Implementação em VHDL e análise comparativa da Transformada Discreta do Cosseno e a aproximação de Lengwehasatit-Ortega

Abstract

The high volume of images transmitted daily over the internet consumes a significant portion of bandwidth and processing capacity. To optimize compression and maintain quality, digital signal processing tools like the Discrete Cosine Transform (DCT) are utilized. The DCT is a mathematical operation that concentrates most of the signal's energy in low frequencies, making it highly useful in image compression algorithms. The calculation of the Discrete Cosine Transform is performed using matrix multiplication, where the elements of the transformation matrix are floating-point numbers. To simplify these calculations, various approximations for the Discrete Cosine Transform that use as many integers as possible in their transformation matrices can be found in the literature. Due to the recurrent matrix calculations in modern computational systems, especially for image processing and artificial intelligence, many systems feature ASICs (Application Specific Integrated Circuits) or parts of SoCs (System on Chip) dedicated to this task. In this work, several DCT approximations were evaluated in the context of image compression. The Lengwehasatit-Ortega approximation, which showed the best performance, along with the exact DCT, were implemented in VHDL and synthesized in FPGA. It was observed that, following the same design philosophy, the approximation consumed significantly fewer hardware resources, as expected.