Sophisticated systems take advantage of approximate circuits for energy management. A gate-level structure is introduced to make a novel imprecise full adder (FA) cell by the gate diffusion input (GDI) strategy. The carbon nanotube field-effect transistor (CNTFET) technology lowers the FA power, and the swing issue is resolved by the dynamic threshold (DT) technique. The FA specifications are 10 transistors, two internal nodes, 0.191-μm 2 area, three errors, and an error rate (ER) of 37.5%. Some inputs are directly passed to the final stage of the FA to reduce the delay and dynamic power. The FA is used in three 4:2 compressors with 12, 16, and 20 transistors, respectively. The compressors are based on the modified stacking concept to attain low power, small area, and high speed. The compressors are used up in the partial product reduction tree (PPRT) of a new 8-bit inexact multiplier. Regarding the multiplier, the power-delay product (PDP) is decreased by 25.21%, and the normalized mean error distance (NMED) shows high accuracy. An imprecise discrete cosine transform (DCT) is implemented by the multiplier for image compression, and compared with the literature, the peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM) are amended by 8.26% and 7.29%, respectively.