Inverse synthetic aperture radar (ISAR) imaging is a crucial technique for achieving high-resolution radar imaging. Its range resolution is primarily attributed to the bandwidth, while the cross-range resolution is derived from the relative motion between the target and the radar. However, uncertain relative motion also leads to the need for motion compensation in the imaging process of ISAR. Translational compensation in motion compensation usually includes range alignment (RA) and phase correction. The echoes after range compression at different slow times exhibit offsets in the range dimension due to relative motion. The core challenge addressed by range alignment techniques is how to compensate for these offsets, ensuring that signals from the same scatter point at different slow times align within the same range cell. The quality of range alignment directly influences the difficulty of subsequent phase correction and the final focusing accuracy in ISAR imaging. Therefore, research on range alignment methods has consistently garnered attention from researchers in relevant fields.
Traditional approaches attempt to compensate for every offset in range profiles (RP), aiming to optimize a specific evaluation metric. Two common traditional methods are the cross-correlation method and the minimum entropy (ME) method [
1,
2]. The cross-correlation method involves finding the maximum value of the correlation function, while the minimum entropy method seeks to minimize the entropy function. Due to its superior compensation accuracy, the minimum entropy method has been widely employed and has evolved in its application. Currently, there are many minimum entropy methods with targeted enhancements [
3,
4,
5,
6,
7]. In 2009, a method to improve efficiency by minimizing the average range profile (ARP) of entropy was proposed [
3]. In 2013, scholars proposed a coordinate descent algorithm to solve the optimization problem implemented by the quasi-Newton algorithm and improved the entropy minimization method under a low signal-to-noise ratio [
4]. In 2015, scholars proposed a fast MEA method based on Newton’s method to improve computational efficiency [
5]. In 2016, scholars used local quadratic curves to approximate the minimum entropy to improve accuracy [
6]. In 2018, a more robust minimum entropy method was proposed by finding the Doppler centroid [
7]. Some parameterized methods can effectively estimate motion parameters under stable imaging conditions [
8,
9,
10,
11,
12]. In 2019, a noise-robust compensation method was proposed that used tracking information and parameter minimum entropy optimization to compensate for the 2-D spatial-variant phase errors of the maneuvering target [
8]. In 2021, scholars proposed a translational motion compensation method based on parabolic curve detection and entropy minimization in spaceborne ISAR imagery for space targets [
9]. In 2022, a noise-robust high-speed motion compensation algorithm was proposed using the continuity of a high-speed moving target’s velocity [
10]. In 2022, scholars proposed an improved parametric translational motion compensation algorithm based on signal phase order reduction (SPOR) and minimum entropy [
11]. In 2022, scholars proposed a noise-robust translational motion compensation method based on high-order local polynomial transform-generalized scaled Fourier transform (HLPT-GSCFT) [
12]. However, the prerequisite for achieving high precision with most traditional minimum entropy methods is to iterate every offset to compute entropy values, leading to time-consuming and inefficient processes. With the rapid development of deep learning methods in recent years, utilizing deep learning networks to enhance the efficiency of the ISAR imaging process has become a current research focus. Some scholars are dedicated to applying Fully Convolutional Network (FCN) architectures to generate focused ISAR images directly [
13,
14,
15,
16] or predict polynomial model parameters for phase error [
17,
18]. In 2019, an estimation method of translational parameters based on the deep learning theory was proposed [
17]. In 2020, scholars realized the potential of convolutional neural networks (CNNs) in compressed sensing (CS) ISAR imaging and designed an FCN structure for imaging [
13]. In 2020, scholars designed a convolution iterative shrinkage-thresholding (CIST) network structure for imaging under the framework of FCN [
14]. In 2020, an ISAR imaging algorithm based on the keystone transform and u-net structure was proposed [
15]. In 2022, scholars proposed a noniterative autofocus scheme based on deep learning and the minimum entropy criterion [
18]. In 2023, an ISAR autofocus algorithm based on FCN combined with transfer learning was proposed [
16]. Specifically, for sparse aperture ISAR (SA-ISAR) imaging, many scholars choose the alternating direction method of multipliers (ADMMs) [
19,
20,
21,
22] or approximate message passing (AMP) [
23] as the foundation to construct iterative networks for optimizing and improving the imaging process. The most recently proposed focused imaging methods that employ deep learning do not primarily address the range alignment process. This has garnered researchers’ attention towards the recent application of deep learning in range alignment. In 2019, scholars proposed a CV-GRUNet to learn the aligned range profiles [
17]. In 2022, scholars proposed an RNN-based range alignment (RNN-RA) method to learn the aligned range profiles [
24]. In 2023, scholars proposed a CNN-RNN attention mechanism network range alignment (CRAN-RA)-based method to predict the aligned range profiles [
25]. From the research results, it can be observed that both the RNN-RA method and CRAN-RA method exhibit excellent performance on their respective constructed datasets. However, the generalization of the networks requires further validation.
From the state of the art, it is evident that deep learning networks hold significant potential for enhancing the efficiency of the ISAR imaging process. However, directly transferring existing neural network structures from the computer vision (CV) domain to replace current ISAR imaging theories may encounter challenges related to poor generalization and limited practicality. Selecting deep learning networks to enhance reliable technologies is currently an effective strategy. Therefore, inspired by the existing deep learning networks applied to range alignment, this paper proposes a range alignment method based on the CRAN architecture and the regional multi-scale minimum entropy (RMSME) method. The proposed method first employs a deep learning network structure under the CRAN architecture constructed in this paper for the rapid coarse localization of range migration. Subsequently, the RMSME method designed in this paper is utilized to search for local optimal solutions. This method maximizes the advantages of speed in deep learning networks while ensuring robustness and accuracy. The main contributions of this paper are as follows:
(1) This paper proposes a range alignment method based on CRAN and the regional multi-scale minimum entropy method, exploring a fusion of deep learning and the minimum entropy method.
(2) We constructed an unaligned range profile dataset based on three types of scattering point data and two motion patterns. Comparative experiments were conducted between the proposed method and other approaches, followed by measured data validation.