with only a small percentage of coefficients, achieving significant data reduction. This comparative analysis determines the most effective method for various types of images. After analyzing the digital results from these curves, we generate and discuss the reconstructed image outcomes in detail. The digital and visual results presented at the conclusion demonstrate the robustness of the proposed strategy. We also explore potential applications in fields such as medical imaging, remote sensing, and multimedia storage, highlighting its versatility. Our findings suggest that the novel representation combined with DCT is highly effective, offering substantial storage space savings while maintaining image quality. These results are significant for theoretical research and practical implementations, providing a foundation for future advancements in image compression technologies.