We propose a holographic microscopy method based on single-pixel imaging technology (HM-SPI). We used a holographic microscopy method based on in-line Gabor holography. In single-pixel imaging technology, cyclic binary masks and amplitude-phase masks are used instead of cyclic Hadamard masks. These masks are generated using the quadratic residue and twin-prime techniques. Numerical results are presented for both cases. Unlike the traditional approach of using DMD technology, our model considers a photodetector as a single-pixel detector. We propose a method based on the fast Fourier transform (FFT) algorithm to reconstruct the original field, which has a computational complexity of O(NlogN). This approach opens up prospects for the development of compact holographic systems capable of operating across a wide spectral range and under limited computational resources.