Zero Knowledge Focusing in Millimeter-Wave Imaging Systems Using Gradient Approximation

This communication addresses the focusing problem in the millimeter-wave imaging systems. We categorize the focusing problem into the frequency focusing for wideband systems and the range focusing for narrowband systems. In an out-of-focus wideband system, a shifted shadow of the object is present in the reconstruction, whereas for a range out of the focused system, the recovered images are blurred. To overcome these issues, first, we theoretically show that the defocusing variations for both categories are bounded. Then, we present a universal formulation for focusing problem, which covers both wideband and narrowband systems. As the true focused images are sharp at the boundaries of the objects, our strategy for solving the problem is to maximize a defined sharpness metric. Moreover, we propose an autofocusing zero-knowledge algorithm, which concerns with maximizing the sharpness metric from an unknown object, while the exact gradient of the cost function is unknown. The proposed method is suitable for practical applications since it is simple, fast, and computationally efficient. The simulation results on synthetic and measured data are promising and support our claims that the proposed method increases the quality of the reconstruction.