Millimeter wave (mmWave) imaging is becoming an increased area of interest due to the advancement of commercially available low-cost on-chip mmWave devices and the unique features mmWaves offer. Millimeter waves, unlike optical waves, can penetrate through common visibly degraded environments caused by smoke, fog, or dust. This unique advantage makes mmWave imaging ideal for security monitoring, autonomous vehicles, and simultaneous localization and mapping (SLAM) applications. However, the main limitation of current mmWave devices is they suffer from low angular resolution due to small physical apertures and conventional signal processing techniques. Constructing large physical arrays is expensive and leads to computational challenges due to the increased readout bandwidth. Deep learning approaches have been investigated to achieve high resolution mmWave imaging using downsampled apertures. However, these deep learning techniques typically require large amounts of training data and have limited generalizability. Recently, untrained neural networks (NN) have shown outstanding performance on challenging computational imaging inverse problems such as denoising, inpainting, and deblurring without using any training data. In this work, we design and evaluate the performance of untrained neural networks and sub-sampled apertures for sparse multi-input multi-output (MIMO) radar imaging.

We approach the design of our proposed sparse radar imaging method from two aspects: aperture sub-sampling scheme and NN architecture. We design a minimum redundant array (MRA) inspired sub-sampled aperture that reduces the radar read-out bandwidth by 75% compared to conventional MIMO multiple radar chip Nyquist sampled aperture designs. This allows our method to work with a single radar chip and demonstrates that there is significant compressed sensing that can be applied in radar aperture design. The second design aspect of our method is the NN architecture, where we analyzed state-of-art untrained designs using convolutional neural networks (CNN) and multi-layer perceptions (MLP). Through extensive experiments, we find that current untrained NN designs work well for natural images but achieve subpar performance on radar images. We propose a CNN decoder architecture inspired by Deep Decoder that is highly optimized for sparse radar imaging. In our experiments we show that our NN architecture significantly outperforms competing untrained methods.

A crucial component in evaluating the performance of untrained methods for sparse radar imaging is analyzing the image reconstruction quality, generalizability to scene changes, and inference time. We find that the proposed untrained method is capable of performing joint deblurring and denoising without requiring any training data. The proposed method suppresses aliasing artifacts from the sparse aperture design as well as sinc-like artifacts from the finite aperture size. We demonstrate that the proposed method achieves high reconstruction quality in a variety of outdoor and indoor scenes using real experimental data collected with a 76-81 GHz mmWave radar. One of the main limitations of untrained methods is the slower inference time compared to trained methods. In response, we propose a new initialization scheme that leverages the fact that between radar frames the scene does not change significantly and thus we use the weights of the trained NN from the previous frame for initialization. We demonstrate that, using our new untrained NN initialization scheme we can achieve a 5× speed up in inference time compared to using random initialization.

Overall, this work advocates for the use of untrained NN to achieve high resolution sparse radar imaging. We find that our proposed sub-sampled aperture and untrained NN architecture out perform competing untrained baselines and achieves similar imaging performance to conventional approaches using a Nyquist sampled aperture. Additionally, we find that the proposed method is robust to environmental changes and can achieve inference times on the order of seconds with novel NN initialization schemes.