Deep image prior based high resolution isar imaging for missing data case

Abstract

Radio detection and ranging or Radar as an abbreviation form, is a system that aims to detect the location, shape, and speed of objects that are named as targets. Earlier Radar systems were used for high level applications such as defence systems, airplanes, air surveillance and traffic control, etc. Later, it took place in daily life applications like smart cars, smart home devices, vital sign detection and a lot more to satisfy the needs of human life. Basically, radar sends electromagnetic waves from its transmitter and these waves reflect from the surface of objects, then the receiver of the radar collects these backscattered signals to process. Such a basic way, target speed and range can be extracted by applying 1-D signal processing on backscattered waves. Apart from the 1-D application, 2-D radar signal processing can extract the target shape on cross-range domain. In order to generate a radar image, electromagnetic waves, which are in different frequencies are sent to target and target is observed from different angles. Frequency sweeping can be done by some well known methods like stepped frequency or linear frequency modulation, thus the signals that have variable frequency can be generated by the same antenna. For moving targets, inverse synthetic aperture is used, which uses the relative motion of the target to use it as an observation angle. Synthetic Aperture Radar (SAR) is the case when radar is moving and the target is stationary whereas in Inverse Synthetic Aperture Radar (ISAR), radar is stationary and target is moving. As previously noted, such a manipulation on relative speed is used to generate ISAR/SAR data and polar format algorithm is used for Polar to Cartesian Coordinates conversion. Later 2D inverse Fourier transform can be applied to raw data to extract a radar image, which is also named as the Range Doppler (RD) image of the target. Besides good imaging performance capability, various challenges have to be handled in ISAR imaging. Some serious problems may arise during measurements that are challenging and this phenomenon affects the quality of the ISAR image. One of the well known problems is missing data case. Undesirable interference, an external jamming signal, beam blockage, or some other technical problem may lead to the missing data when receiving backscattered electromagnetic waves that are reflected from the target. There is also Compressive Sensing (CS) method that aims to generate radar images with less samples. For both cases, the conventional RD imaging method will perform poor imaging result. Missing data is a common problem for many radar related fields. In order to overcome missing data problem 1-D signal reconstruction algorithms are proposed such as Matching Pursuit (MP) and Basis Pursuit (BP). These approaches represent signals with dictionaries instead of conventional Fourier based superpositioned sinusoids. Although they are useful, 1-D reconstruction algorithms can not be applied directly to the 2-D signals, thus, Kronocker product based solutions are proposed to reconstruct 2-D signals with 1-D reconstruction algorithms. Such a process has a high computational cost in addition to the excessive memory requirement, so that 2-D sparse signal reconstruction algorithms are proposed. 2-D Smoothed L0 norm (2-D SL0) is the 2-D form of the 1-D Smoothed L0 norm sparse signal reconstruction algorithm and it proposed to reconstruct 2-D signal with low computational cost and low memory requirement by comparing to the 1-D signal reconstruction methods. Many successful studies have been done with the proposed 2-D SL0. There are also other methods available which are proposed to recover missing entries by exploiting the low rank feature of the matrix. Go Decomposition (GoDec), Low Rank Matrix Fitting (LMAFIT) and Nuclear Norm Minimization (NNM) are used to recover missing data on many applications that are focused on real data, so these are also not directly applicable to the ISAR raw data. There is also the Augmented Lagrangian Multiplier (ALM) for constrained optimization problems. ALM can also be applied to matrix completion problems, but primal variables of the algorithm can only be solved inexactly; thus, Inexact Augmented Lagrangian Multiplier (IALM) is proposed for matrix completion. Apart from the well known matrix completion methods, it can be directly applied to the complex data. Recently, deep learning based approaches are quite famous to recover missing parts of real images. Deep learning based approaches usually require a high amount of training data that contains corrupted images as input and original images as target to train deep convolutional neural networks to achieve tasks such as denoising, inpainting, and super-resolution. Previously, some studies trained deep networks to do such tasks on ISAR images. As it was mentioned before, the ISAR image is generated by the traditional RD algorithm. Deep learning based approaches use the amplitude of the 2-D IFFT result so that they neglect the imaginary part of 2-D IFFT result. In this study, a novel deep learning based ISAR data reconstruction method is proposed. Unlike existing studies, the proposed model uses complex data instead of the conventional RD image. Deep Image Prior (DIP) is used as a deep learning model that does not require a pre-training process to complete missing cases on input data. DIP directly can perform iteratively on single occluded data thanks to its hand crafted prior feature. In order to reconstruct ISAR raw data, the occluded matrix is separated into its real and imaginary parts, and missing entries in the backscattered field matrix are completed sequentially and separately. Thus, ISAR raw data construction is done by a deep learning model that does not need pre-training. In order to check the validity and robustness of the proposed model, three different comparison methods are used, such as IALM, 2-D SL0 and NNM. NNM performs on real data normally so that same separation process applied to raw ISAR data for NNM. In the experimental results, two simulated and one real ISAR data are tested under four different missing scenarios such as pixel-wise, equal random missing in each column, column-wise and compression cases. For all four missing scenarios, three different missing ratios are applied to the test data, like %30, %50 and %70, respectively. The results show that the proposed method outperforms existing ones both visually and quantitatively.