Synthetic aperture radar (SAR) operates as an active remote sensing imaging device within the microwave frequency band [
1], capable of creating two-dimensional high-resolution images of observed scenes [
2]. Increased resolution enhances the detail of scene and target information, which underscores the consistent drive towards high resolution in SAR technology development. For instance, microwave photonic (MWP) SAR can transmit signals with over 5 GHz bandwidth, yielding images with centimeter-level resolution [
3,
4,
5]; spaceborne SAR, such as Capella, achieves high azimuth resolution through long-time staring spotlight processing [
6,
7]. However, these high-resolution SAR imaging techniques are confronted with problems such as severe echo signals coupling and significant parametric spatial variability, making batch-processing frequency domain algorithms (such as Chirp Scaling (CS), Omega-K, etc.) limited in their applications and unable to achieve the desired focusing precision. In contrast, the classical backprojection (BP) algorithm conducts point-by-point phase compensation and coherent accumulation and does not necessitate approximation during the processing. This results in high imaging accuracy and broad applicability, thus meeting the demands for high-resolution SAR imaging [
8,
9].
However, the main issue with the BP algorithm lies in its high computational complexity and low processing efficiency. Currently, to improve the processing efficiency of the BP algorithm, there are mainly two types of methods. One type of method modifies the model and structure of the classical BP algorithm to form a fast BP algorithm, such as fast backprojection (FBP) [
10], fast factorized backprojection (FFBP) [
11], and Cartesian factorized backprojection (CFBP) [
12]. However, these fast BP algorithms increase model complexity, and the imaging process involves approximations, which somewhat compromises the image quality [
13,
14]. Another type of method maintains the structure of the classical BP algorithm model, with primary enhancements focused on the core steps that impact the efficiency of the BP algorithm, notably the performance of interpolation, and deeply analyzes the characteristics of the BP algorithm to fully combine the computational benefits of advanced processing devices such as graphics processing units (GPUs) to achieve parallel acceleration [
15,
16,
17,
18,
19]. At present, the interpolation methods commonly used in engineering that are suitable for the BP algorithm include linear or neighbor interpolation after FFT upsampling, sinc interpolation, and weighted sinc interpolation, etc. Literature [
20] pointed out that the projection of ground range uniform grids to slant range non-uniform grids in the BP algorithm constitutes a type of non-uniform sampling, which can employ the non-uniform fast Fourier transform (NUFFT) method [
21] to implement interpolation from the frequency domain data after range compression to image grids. This method was optimized on the GPU, yielding positive results. The study [
22] utilizes 2-D NUFFT to carry out the two-dimensional interpolation required in FBP and FFBP, mitigating the truncated error effect in conventional interpolation methods. Nonetheless, NUFFT remains complex and leaves room for efficiency improvement. In 2020, Lin et al. [
23] proposed an improved cubic spline interpolation (ICSI) method, which optimized the solution conditions of the traditional cubic spline interpolation, and improved the frequency response performance of the interpolation kernel by additional coefficient solving degrees of freedom, which can maintain the low computational complexity of traditional cubic spline interpolation while enhancing interpolation accuracy. Lin et al. have successfully applied this method to wireless communication signal processing [
24].
This paper, inspired by previous research, is the first to incorporate the ICSI method into the BP algorithm. It combines this method with time-shift upsampling to propose an efficient BP algorithm based on time-shift upsampling-improved cubic spline interpolation (TSU-ICSI). By harnessing the parallel features of the proposed BP algorithm and the architectural characteristics of GPUs, we have realized an efficient BP algorithm based on TSU-ICSI combined with GPU parallel computing, which has achieved better performance than that of previously established interpolation methods.
The rest of this paper is organized as follows. In
Section 2, we introduce the signal model, algorithm flow, parameter selection, and computational complexity analysis of the BP algorithm based on TSU-ICSI. In
Section 3, an efficient GPU-based TSU-ICSI BP implementation method is presented. In
Section 4, we conduct both simulation and measured data experiments on the proposed method, confirming its effectiveness and analyzing its contribution to enhancing processing efficiency. A discussion and conclusions are given in
Section 5 and
Section 6, respectively.