Synthetic aperture focusing techniques (SAFT) make the spatial resolution of the conventional ultrasound imaging from a single-element focused transducer more uniform in the lateral direction. In this work, two new frequency-domain (FD-SAFT) algorithms are proposed, which are based on the synthetic aperture radar's wavenumber algorithm, and 2-D matched filtering technique for the image reconstruction. The first algorithm is the FD-SAFT virtual source (FD-SAFT-VS) that treats the focus of a focused transducer as a virtual source having a finite size and the diffraction effect in the far-field is taken into consideration in the image reconstruction. The second algorithm is the FD-SAFT deconvolution (FD-SAFT-DE) that uses the simulated point spread function of the imaging system as a matched filter kernel in the image reconstruction. The performance of the proposed algorithms was studied using a series of simulations and experiments, and it was compared with the conventional B-mode and time-domain SAFT (TD-SAFT) imaging techniques. The image quality was analyzed in terms of spatial resolution, sidelobe level, signal-to-noise ratio (SNR), contrast resolution, contrast-to-speckle ratio, and ex vivo image quality. The results showed that the FD-SAFT-VS had the smallest spatial resolution and FD-SAFT-DE had the second smallest spatial resolution. In addition, FD-SAFT-DE had generally the largest SNR. The computation run time of FD-SAFT-VS and FD-SAFT-DE, depending on the image size, was lower by 4 to 174 times and 4 to 189 times, respectively, compared to the TD-SAFT-virtual point source.