Compressive sampling in passive millimeter-wave imaging

We present a Hadamard transform based imaging technique and have implemented it on a single-pixel passive millimeter-wave imager in the 146-154 GHz range. The imaging arrangement uses a set of Hadamard transform masks of size p × q at the image plane of a lens and the transformed image signals are focused and collected by a horn antenna of the imager. The cyclic nature of Hadamard matrix allows the use of a single extended 2-D Hadamard mask of size (2p-1) × (2q-1) to expose a p × q submask for each acquisition by raster scanning the large mask one pixel at a time. A total of N = pq acquisitions can be made with a complete scan. The original p × q image may be reconstructed by a simple matrix operation. Instead of full N acquisitions, we can use a subset of the masks for compressive sensing. In this regard, we have developed a relaxation technique that recovers the full Hadamard measurement space from subsampled Hadamard acquisitions. We have reconstructed high fidelity images with 1/9 of the full Hadamard acquisitions, thus reducing the image acquisition time by a factor of 9.