Computational imaging (CI) techniques realized by dynamic metasurface antennas (DMAs) offer significant advantages in the hardware design reducing the cost of such systems. In this paper, we present a physical layout based solely on DMA panels that can be used to synthesize electrically large apertures suitable for microwave imaging. Although hardware is significantly simplified, the challenge of using CI DMA-based systems presents itself in the signal processing layer. This is because in microwave CI the transfer function of the antennas is used to encode information from the imaged target scene and compress it into a single (or a few) channel(s). As a consequence, real-time Fourier-based image reconstruction algorithms cannot be directly applied because of the nature of the compressed back-scattered signals. In this work, we propose an algorithm that employs a decompression step such that the signal is converted to a suitable form for spatial frequency domain processing. The proposed technique mitigates the challenges of applying the algorithm in the near-field. Crucially, it also eliminates the need for a computationally expensive Stolt interpolation step, which can be a significant bottleneck for conventional Fourier-based image reconstruction algorithms. Numerical and experimental CI results are presented to validate the ability of the proposed system and algorithm to produce reconstructed images of good quality. The benefits of the proposed algorithm in terms of execution time and storage requirements are also explored in this work.