• Using the carbon nanotube field-effect transistors technology to design approximate arithmetic circuits. • The gate diffusion input and dynamic threshold techniques are integrated to attain efficient circuits. • The presented approximate full adders show reliable performance during image processing. • The approximate full adders applied in bioimage processing. • Fat and water can be detected in bioimages by the presented approximate cells. Two new approximate full adders (FAs) are proposed by the multiplexers (MUXs) and OR gates with the gate diffusion input (GDI) technique. The cells are named GDI-based MUX approximate FAs (GMAFAs), GMAFA1, and GMAFA2. The threshold voltage drop of the GDI-based circuits is solved by carbon nanotube field-effect transistors (CNTFETs) technology and the dynamic threshold (DT) technique. The FAs have accurate C out , approximate Sum, and a low number of transistors. They are low-power, high-speed, and energy-efficient for ripple-carry adders (RCAs). The GMAFA1 and GMAFA2 have a total area of 0.068 µm2 and 0.119 µm2, respectively, which demonstrate 27.8% and 54.55% improvement in power-delay-area-product (PDAP) in comparison with the best references. The results of error distance (ED), normalized mean error distance (NMED), power signal-to-noise ratio (PSNR), and energy-saving confirm the accuracy of the presented cells for image processing applications. [Display omitted] [ABSTRACT FROM AUTHOR]