## 1 Introduction  
Spectral domain optical coherence tomography (SD-OCT) is a powerful and efficient imaging modality for the diagnosis and treatment of diseases in a variety of tissues, especially the skin and eyes [1; 2; 3; 4]. In SD-OCT, imaging speed and lateral resolution are significant imaging performance indicators. The imaging speed depends mainly on the scanning speed of sample arm and the acquisition time of the spectrometer, and the lateral resolution is determined by the size of the focal spot of the light beam incident on the sample. Compressive sensing SD-OCT (CS-SDOCT) has emerged as an increasingly popular research topic with a view to reducing the imaging time and data volume [5; 6; 7; 8; 9]. In our previous works and most other studies on CS-SDOCT, the image is reconstructed using a fraction of the wavenumber \(k\) domain data required by the Nyquist theory, i.e., the under-sampling is only done in each A-scan [7; 10; 11]. Undoubtedly, if the B-scan and C-scan data are also under-sampled, the data volume can be further compressed and the imaging time can be further shortened. Therefore, two-dimensional (2D) and three-dimensional (3D) CS-SDOCT have been widely studied, in which under-sampling is conducted in two or three directions of the spectral volume [12; 13; 14]. Although the CS algorithm is time consuming, the acquisition speed is greatly increased, which is advantageous for the imaging of moving objects such as the eyes. For example, in order to obtain a 3D reconstruction of the anterior segment during lens adjustment, blinking, and pupillary responses to light stimulation, an optical coherence tomography (OCT) system with up to 135,000 A-scans per second was designed with a data volume greater than 1 G [15]. An expensive, large array, high speed camera with a high sampling rate is need in this case. In addition, transferring and processing large amounts of data is also challenging. Therefore, it is necessary and meaningful to explore CS-OCT. In common Gaussian beam-based SD-OCT systems, there is an inherent trade-off between the lateral resolution and imaging depth. Therefore, in consideration of the imaging depth, a Gaussian beam with a large depth of focus (DOF) and a large focal spot is usually used for imaging, thus leading to a low lateral resolution. Interferometric synthetic aperture microscopy (ISAM) which provides 3D object structure by solving the inverse scattering problem [16], is a method that can achieve focal-plane lateral resolution throughout the imaging depth [17; 18; 19; 20]. Therefore, the use of the ISAM method allows for both high lateral resolution and large imaging depth. At present, short wavelength OCT systems have been demonstrated to achieve high resolution, and we can predict that the use of ISAM can achieve a spatially invariant high lateral resolution over the entire imaging depth in short wavelength OCT systems [21]. In this study, we combine the advantages of 2D CS-SDOCT and ISAM in terms of data volume, imaging speed, and lateral resolution to obtain high-quality OCT images with less data volume. A typical SD-OCT dataset consists of an array of interference spectra measured at thousands of linearly spaced wavenumbers (A-scan) for each transverse scanning position (B-scan). First, the selected A-scans in each B-scan are reconstructed from their under-sampled \(k\)-space measurements individually through the one-dimensional (1D) compressive sensing (CS) reconstruction algorithm. Then, the reconstruction algorithm is applied to each selected B-scan row-by-row, followed by correcting the lateral resolution using ISAM theory. Finally, an OCT image with spatially invariant lateral resolution throughout the imaging depth is reconstructed from 2D under-sampled data. Our proposed method and CS reconstruction strategy were first verified by simulation, and then an OCT image of the acinar cells of an orange with improved lateral resolution was obtained using under-sampled 2D data (sampling rate of 50% \(\times\) 50%).