Synthetic Aperture Radar Data Processing Research Articles

Mapping Rice Area in the Cauvery Delta Zone of Tamil Nadu Using Sentinel 1A Synthetic Aperture Radar (SAR) Data

Since remote sensing based crop inventory provides accurate and timely information as compared to the conventional survey methods of estimating area, Multi-temporal Sentinel 1A Synthetic Aperture Radar data was used for the estimation of rice area during Samba season 2022 in the Cauvery delta zone comprising Thanjavur, Thiruvaru, Mayiladuthurai, and Nagapatnam districts of Tamil Nadu. SAR data was preferred over optical satellite data due to excess cloud cover during cropping the major season in Tamil Nadu. Temporal back-scatter (dB) signature of rice crop was generated from the multi-temporal processed SAR data utilizing the modules of a fully automated MAPscape software aiding the discriminating of the crop from others. The signatures revealed that the dB levels to be the lowest during agronomic floods, reached the highest during maximum tillering stage and started declining thereafter. Multi-temporal feature extraction module of Mapscape was used to estimate rice area and validated for accuracy using ground truth data collected during survey. A total of 3.05 lakh ha of rice area was estimated with an overall accuracy of 90.8 % and 0.82 kappa coefficient. Largest area of 1.12 lakh ha was recorded in Thanjavur followed by Thiruvarur and Mayiladuthurai with 0.95 and 0.51 lakh ha respectively.

A novel semi-empirical model for crop leaf area index retrieval using SAR co- and cross-polarizations

The retrieval of continuous leaf area index (LAI) in space and time from remote sensing is beneficial for cropland monitoring and management. Synthetic Aperture Radar (SAR) with the advantages of all-weather operation and fine spatial resolutions has been utilized in various agricultural applications. Although the water cloud model (WCM) has been extensively used for LAI estimation over croplands, it is modified for application to crop canopies with large gaps. The requirement of prior information on soil moisture is also a hinderance for the model application. In this study, WCM is theoretically modified to consider the correlation of active microwave propagation through the canopy in downward and upward directions. Such a modification is particularly important for sparse vegetation with large gaps between crop plants in the early stage of the growing season. A parameter with explicit physical meaning, i.e. the full-vegetation backscattering coefficient, was defined to simplify our model scheme and make the model applicable for the whole growing season. In addition, a physics-based SAR data processing scheme is developed to entangle the influences of LAI and soil moisture on SAR backscatter by taking advantage of the multiple polarizations of RADARSAT-2 (R2) SAR data. In this way, LAI was estimated using modified WCM without the prior knowledge of soil moisture. To evaluate LAI retrieved from the R2 datasets (R2 LAI), ground-based LAI measurements were made at the experimental area of SMAPVEX16-MB in Canada with twenty approximately 800 m х 800 m plots in soybeans and corn. R2 LAI was well correlated to these ground-based LAI (n = 15, R2 = 0.63, RMSE = 0.99 m2·m−2 for soybeans; n = 5, R2 = 0.66, RMSE = 1.20 m2·m−2 for corn). LAI was also retrieved from optical data acquired by Sentinel-2/MSI (S2), denoted as S2 LAI. The R2 LAI and S2 LAI are well correlated and achieved coefficients of determination (R2) of 0.76 and 0.71 and root mean square errors (RMSE) of 1.1 and 1.4 m2·m−2 for soybeans and corn, respectively. The seasonal variations of R2 LAI and S2 LAI are generally similar except at the end of the growing season when S2 LAI is considerably larger than R2 LAI. S2 LAI followed the trend of the reduction in leaf chlorophyll content, while R2 LAI reduced only slightly due to the decrease in leaf water content near the end the growing season. R2 LAI represents the total standing leaf area useful for surface energy balance estimation, while S2 LAI responds to green leaf area useful for crop productivity modeling.

Parallel Optimization for Large Scale Interferometric Synthetic Aperture Radar Data Processing

Interferometric synthetic aperture radar (InSAR) has developed rapidly over the past years and is considered as an important method for surface deformation monitoring, benefiting from growing data quantities and improving data quality. However, the handing of SAR big data poses significant challenges for related algorithms and pipeline, particularly in large-scale SAR data processing. In addition, InSAR algorithms are highly complex, and their task dependencies are intricate. There is a lack of efficient optimization models and task scheduling for InSAR pipeline. In this paper, we design parallel time-series InSAR processing models based on multi-thread technology for high efficiency in processing InSAR big data. These models concentrate on parallelizing critical algorithms that have high complexity, with a focus on deconstructing two computationally intensive algorithms through loop unrolling. Our parallel models have shown a significant improvement of 10–20 times in performance. We have also developed a parallel optimization tool, Simultaneous Task Automatic Runtime (STAR), which utilizes a data flow optimization strategy with thread pool technology to address the problem of low CPU utilization resulting from multiple modules and task dependencies in the InSAR processing pipeline. STAR provides a data-driven pipeline and enables concurrent execution of multiple tasks, with greater flexibility to keep the CPU busy and further improve CPU utilization through predetermined task flow. Additionally, a supercomputing-based system has been constructed for processing massive InSAR scientific big data and providing technical support for nationwide surface deformation measurement, in accordance with the framework of time series InSAR data processing. Using this system, we processed InSAR data with the volumes of 500 TB and 700 TB in 5 and 7 days, respectively. Finally we generated two maps of land surface deformation all over China.

SAR image formation scheme implementation and endorsement sprouting from Level-0 data decoding

Synthetic Aperture Radar (SAR) data processing evolving from level-0 raw data is complicated, especially in data decoding, manifesting in obtaining a well-focused SAR image. This paper is intended to present a complete MATLAB-based SAR data processing tool, which helps the end-user to treat simply the steps of image generation. This paper would enrich the research community in the field of SAR processors, especially in the area of understanding, handling, and developing a SAR processor based on space packet protocol standard (STD 01) used in many SAR systems such as Sentinel-1, ERS-1, CubeL, JPSS-2, 3, and 4. Also, this work opens the door for researchers to decode other space packet protocol standards and even to create an algorithm based on fully understanding the image formation algorithm from its roots. Moreover, the work in this paper could be a stepping-stone for the beginner in the field of SAR signal processing to become familiarized with SAR image generation procedures. The level-0 raw data used in this paper is based on Sentinel 1 SAR satellite obtained from the European Space Agency Copernicus website, a free open-source for level-0 and level-1 data types. The MATLAB program allows users to compare their generated image with the level-1 single-look complex (S1-L1-SLC) image utilizing entropy, contrast, and sharpness image quality metrics.The results showed that the images produced by the proposed algorithm are comparable to Sentinel-1 level-1 SAR images for the same scene and achieved satisfactory accuracy under the requirements for image quality.

A Novel Method for Staggered SAR Imaging in an Elevation Multichannel System

Synthetic aperture radar (SAR) is an advanced remote sensing technique, capable of observing Earth’s surface independent of weather conditions and sunlight illumination. Restricted by the minimum antenna area, however, conventional spaceborne SAR systems cannot achieve high azimuth resolution in a wide swath. In addition, blind ranges are present as the constant pulse repetition interval (PRI) is used. To solve these problems, a PRI-staggered elevation multichannel SAR (EMC-SAR) system is employed in this article. By transmitting the continuously PRI-varied sequence, the blind ranges are located at different regions in different receive instants, effectively avoiding the loss of coverage in elevation. In this system, three issues are required to be addressed: 1) recovering the missed data located at blind ranges; 2) suppressing range ambiguous components; and 3) restoring the PRI-varied signal into a regular grid. To deal with these problems, we propose a novel SAR imaging method for a PRI-staggered EMC-SAR system. To be applied on-ground, assume downlinking of the individual elevation channels. First, the modified <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -insensitive loss tube regression with the L2 regularization method is applied to recover the missed data. Then, the range ambiguous components are suppressed by performing digital beamforming (DBF) based on the elevation multichannel technique, where the covariance matrix is constructed by using an iterative adaptive algorithm. After that, a generalized scaling transform is employed to restore the PRI-varied signal into a uniform sampled grid. Finally, a well-focused SAR image can be obtained by performing the conventional SAR imaging techniques. The effectiveness of the proposed method is validated by both simulated and real SAR data processing results.

Study on processing synthetic aperture radar data based on an optical 4f system for fast imaging.

Due to the huge amount of collected echo data caused by the working principle of synthetic aperture radar (SAR), the use of digital processing relies heavily on the performance of digital chips. Because of the limitation of Moore's law, the technology of digital signal processing exposes the limitation of computing speed and power consumption in the face of SAR processing. Against this background, the optical processing method based on the optical 4f system is introduced into SAR imaging. A spatial light modulator (SLM) is placed on the input surface and spectrum surface of the 4f system to load the echo data of the SAR and the matched filter function of the SAR. Using optical Fourier transform to realize the core calculation of SAR data processing can solve the difficulty of processing time-consuming due to the large amount of calculation. In the process of Fourier transform, instead of using a solid glass lens, we use a phase-type Fresnel lens diagram in the SLM to realize the function of Fourier, which avoids the need for special design of Fourier lens. It also greatly reduces the volume and weight of the whole machine, which provides a reference method for real-time imaging of spaceborne SAR.

Novel optimal time selection method for synthetic aperture radar data processing via expectation‐maximization algorithm

A novel optimal time selection method for synthetic aperture radar (SAR) data processing via the expectation-maximization (EM) algorithm is proposed, which can reduce the computational complexity and improve the image quality simultaneously. First, the Doppler frequency feature after the SAR processing is analyzed from the point of probability. Then, the Doppler frequency is modelled as the Gaussian mixture model (GMM), and the issue of optimal time selection can be implemented by the parameter estimation of GMM. The results of simulated and real measured data are given to demonstrate the effectiveness of the proposed method.

Optimal parameters selection of the Frost filter based on despeckling efficiency prediction for Sentinel SAR images

Synthetic aperture radar (SAR) images have found numerous applications. However, further analysis of SAR images including interpretation, classification, segmentation, etc. is an extremely challenging task due to the presence of highly intensive speckle noise. Therefore, image despeckling is one of the main stages in preliminary SAR data processing. Over the past decades, a large number of different image despeckling techniques have been proposed ranging from local statistics filters to deep learning based ones. In this study, we analyze one of the most known and widely used local statistics Frost filter. Despeckling efficiency of the Frost filter significantly depends on the sliding window size and tuning (also called damping) factor. Here, we present a method for optimal parameters selection of the Frost filter for a given image based on despeckling efficiency prediction. Despeckling efficiency prediction for the Frost filter is carried out using a set of statistical and spectral input parameters and multilayer neural network. It is shown that such a prediction can be performed before applying image despeckling with a high accuracy and it is faster than despeckling itself. Both simulated speckled images and real-life Sentinel-1 SAR images have been used for extensive evaluation of the proposed method.

Autofocus-Based Estimation of Penetration Depth and Permittivity of Ice Volumes and Snow Using Single SAR Images

An intrinsic challenge in the geophysical interpretation of low-frequency synthetic aperture radar (SAR) imagery of semitransparent media, such as ice sheets, is the position ambiguity of the scattering structures within the glacial volume. Commonly tackled by applying interferometric and tomographic techniques, their spaceborne implementation exhibits by orders higher complexity compared to missions relying on single SAR images, making them cost expensive or, in the context of planetary missions, even impossible due to limited navigation capability. Besides, even these sophisticated techniques are commonly biased due to inaccurate permittivity estimates, leading to geometric distortions up to several meters. We present a novel inversion procedure to estimate volume parameters of ice sheets, namely, the depth of the scattering layer within the glacial volume and the dielectric permittivity of the ice, based on single-image single-polarization SAR acquisitions. The information is inherent in the processed SAR data as phase errors on the azimuth signals resulting from uncompensated nonlinear propagation of the radar echoes through ice. We suggest a local map-drift autofocus approach to quantify and spatially resolve the phase errors and an inversion model to relate them to the penetration depth and permittivity. Testing the proposed technique using P-band SAR data acquired using DLR’s airborne sensor F-SAR during the ARCTIC15 campaign in Greenland shows promising results and good agreement with tomographic products of the analyzed test site.

Dually Supervised Track-Before-Detect Processing of Multichannel Video SAR Data

Track-Before-Detect (TBD) algorithm has been used to track weak moving target shadow in video synthetic aperture radar (SAR), where strong maneuverability may deteriorate tracking performance. Fortunately, the Doppler characteristic of target can additionally provide velocity guidance for tracking. This article presents ground moving target indication (GMTI) results of the multi-channel video SAR raw data, and a tracking approach is proposed based on the Doppler supervision in an improved dynamic programming-based TBD (DP-TBD) framework that uses a dual-domain merit function. Both the sequential high-resolution SAR images and low-resolution Range-Doppler (RD) spectra are used, and the clutter in RD spectrum is suppressed by using an adaptive displaced phase center antenna (ADPCA) technique. Fine states can be searched in dual-domain through resampling from random expansion in state initialization and transition. The inverse shadow amplitude and Doppler energy of the same potential target are simultaneously integrated to determine whether the target exists. The proposed Dual-DP-TBD can deal with the tracking of a time-varying number of targets in successive measurements. Compared to other TBD algorithms, this approach has fewer missing alarms and false alarms thanks to precise velocity estimation constrained from diverse features both in SAR image and RD spectrum.

SAF-3DNet: Unsupervised AMP-Inspired Network for 3-D MMW SAR Imaging and Autofocusing

The sparse imaging method based on compressed sensing (CS) is widely used in the field of millimeter-wave (MMW) synthetic aperture radar (SAR) imaging. However, 3D sparse imaging is limited by the difficult parameter tuning, the huge computational load, and the low processing efficiency. In addition, due to the motion errors and model mismatch, it is difficult to obtain well-focused results without error correction techniques. To address these issues, we propose a deep learning framework that integrates 3D sparse imaging and autofocusing, named 3D Sparse Autofocusing Network (SAF-3DNet) for MMW SAR data processing. The network is constructed based on an auto-encoder, which can optimize parameters without effective ground truth. The backbone structure of the encoder is expanded by approximate message-passing (AMP), and the operators in the frequency domain are used to replace the traditional matrix-vector CS model, which avoids large-scale matrix multiplication and other operations, and greatly improves the operation efficiency. In addition, the 2D phase error estimation in the cross-range plane is embedded into the sparse imaging models, enabling simultaneous 3D imaging and autofocusing. The decoder is designed as a mapping from the autofocusing results to the echo data. Experimental results based on both simulated and measured data demonstrate the proposed SAF-3DNet can achieve well-focused 3D reconstruction within an ephemeral time, which expresses the potential of 3D MMW SAR real-time and high-quality imaging.

An Improved Time-Domain Autofocus Method Based on 3-D Motion Errors Estimation

Spatial-variant phase errors (PEs) are important factors which defocus the synthetic aperture radar (SAR) image. In time-domain SAR imaging, the exact calculation of instantaneous range is carried out to realize imaging. Accurate trajectory is the key to compensate spatial-variant PEs and ensure image focus. Thus, an improved time-domain autofocus method based on three-dimensional motion errors (3-D MEs) estimation is proposed in this article. First, an improved maximizing-maximum-pixel-value method is used to estimate nonspatial-variant PEs. Meanwhile, a theoretical explanation combined with <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>-dimensional Euclidean space is described. Then, residual PEs and wrapped PEs are discussed successively. A part-overlapped partitioning scheme for sub-block images (SBIs) and a wrapped-PE model are proposed for 3-D MEs estimation. Then, the estimation problem is turned into a mixed integer programming problem, which can be solved by the combination of genetic algorithm (GA) and Tikhonov regularization. Finally, the well-focused image is obtained through updated trajectory. The effectiveness of the proposed method is proven by results of simulation and real SAR data processing.

Scene Adaptive Phase Inconsistency Estimation for Multi-channel ScanSAR System

Operating multi-channel synthetic aperture radar (SAR) in ScanSAR mode enables an ultrawide-swath and high-resolution imagery. A critical step in multi-channel SAR data processing is to accurately estimate and compensate phase inconsistency between channels. However, the Doppler spectrum distribution of ScanSAR relies heavily on the characteristic of illuminated regions, which may make the traditional time-domain phase estimation method failure under nonuniform scenes. In order to ensure that the performance of phase estimation is robust with respect to the variation of scenes, an innovative scene adaptive phase inconsistency estimation method for the ScanSAR system is presented in this letter, which can estimate channel phase error more accurately by extracting scene-center frequency from received data. The performance of the presented approach is evaluated using real airborne multi-channel SAR data. Experimental results show that the modified phase inconsistency estimation method is more effective and adaptable to different scenes compared with the conventional method.

Imaging and Relocation for Extended Ground Moving Targets in Multichannel SAR-GMTI Systems

In a multichannel synthetic aperture radar (SAR) system, because of the target uncooperative motion, a ground moving target (GMT) is usually smeared, distorted, and shifted in an SAR image. In this article, a novel approach for multichannel SAR-GMT indication (GMTI) processing is proposed. The main innovations of this method are that a GMT can be well refocused and relocated since the target high-order Doppler parameters can be precisely estimated based on a high-order polynomial phase signal (PPS) model, and the target statistical amplitude and phase information is jointly applied to improve the radial velocity estimation robustness. Compared with the current SAR-GMTI algorithms, the improvements of this method over the existing methods are: 1) the topography interferometric phase can be effectively compensated by applying an adaptive 2-D spectrum filtering technique via iterative processing; 2) a GMT can be well imaged since the target Doppler chirp rate and the quadratic chirp rate can be well estimated via the 2-D coherent integration in the time&#x2013;frequency plane; and 3) a GMT can be precisely relocated into its original position by applying the generalized amplitude and phase weighting technique. Real-measured SAR data processing results are presented to validate the effectiveness and feasibility of the proposed method.

Frequency-Scaling-Based Spaceborne Squint SAR Sparse Imaging

In synthetic aperture radar (SAR), due to the characteristics of squint data in spaceborne imaging geometry, a more accurate range cell migration correction (RCMC) operation is necessary. Furthermore, imaging degradation due to ignoring range-variant filtering needed for secondary range compression (SRC) limits SAR imaging. In addition, due to enormous computational complexity required for squint SAR data processing, the existing imaging methods, for instance, chirp scaling algorithm (CSA) and range-Doppler algorithm (RDA) are no longer sufficient, especially for large-scale scenes. In order to solve above problems, this paper presents a novel spaceborne squint SAR sparse imaging method, which could not only eliminate the effects of squint to a certain extent, but also improve the performance of focused SAR image. Compared with matched filtering (MF) based squint imaging algorithm, the proposed method can obtain the SAR images with higher quality from full- or down-sampled echo data.

High Performance Computing in Satellite SAR Interferometry: A Critical Perspective

Synthetic aperture radar (SAR) interferometry has rapidly evolved in the last decade and can be considered today as a mature technology, which incorporates computationally intensive and data-intensive tasks. In this paper, a perspective on the state-of-the-art of high performance computing (HPC) methodologies applied to spaceborne SAR interferometry (InSAR) is presented, and the different parallel algorithms for interferometric processing of SAR data are critically discussed at different levels. Emphasis is placed on the key processing steps, which typically occur in the interferometric techniques, categorized according to their computational relevance. Existing implementations of the different InSAR stages using diverse parallel strategies and architectures are examined and their performance discussed. Furthermore, some InSAR computational schemes selected in the literature are analyzed at the level of the entire processing chain, thus emphasizing their potentialities and limitations. Therefore, the survey focuses on the inherent computational approaches enabling large-scale interferometric SAR processing, thus offering insight into some open issues, and outlining future trends in the field.

Creating a thematic geodatabase for monitoring the landslide processes of the landslide circus “Dalgia yar”

Impact on the process of landslide origin and activation is result of many factors both endogenous and exogenous. The purpose of this study is to provide possibility for analysis and assessment of the geo-processes in the “Dalgia yar” landslide located at Northern Black Sea coast of Bulgaria in order to prevent risks and disasters of natural and anthropogenic origin. An important stage was to seamlessly include data from different sources such as geodetic measurements, satellite SAR (Synthetic-aperture radar) data as well as geological and geophysical data. The established geodatabase structures the collected information on dangerous geo-processes in the mentioned area and introduces them into the GIS (Geographic information system) environment. Its purpose is to facilitate the analysis of the available geological data for this landslide and to integrate them with results of measurements from regular monitoring. Interferometric images (IFIs), data from permanent GNSS (Global Navigation Satellite Systems) stations and from local geodynamic GNSS network, geological, seismic and geophysical data, updated geological maps and maps of the risk of landslide processes are included in the database. The IFIs have been produced using well established procedure for processing large number of Sentinel-1 SAR data of the purposely created local archive. Other key element used to improve the final results of SAR data processing and important part of the geodatabase is the precise Digital Elevation Model (DEM), which is much better in terms of horizontal and vertical resolutions than the open accessed ones (SRTM). The coordinates and velocities of the GNSS points are obtained from adjustment and analysis of two epoch measurements of the geodynamic control network of landslides “Dalgia yar”. Since the area has complex geological structure, small scale maps reflecting the geological and geophysical hazards are integral part of the geodatabase. Having all this information the analysis concerning the ongoing geodynamical processes in the study area is significantly improved and more reliable information is produced for better regional planning by the local authorities and residents.

Staring Spotlight SAR with Nonlinear Frequency Modulation Signal and Azimuth Non-Uniform Sampling for Low Sidelobe Imaging

In synthetic aperture radar (SAR) imaging, geometric resolution, sidelobe level (SLL) and signal-to-noise ratio (SNR) are the most important parameters for measuring the SAR image quality. The staring spotlight mode continuously transmits signals to a fixed area by steering the azimuth beam to acquire azimuth high geometric resolution, and its two-dimensional (2D) impulse response with the low SLL is usually obtained from the 2D weighted power spectral density (PSD) by the selected weighting window function. However, this results in the SNR reduction due to 2D amplitude window weighting. In this paper, the staring spotlight SAR with nonlinear frequency modulation (NLFM) signal and azimuth non-uniform sampling (ANUS) is proposed to obtain high geometric resolution SAR images with the low SLL and almost without any SNR reduction. The NLFM signal obtains non-equal interval frequency sampling points under uniform time sampling by adjusting the instantaneous chirp rate. Its corresponding PSD is similar to the weighting window function, and its pulse compression result without amplitude window weighting has low sidelobes. To obtain a similar Doppler frequency distribution for low sidelobe imaging in azimuth, the received SAR echoes are designed to be non-uniformly sampled in azimuth, in which the sampling sequence is dense in middle and sparse in both ends, and azimuth compression result with window weighting would also have low sidelobes. According to the echo model of the proposed imaging mode, both the back projection algorithm (BPA) and range migration algorithm (RMA) are modified and presented to handle the raw data of the proposed imaging mode. Both imaging results on simulated targets and experimental real SAR data processing results of a ground-based radar validate the proposed low sidelobe imaging mode.

Measuring Ocean Surface Current in the Kuroshio Region Using Gaofen-3 SAR Data

The Kuroshio is the strongest warm current in the western North Pacific, which plays a crucial role in climate and human activities. In terms of this, the accurate acquisition of ocean surface current velocity and direction in the Kuroshio region is of great research value. Gaofen-3 synthetic aperture radar (SAR) provides data support for the study of ocean surface current measurements in the Kuroshio region, but no relevant experimental result has been published yet. In this paper, four available stripmap mode SARs’ data acquired by Gaofen-3 in the Kuroshio region are used for measuring the ocean surface current field. In general, the Doppler centroid anomaly (DCA) estimation is a common method to infer ocean surface currents from single-antenna stripmap data, but only the radial velocity component can be retrieved. In order to measure current vectors, a novel method combining the sub-aperture processing and the least squares (LS) technology is suggested and demonstrated by applying to the Gaofen-3 SAR data processing. The experiment’s results agree well with model-derived ocean current data, indicating that the Gaofen-3 SAR has the capability to accurately retrieve the ocean surface current field in the Kuroshio region and motivate further research by providing more data.

Spiral SAR Imaging with Fast Factorized Back-Projection: A Phase Error Analysis.

This paper presents a fast factorized back-projection (FFBP) algorithm that can satisfactorily process real P-band synthetic aperture radar (SAR) data collected from a spiral flight pattern performed by a drone-borne SAR system. Choosing the best setup when processing SAR data with an FFBP algorithm is not so straightforward, so predicting how this choice will affect the quality of the output image is valuable information. This paper provides a statistical phase error analysis to validate the hypothesis that the phase error standard deviation can be predicted by geometric parameters specified at the start of processing. In particular, for a phase error standard deviation of ~12°, the FFBP is up to 21 times faster than the direct back-projection algorithm for 3D images and up to 13 times faster for 2D images.