Edge images are often used in computer vision, cellular morphology, and surveillance cameras, and are sufficient to identify the type of object. Single-pixel imaging (SPI) is a promising technique for wide-wavelength, low-light-level measurements. Conventional SPI-based edge-enhanced techniques have used shifting illumination patterns; however, this increases the number of the illumination patterns. We propose two deep neural networks to obtain SPI-based edge images without shifting illumination patterns. The first network is an end-to-end mapping between the measured intensities and entire edge image. The latter comprises two path convolutional layers for restoring horizontal and vertical edges individually; subsequently, both edges are combined to obtain full edge reconstructions, such as in the Sobel filter.