Compressed sensing (CS) techniques allow for faster imaging when combined with scan architectures, which typically suffer from speed. This technique when implemented with a subterahertz (sub-THz) single detector scan imaging system provides images whose resolution is only limited by the pixel size of the pattern used to scan the image plane. To overcome this limitation, the image of the target can be oversampled; however, this results in slower imaging rates especially if this is done in two-dimensional across the image plane. We show that by implementing a one-dimensional (1-D) scan of the image plane, a modified approach to CS theory applied with an appropriate reconstruction algorithm allows for successful reconstruction of the reflected oversampled image of a target placed in standoff configuration from the source. The experiments are done in reflection mode configuration where the operating frequency is 93 GHz and the corresponding wavelength is λ = 3.2 mm. To reconstruct the image with fewer samples, CS theory is applied using masks where the pixel size is 5 mm × 5 mm, and each mask covers an image area of 5 cm × 5 cm, meaning that the basic image is resolved as 10 × 10 pixels. To enhance the resolution, the information between two consecutive pixels is used, and oversampling along 1-D coupled with a modification of the masks in CS theory allowed for oversampled images to be reconstructed rapidly in 20 × 20 and 40 × 40 pixel formats. These are then compared using two different reconstruction algorithms, TVAL3 and ℓ1-MAGIC. The performance of these methods is compared for both simulated signals and real signals. It is found that the modified CS theory approach coupled with the TVAL3 reconstruction process, even when scanning along only 1-D, allows for rapid precise reconstruction of the oversampled target.