The backward projection algorithm belongs to the time-domain algorithm in synthetic aperture radar imaging algorithms and is often used as a comparative algorithm for mixed domain or frequency-domain algorithms. This article designs a one-dimensional sparse topological linear array equivalent to a one-dimensional dense linear array through phase compensation, and derives the matched filtering algorithm and wavenumber-domain backward projection algorithm. The numerical simulation results show that the simulated multi-point target point spread function has a horizontal and vertical direction of about 3.5 mm and a distance direction of about 12.6 mm, verifying the correctness of the matched filtering algorithm and the wavenumber-domain backward projection algorithm. By building a physical system, matching filtering algorithm, wavenumber-domain backward projection algorithm, and backward projection algorithm were used to image the line pair resolution plate, with horizontal and vertical resolutions of 4 and 5 mm, respectively. The simulation results were in good agreement with the theoretical resolution. Finally, for the simulated imaging of the actual target, the matched filtering algorithm took 4.461 s, the wavenumber-domain backward projection algorithm took 54.477 s, and the backward projection algorithm took 684.985 s, which is consistent with the theoretical complexity of the three algorithms. The median filtering gradient similarity value in the images of the three algorithms is about 0.9, and the image contrast value is about 6.6, verifying the effectiveness of the matched filtering algorithm and the wavenumber-domain backward projection algorithm.