# Sparse microwave imaging: A new concept in microwave imaging technology

Sparse microwave imaging is a novel concept in microwave imaging that is intended to deal with the problems of increasing microwave imaging system complexity caused by the requirements of the system applications. Under the support of the 973 program "Study of theory, system and methodology of sparse microwave imaging", Chinese scientists have conducted considerable research into most aspects of sparse microwave imaging, including its fundamental theories, system design, performance evaluation and applications. Their work, consisting of a series of papers, was published in Science China Information Sciences 2012, vol. 55 (8), as a special issue on sparse microwave imaging. An overview of their work can be found in the paper written by Professor Wu YiRong and his Science and Technology group from the Microwave Imaging Laboratory at the Institute of Electronics of the Chinese Academy of Sciences, entitled "Sparse microwave imaging: Principles and Applications".

Microwave imaging is one of the two major tools of remote sensing, and has been widely used in fields such as agriculture, forestry, oceanic monitoring, topography mapping and military reconnaissance. The best known modern microwave imaging technology used in remote sensing is synthetic aperture radar (SAR), which transmits an electromagnetic wave toward the scene from a platform moving in a straight line, receives the radar echo and produces a high resolution microwave image via signal processing. Compared with optical sensing, microwave imaging has the ability to provide all-weather round-the-clock observation, and can be applied to deal with some special sensing requirements, including moving target detection and digital elevation model extraction.

As microwave imaging technology has been used in increasing numbers of fields, the users have of course raised demands for numerous new requirements for their microwave imaging systems. Among them, high resolution and a wide mapping swath are the basic requirements for modern microwave imaging systems. High resolution means that more details can be observed, and the wide mapping swath means larger observation areas.

According to microwave imaging theory – a theory that has not changed for over 60 years following the invention of SAR technology – the signal bandwidth and the system sampling rate determine the achievable resolution and swath of the microwave imaging system. The only way to improve the signal bandwidth and sampling rate is to increase the system complexity, i.e., to use hardware that is larger, heavier and demands greater power consumption. However, we must eventually reach a limit to the increases in system complexity, and Moore's Law could not hold forever. The concept of sparse microwave imaging was therefore developed.

Sparse microwave imaging introduces sparse signal processing theory to microwave imaging as a replacement for conventional signal processing schemes based on matched filtering. Sparse signal processing was a concept that was developed by mathematicians in the late 1990s, and includes a set of mathematical tools designed to deal with sparse signals – a signal is sparse when most of the elements of the signal are (or are very close to) zero. Thanks to the extraordinary work known as compressive sensing by D. Donoho, E. Candès and T. Tao over the last decade, sparse signal processing theory, and compressive sensing theory in particular, has become a focal point for research in current signal processing fields. Essentially, sparse signal processing theory asserts that, if a signal is sparse, then it can be measured with far fewer samples than would be required for traditional sampling schemes, and can then be perfectly reconstructed from these few samples via sparse reconstruction algorithms.

If we introduce sparse signal processing theory to microwave imaging, we can then achieve sparse microwave imaging. However, while the concept sounds simple, the combination of sparse signal processing with microwave imaging is in fact quite a complex problem. The difficulties include: the method used to obtain a sparse representation of a scene, determination of the constraints of sparse observation, and efficient and robust reconstruction of the microwave image from the sparse observation data.

Consider, for example, the sparse representation problem. We know that sparse signal processing theory can only deal with sparse signals, but, unfortunately, the observed scenes are usually not sparse. In optical sensing, although an optical picture is not always sparse, it can be expected to have a sparse representation in a transform domain such as the discrete cosine transform (DCT) domain or a wavelet domain. However, we are not so lucky in microwave imaging. To date, no universally applicable transform domain has been found that would enable microwave imaging scenes to have sparse representations. We can only deal with a scene that it is sparse itself.

Another example is the reconstruction algorithm. Mathematicians have developed many sparse reconstruction algorithms with various features, and some of them can feasibly be used in sparse microwave imaging, but one problem remains: calculation efficiency. The size of microwave imaging scenes is always very large, especially in wide mapping swath applications. Experimental results show that the calculation time duration – which can usually be counted in months – is unacceptable when the scene is large. In positive news, some accelerated algorithms have been derived by Chinese scientists.

Sparse microwave imaging theory and technology can be applied in two ways: to design new systems, and to improve existing microwave imaging devices. As a new microwave imaging concept, we can of course design optimized microwave imaging systems using sparse microwave imaging theory for guidance. We can also use the signal processing methods of sparse microwave imaging to improve the imaging performance of the existing microwave devices, e.g. to increase the image distinguishability, reduce the sidelobes and reduce ambiguity. Discussions on both of these topics can be found in the special issue.

Sparse microwave imaging is believed to have the ability to resolve the conflict between growing microwave imaging performance requirements and increasing system complexity. Under this new microwave imaging concept, the system complexity could be reduced remarkably without adversely affecting the imaging performance. Although there are many problems with the technology that need to be solved, sparse microwave imaging can be expected to have a bright future.