TEMPORAL RATE UP-CONVERSION OF SYNTHETIC APERTURE RADAR VIA LOW-RANK MATRIX RECOVERY Minh Dao 1 , Lam Nguyen 2 , and Trac D. Tran 1 1 Department of Electrical and Computer Engineering, The Johns Hopkins University, MD 21218 2 U.S. Army Research Laboratory, MD 20783 ABSTRACT The radar data to form synthetic aperture radar (SAR) im- agery is normally transmitted and received by moving plat- forms like aircraft or vehicles. In many situations, the plat- forms move at high speed; which reduces the number of sam- pling records collected to the synthetic aperture, hence de- grades the quality of the reconstructed SAR images. There- fore, it is necessary to develop an algorithm that is capable of increasing the temporal frequency rate of the received data. In this paper, we propose a novel technique to generate inter- mediate records from the existing ones by a locally-adaptive low-rank matrix recovery framework. The system first fills in the blank records using a bi-directional motion estimation scheme. The initialized aperture records are then refined by a robust low-rank matrix completion algorithm using the refer- ence from neighborhood clean records. Experiments demon- strate that the proposed method provides comparative results when up-converting the aperture rate by a factor of two or four, both in mean square error of the raw SAR signal and PSNR performance of the recovered SAR images. Index Terms— Synthetic aperture radar (SAR), rate up- conversion, low-rank matrix completion, robust PCA. 1. INTRODUCTION A synthetic aperture radar transmits and receives electromag- netic waves by a sensor attached to a platform moving along the cross-range direction to generate the synthetic aperture [1]. The system shoots and collects signals at a constant pulse repetition interval (PRI) along the radar path to produce equally spaced aperture records. The collected data is then processed by a backprojection algorithm to form high resolu- tion SAR imagery. The more number of sensing records the system receives, the sharper and higher quality the formed im- age is. An aperture rate up-conversion algorithm is therefore important. Generally, if we can double the number of sensing records, the vehicle carrying the radar system can boost the travelling speed by a factor of two. The problem of inserting new sensing records between the existing ones can be considered as the problem of completing full missing aperture records along the temporal domain and has not been thoroughly researched for SAR data. Most of the existing completion techniques solve for the cases of re- covering missing or corrupted samples [2, 3] or interpolating the signal in the spectral domain. However, almost no meth- ods have been successful in tackle the challenging problem of recovering whole missing sensing records without damaging image structures and details. Recent advances on low-rank matrix recovery techniques have opened a new trend in approaching completion prob- lems. Matrix recovery problem is a robust framework to recover incomplete or corrupted data by extracting low- dimensional structures from high-dimensional observations. Matrix completion [4] and robust principal component analy- sis (robust PCA or RPCA) [5] are two highly applicable low- rank matrix recovery techniques in which matrix completion retrieves missing elements while RPCA recovers an under- lying low-rank matrix from its sparse but grossly corrupted entries. These two problems have been beneficial in solv- ing a wide range of applications including background mod- eling, target tracking [5], image alignment [6] or video com- pletion [7] problems. Nevertheless, these techniques cannot be directly applied for matrices with fully missing rows or columns. Furthermore, most of the existing applications as- sume global low-rank property of the input data which is not commonly true for the case. With consideration of these ob- servations, we propose a new method to take full advantage of matrix completion and RPCA methods to effectively inter- polate full aperture records of SAR data. The way to construct dictionary of the proposed method is different from existing techniques in the sense that it uses the reference from the neighboring signal, while for most of other SAR sparsity-driven completion approaches [2, 3], the dictionary is formed based on the transmitting signal of the SAR system. The advantage of the local-based dictionary formation is that it can make use of the high temporal cor- relation of SAR data. The algorithm is then summarized by two main steps: 1. the initialization step fills in new records by a simple motion-estimated scheme; and 2. the refinement step updates the records by a proposed robust matrix comple- tion using confident weights obtained from the first step. For simple instruction, the detailed algorithm in this paper only describes the case of temporal upsampling by a factor of two. 2358 978-1-4799-2341-0/13/$31.00 ©2013 IEEE ICIP 2013