High-quality Image Reconstruction Research Articles

Real-time, wide-field and high-quality single snapshot imaging of optical properties with profile correction using deep learning.

The development of real-time, wide-field and quantitative diffuse optical imaging methods to visualize functional and structural biomarkers of living tissues is a pressing need for numerous clinical applications including image-guided surgery. In this context, Spatial Frequency Domain Imaging (SFDI) is an attractive method allowing for the fast estimation of optical properties using the Single Snapshot of Optical Properties (SSOP) approach. Herein, we present a novel implementation of SSOP based on a combination of deep learning network at the filtering stage and Graphics Processing Units (GPU) capable of simultaneous high visual quality image reconstruction, surface profile correction and accurate optical property (OP) extraction in real-time across large fields of view. In the most optimal implementation, the presented methodology demonstrates megapixel profile-corrected OP imaging with results comparable to that of profile-corrected SFDI, with a processing time of 18 ms and errors relative to SFDI method less than 10% in both profilometry and profile-corrected OPs. This novel processing framework lays the foundation for real-time multispectral quantitative diffuse optical imaging for surgical guidance and healthcare applications. All code and data used for this work is publicly available at www.healthphotonics.org under the resources tab.

4D-AirNet: a temporally-resolved CBCT slice reconstruction method synergizing analytical and iterative method with deep learning

Four-dimensional (4D) cone-beam CT (CBCT) reconstructs temporally-resolved phases of 3D volumes often with the same amount of projection data that are meant for reconstructing a single 3D volume. 4D CBCT is a sparse-data problem that is very challenging for high-quality 4D CBCT image reconstruction. Here we develop a new method, namely 4D-AirNet, that synergizes analytical and iterative method with deep learning for high-quality temporally-resolved CBCT slice reconstruction. 4D-AirNet is an unrolling method using the optimization framework of fused analytical and iterative reconstruction (AIR), which is based on proximal forward-backward splitting (PFBS). Three different strategies are developed for 4D-AirNet: random-phase (RP), prior-guided (PG), and all-phase (AP). RP-AirNet and PG-AirNet utilize phase-by-phase training and reconstruction, while PG-AirNet also uses a prior image reconstructed with all-phase projection data. Dense connectivity is built into 4D-AirNet networks for improved reconstruction quality. In contrast, AP-AirNet trains and reconstructs all phases simultaneously. In addition, the joint regularization method of DL and conventional spatiotemporal total variation (TV) is investigated. 4D-AirNet methods were evaluated in comparison with conventional iterative (TV) and deep learning (LEARN) methods, using simulated 2D-t CBCT scans from a lung dataset with various sparse-data levels. The reconstruction results suggest 4D-AirNet methods outperform TV and LEARN, and AP-AirNet provides the best reconstruction quality overall.

PFISTA-SENSE-ResNet for parallel MRI reconstruction

Magnetic resonance imaging has been widely applied in clinical diagnosis. However, it is limited by its long data acquisition time. Although the imaging can be accelerated by sparse sampling and parallel imaging, achieving promising reconstructed images with a fast computation speed remains a challenge. Recently, deep learning methods have attracted a lot of attention for encouraging reconstruction results, but they are lack of proper interpretability for neural networks. In this work, in order to enable high-quality image reconstruction for the parallel magnetic resonance imaging, we design the network structure from the perspective of sparse iterative reconstruction and enhance it with the residual structure. Experimental results on a public knee dataset indicate that, as compared with the state-of-the-art deep learning-based and optimization-based methods, the proposed network achieves lower error in reconstruction and is more robust under different samplings.

A MACH Filter-Based Reconstruction-Free Target Detector and Tracker for Compressive Sensing Cameras

Compressive sensing cameras hold the promise of cost-effective hardware, lower data rates, and improved video quality, particularly outside the visible spectrum. However, these improvements involve significant computational cost, as sensor output must be reconstructed in order to form an image viewable by a human. This paper describes a prototype automated detection and tracking system using a compressive sensing camera that does not rely on computationally costly image reconstructions. It operates on raw sensor data for an approximately ten-fold improvement in computation time over a comparable reconstruct-then-track algorithm. The detector is successful at a sensing rate of 0.3, comparable to that required for high-quality image reconstructions. If initialized with the location of a target, the tracker holds the target at a sensing rate of 0.005, below the boundary where reconstruction breaks down. These results show not only that direct tracking from compressive cameras is possible, but also give support to the pursuit of direct inference from compressive sensors of all types.

High-quality photoacoustic image reconstruction based on deep convolutional neural network: towards intra-operative photoacoustic imaging

The use of intra-operative imaging system as an intervention solution to provide more accurate localization of complicated structures has become a necessity during the neurosurgery. However, due to the limitations of conventional imaging systems, high-quality real-time intra-operative imaging remains as a challenging problem. Meanwhile, photoacoustic imaging has appeared so promising to provide images of crucial structures such as blood vessels and microvasculature of tumors. To achieve high-quality photoacoustic images of vessels regarding the artifacts caused by the incomplete data, we proposed an approach based on the combination of time-reversal (TR) and deep learning methods. The proposed method applies a TR method in the first layer of the network which is followed by the convolutional neural network with weights adjusted to a set of simulated training data for the other layers to estimate artifact-free photoacoustic images. It was evaluated using a generated synthetic database of vessels. The mean of signal to noise ratio (SNR), peak SNR, structural similarity index, and edge preservation index for the test data were reached 14.6 dB, 35.3 dB, 0.97 and 0.90, respectively. As our results proved, by using the lower number of detectors and consequently the lower data acquisition time, our approach outperforms the TR algorithm in all criteria in a computational time compatible with clinical use.

Second-order optimized regularized structured illumination microscopy (sorSIM) for high-quality and rapid super resolution image reconstruction with low signal level

Structured illumination microscopy (SIM) is a widely used super resolution imaging technique that can down-modulate a sample's high-frequency information into objective recordable frequencies to enhance the resolution below the diffraction limit. However, classical SIM image reconstruction methods often generate poor results under low illumination conditions, which are required for reducing photobleaching and phototoxicity in cell imaging experiments. Although denoising methods or auxiliary items improved SIM image reconstruction in low signal level situations, they still suffer from decreased reconstruction quality and significant background artifacts, inevitably limiting their practical applications. In order to improve the reconstruction quality, second-order optimized regularized SIM (sorSIM) is designed specifically for image reconstruction in low signal level situations. In sorSIM, a second-order regularization term is introduced to suppress noise effect, and the penalty factor in this term is selected to optimize the resolution enhancement and noise resistance. Compared to classical SIM image reconstruction algorithms as well as to those previously used in low illumination cases, the proposed sorSIM provides images with enhanced resolution and fewer background artifacts. Therefore, sorSIM can be a potential tool for high-quality and rapid super resolution imaging, especially for low signal images.

PhlatCam: Designed Phase-Mask Based Thin Lensless Camera.

We demonstrate a versatile thin lensless camera with a designed phase-mask placed at sub-2 mm from an imaging CMOS sensor. Using wave optics and phase retrieval methods, we present a general-purpose framework to create phase-masks that achieve desired sharp point-spread-functions (PSFs) for desired camera thicknesses. From a single 2D encoded measurement, we show the reconstruction of high-resolution 2D images, computational refocusing, and 3D imaging. This ability is made possible by our proposed high-performance contour-based PSF. The heuristic contour-based PSF is designed using concepts in signal processing to achieve maximal information transfer to a bit-depth limited sensor. Due to the efficient coding, we can use fast linear methods for high-quality image reconstructions and switch to iterative nonlinear methods for higher fidelity reconstructions and 3D imaging.

Optimal deep learning based image compression technique for data transmission on industrial Internet of things applications

AbstractRecently, industrial Internet of things becomes more popular and it involves a group of intelligent devices linked to create systems which observe, gather, communicate, and investigate data. In this view, the demand for compression techniques in remote sensing images is increasing since low complexity technique is required in spacecraft. Deep learning, for instance, convolutional neural network (CNN) has gained more attention in the domain of computer vision, particularly for high‐level applications like detection along with interpretation. At the same time, it is difficult to resolve the low‐level applications like image compression and it is investigated in this article. This article presents an optimal compression technique using CNNs for remote sensing images. The proposed method uses CNN for learning the compact representation of the original image which held the structural data and was then coded by Lempel Ziv Markov chain algorithm. Next, the encoded image was reconstructed to retrieve the original image with high reconstructed image quality. The proposed optimal compression technique is compatible with the available image codec standards. Wide range of experiments was carried out and the results were compared with binary tree and optimized truncation, JPEG, and JPEG2000 in terms of compression efficiency, reconstructed image quality, and space saving (SS). The obtained results apparently proved the effectiveness of the presented method, which attains an average peak signal to noise ratio of 49.90 dB and SS of 89.38%.

SiO2 NPs-PQ/PMMA Photopolymer Material Doped with a High-Concentration Photosensitizer for Holographic Storage.

Dispersing nanoparticles and increasing the photosensitizer concentration have been regarded as effective approaches for improving the performance of a holographic storage material. In this paper, SiO2 nanoparticle (NP)-dispersed PQ/PMMA nanocomposite material (SiO2 NP-PQ/PMMA) with a high PQ doping concentration was prepared. By introducing the co-monomer methyl isobutyl ketone (MIBK) that comes from an SiO2 NP colloidal solution, the concentration of PQ in the system increased to 1.2 wt %. We investigated the performance of polarization holographic recordings in both traditional PQ/PMMA and nanocomposite material SiO2 NP-PQ/PMMA with the orthogonally polarized signal and reference waves. With the dispersion of the SiO2 NPs colloidal solution and the increase in the PQ concentration, diffraction efficiency and photoinduced birefringence were multiplied. In addition, high-quality holographic image reconstruction was achieved by our homemade material.

Sub-Nyquist computational ghost imaging with deep learning.

We propose a deep learning computational ghost imaging (CGI) scheme to achieve sub-Nyquist and high-quality image reconstruction. Unlike the second-order-correlation CGI and compressive-sensing CGI, which use lots of illumination patterns and a one-dimensional (1-D) light intensity sequence (LIS) for image reconstruction, a deep neural network (DAttNet) is proposed to restore the target image only using the 1-D LIS. The DAttNet is trained with simulation data and retrieves the target image from experimental data. The experimental results indicate that the proposed scheme can provide high-quality images with a sub-Nyquist sampling ratio and performs better than the conventional and compressive-sensing CGI methods in sub-Nyquist sampling ratio conditions (e.g., 5.45%). The proposed scheme has potential practical applications in underwater, real-time and dynamic CGI.

Spatiotemporal double-phase hologram for complex-amplitude holographic displays

This Letter describes an approach to encode complex-amplitude light waves with spatiotemporal double-phase holograms (DPHs) for overcoming the limit of the space-bandwidth product (SBP) delivered by existing methods. To construct DPHs, two spatially macro-pixel encoded phase components are employed in the SBP-preserved resampling of complex holograms. Four generated sub-DPHs are displayed sequentially in time for high-quality holographic image reconstruction without reducing the image size or discarding any image terms when the DPHs are interweaved. The reconstructed holographic images contain more details and less speckle noise, with their signal-to-noise ratio and structure similarity index being improved by 14.64% and 78.79%, respectively.

Soft-edge Assisted Network for Single Image Super-Resolution.

The task of single image super-resolution (SISR) is a highly ill-posed inverse problem since reconstructing the highfrequency details from a low-resolution image is challenging. Most previous CNN-based super-resolution (SR) methods tend to directly learn the mapping from the low-resolution image to the high-resolution image through some complex convolutional neural networks. However, the method of blindly increasing the depth of the network is not the best choice because the performance improvement of such methods is marginal but the computational cost is huge. A more efficient method is to integrate the image prior knowledge into the model to assist the image reconstruction. Indeed, the soft-edge has been widely applied in many computer vision tasks as the role of an important image feature. In this paper, we propose a Soft-edge assisted Network (SeaNet) to reconstruct the high-quality SR image with the help of image soft-edge. The proposed SeaNet consists of three sub-nets: a rough image reconstruction network (RIRN), a soft-edge reconstruction network (Edge-Net), and an image refinement network (IRN). The complete reconstruction process consists of two stages. In Stage-I, the rough SR feature maps and the SR soft-edge are reconstructed by the RIRN and Edge-Net, respectively. In Stage-II, the outputs of the previous stages are fused and then feed to the IRN for high-quality SR image reconstruction. Extensive experiments show that our SeaNet converges rapidly and achieves excellent performance under the assistance of image soft-edge. The code is available at https://gitlab.com/junchenglee/seanet-pytorch.

Joint Demosaicing and Super-Resolution (JDSR): Network Design and Perceptual Optimization

Image demosaicing and super-resolution are two important tasks in color imaging pipeline. So far they have been mostly independently studied in the open literature of deep learning; little is known about the potential benefit of formulating a joint demosaicing and super-resolution (JDSR) problem. In this article, we propose an end-to-end optimization solution to the JDSR problem and demonstrate its practical significance in computational imaging. Our technical contributions are mainly two-fold. On network design, we have developed a Residual-Dense Squeeze-and-Excitation Networks (RDSEN) supported by a pre-demosaicing network (PDNet) as the pre-processing step. We address the issue of spatio-spectral attention for color-filter-array (CFA) data and discuss how to achieve better information flow by concatenating Residue-Dense Squeeze-and-Excitation Blocks (RDSEBs) for JDSR. Experimental results have shown that significant PSNR/SSIM gain can be achieved by RDSEN over previous network architectures including state-of-the-art RCAN. On perceptual optimization, we propose to leverage the latest ideas including relativistic discriminator and pre-excitation perceptual loss function to further improve the visual quality of textured regions in reconstructed images. Our extensive experiment results have shown that Texture-enhanced Relativistic average Generative Adversarial Network (TRaGAN) can produce both subjectively more pleasant images and objectively lower perceptual distortion scores than standard GAN for JDSR. Finally, we have verified the benefit of JDSR to high-quality image reconstruction from real-world Bayer pattern data collected by NASA Mars Curiosity.

High-Quality MicroCT Rock Imaging: Methodology To Measure and Correct for X-Ray Scatter

Summary Microcomputed tomography (microCT) of cores yields valuable information about rock and fluid properties at pore scale for conventional rock and at rock heterogeneity scale for unconventionals. High levels of uncorrected X-ray scatter in computed tomography (CT) data lead to strong image artifacts and erroneous Hounsfield unit (HU) values, making reconstructed images unsuitable for accurate digital rock (DR) characterization (e.g., segmentation, material decomposition, and others). MicroCT scanners do not include scatter correction techniques. To fill this gap, we developed a new methodology to measure and remove the scatter component from raw projection microCT data collected during rock core scans, and ultimately improving the image quality of scanned cores. Widely used approaches for scatter estimation, based on Monte Carlo (MC) simulations and simplified analytical models, are time-consuming and may lose accuracy when imaging complex unconventional shale cores. In this paper, we propose a more practical approach to perform scatter correction from direct scatter measurements, an approach that is based on the beam-stop array (BSA) method. The BSA method works as follows: The radiation scattered by the core sample is emitted in random directions. By placing an array of small, highly absorbing beads between the source and the core, the primary X-ray signal through the beads is blocked, but the overall object scatter signal is not affected. The observed values in the beads’ shadows on the detector are assumed to be scatter signal. Performing interpolation of the scatter signal between the shadowed by beads pixels on the detector gives an estimate of the scatter signal at every pixel on the detector. Subtracting scatter from projection data yields scatter-corrected data used for 3D CT core image reconstruction. To develop the core scatter correction methodology, we executed the following three tasks: (1) performed modeling of primary and scattered signals to optimize the BSA design (beads size and layout) and scan parameters; (2) developed and implemented an accurate scatter correction algorithm into our 3D microCT image reconstruction workflow; and (3) tested the proposed methodology using four shale core samples from the United States and the Middle East. To better assess the impact of scatter, all experiments with shale core plugs presented in this paper were conducted using source energy of 160 kVp. Our results demonstrated that in many cases, especially with higher attenuating cores, failing to correct for X-ray scatter may result in significant loss of image reconstruction accuracy. We also showed that the developed methodology allows for accurate estimation and removal of scatter from the raw (projection) CT data, enabling reconstruction of high-quality core images that are required for performing DR analysis. To assess the impact of X-ray scatter on the accuracy of DR segmentation, we compared the amount of resolved air-filled space using a stack of image slices by thresholding for the air regions. Our results showed that the amount of detected air-filled space may increase significantly when scatter correction is applied. The presented scatter correction methodology is general and can be used with any microCT scanner used by the petroleum industry to improve image quality and derive accurate HU values. This is of significant importance for quantitative characterization of highly heterogeneous rock with fine structural changes, as is the case for shale. Ultimately, this methodology should expand the operational envelope and value of microCT imaging in the exploration and production workflows.

A Preliminary Experimental Analysis of In-Pipe Image Transmission Based on Visible Light Relay Communication.

The regular inspection of underground facilities such as pipelines is absolutely essential. Pipeline leakage caused by corrosion and deformation must be detected in time, otherwise, it may cause fatal disasters for human beings. In our previous research, a robot chain system (RCS) based on visible light relay communication (VLRC) for pipe inspection has been developed. This system can basically realize the light-based transmission of control command signals and illuminance-based coordinated movement, whereas the collection and transmission approach of the pipe leakage image have not been studied. Compared with former in-pipe wireless communication techniques, VLRC can not only overcome the instability and inefficiency of in-pipe data transmission but also extend the communication range with high transmission rates. The most important feature is that it can provide a stable illumination and high-quality communication for pipe inspection robot and finally improve the energy efficiency. Hence, the aim of this article is to analyze the performance of VLRC-based image transmission in the pipe and in the future provide a high-quality, long-range, and high-efficiency image transmission for complex infrastructure inspection with RCS. The transmission systems based on two signal transmission modes analog image signal relay transmission (AISRT) and digital image frame relay transmission (DIFRT) have been proposed. Multiple experiments including the waveform test, the test of transmission features with different bit error rate (BER), and in the different mediums were conducted between these two systems. The experiment revealed that DIFRT was superior to the AISRT in terms of the relatively high-quality image transmission and reconstruction quality. It could better overcome the attenuation brought by the absorption and scattering effects and finally increased the transmission range than former communication methods. The DIFRT system could also operate at 50 with relatively low BER whether in the air or water. The technique in this research could potentially provide a new strategy for implementations in the stable, effective, high-speed, and long-range image transmission of the robots in some other special environments such as tunnel, mine, and underwater, etc.

Deep artifact-free residual network for single-image super-resolution

Recently, convolutional neural networks have shown promising performance for single-image super-resolution. In this paper, we propose Deep Artifact-Free Residual (DAFR) network which uses the merits of both residual learning and usage of ground-truth image as target. Our framework uses a deep model to extract the high-frequency information which is necessary for high-quality image reconstruction. We use a skip-connection to feed the low-resolution image to the network before the image reconstruction. In this way, we are able to use the ground-truth images as target and avoid misleading the network due to artifacts in difference image. In order to extract clean high-frequency information, we train the network in two steps. The first step is a traditional residual learning which uses the difference image as target. Then, the trained parameters of this step are transferred to the main training in the second step. Our experimental results show that the proposed method achieves better quantitative and qualitative image quality compared to the existing methods.

Volumetric Imaging with a Single Projection Enabled by Deep Learning

Traditionally, a tomographic image is obtained by mathematical inversion of the encoding function of the imaging wave for a given set of measured data from different angular positions. While continuous effort has been made in imaging with reduced angular measurements over the years, tomographic imaging with ultra-sparse sampling has yet to be realized. In this work, we push the sparsity to the limit of a single projection and demonstrate what seemingly unlikely scenario of a single-view tomographic imaging is readily achievable by leveraging from the state-of-the-art deep learning technique and seamless integration of prior knowledge in the deep learning-based image reconstruction process. We develop a hierarchical neural network for X-ray CT imaging with ultra-sparse views and develop a structured training process for deep learning to bridge the dimensionality in X-ray imaging. The essences of our approach are the introduction of a novel feature domain transformation between a 2D projection and 3D volumetric CT image, and the construction of a robust encoding/decoding framework. To evaluate the feasibility of the proposed approach, the trained network is deployed on our generated dataset. We collect 3D CT dataset from clinical patient’s database, and digitally produce projection images from CT images using the geometry consistent with a clinical on-board cone-beam CT system for radiation therapy. Data augmentation with a series of translation, rotation, and organ deformation to the 3D CT are used to produce annotated data pairs that mimic different imaging situations. After adequate training, we deploy the deep learning model inference for single-view 3D volumetric reconstruction on two cases. The reconstructed results are compared with ground truth both qualitatively and quantitatively. From results’ illustration, we observe the deep learning-derived images closely resemble the target images, indicating the potential of the proposed model for volumetric imaging. For quantized computation, the averaged MAE/RMSE/SSIM/PSNR values over all testing samples for single-view reconstruction are 0.018, 0.177, 0.929, and 30.523, respectively, for case 1. The indices for case 2 are found to be 0.025, 0.385, 0.838, and 27.157, respectively. The qualitative and quantitative results demonstrate that our model is capable of achieving high-quality 3D image reconstruction even with only a single or few 2D projection. We have presented a novel deep learning framework for volumetric imaging with ultra-sparse data sampling. The mechanism here is fundamentally different from the traditional approaches in that the image formation is driven by prior knowledge casted in the deep learning model. This work pushes the boundary of tomographic imaging to the single-view limit. Practically, the single-view imaging may present a useful solution in some image-guided interventional procedures with simplified imaging system design.

A Novel Blind Restoration and Reconstruction Approach for CT Images Based on Sparse Representation and Hierarchical Bayesian-MAP

Computed tomography (CT) image reconstruction and restoration are very important in medical image processing, and are associated together to be an inverse problem. Image iterative reconstruction is a key tool to increase the applicability of CT imaging and reduce radiation dose. Nevertheless, traditional image iterative reconstruction methods are limited by the sampling theorem and also the blurring of projection data will propagate unhampered artifact in the reconstructed image. To overcome these problems, image restoration techniques should be developed to accurately correct a wide variety of image degrading effects in order to effectively improve image reconstruction. In this paper, a blind image restoration technique is embedded in the compressive sensing CT image reconstruction, which can result in a high-quality reconstruction image using fewer projection data. Because a small amount of data can be obtained by radiation in a shorter time, high-quality image reconstruction with less data is equivalent to reducing radiation dose. Technically, both the blurring process and the sparse representation of the sharp CT image are first modeled as a serial of parameters. The sharp CT image will be obtained from the estimated sparse representation. Then, the model parameters are estimated by a hierarchical Bayesian maximum posteriori formulation. Finally, the estimated model parameters are optimized to obtain the final image reconstruction. We demonstrate the effectiveness of the proposed method with the simulation experiments in terms of the peak signal to noise ratio (PSNR), and structural similarity index (SSIM).

Imaging Through Turbid Media With Vague Concentrations Based on Cosine Similarity and Convolutional Neural Network

Underwater imaging has been extensively studied to bypass the limitation aroused by scattering and absorption of water solutions. It is highly meaningful to the development of optical imaging, especially in turbid media. The existing methods developed for reconstruction of original images from speckle patterns are applied in a stable medium, which obstruct wider applications in unpredictable media. Hence, it is crucial to take changeable environments into consideration to circumvent the limits of the extant methods. In this paper, we propose a new approach based on cosine similarity for speckle classification and convolutional neural network (CNN) for the reconstruction. The targets are placed in variant densities of turbid water mixed with certain of milk, and their corresponding intensity speckle patterns are recorded by a camera. It is verified that utilization of cosine similarity for the classification of patterns recorded in changeable media ensures high fidelity for label predictions. For a speckle pattern obtained in totally unidentified media, it can make a prediction of the density which has a high probability of accuracy. We can exploit the classified density to automatically select the most appropriate datasets to train a CNN model and then make predictions in real time with the trained CNN model. The combined model presented in this paper is tolerant to the uncertainty of turbidity. Moreover, it guarantees high-accuracy pattern classification and high-quality image reconstruction. It is feasible for potential applications in harsh water solutions with unknown perturbations of concentrations.

Diffraction-field-adaptive computational imaging for static and moving targets

Single-pixel computational imaging (SPCI) reconstructs a target image from multi-measurements of the correlation between the target and a series of speckle masks. Accurate acquisition of diffraction fields plays an essential role in image formation of SPCI. Loss and distortions in diffraction fields generally lead to the deterioration of the image quality or the failure of imaging. Here, we propose a diffraction-field-adaptive method that provides high-quality image reconstruction for SPCI. In particular, we introduce an adaptive method to accurately calculate the diffraction field in the reference path, where the calculation width of the diffraction field can change itself automatically to make the sampling satisfy Nyquist sampling theorem. Whether the target moves or keeps static, the diffraction field can be accurately obtained and the distortions during light transmission can be reduced by the proposed method. A SPCI model is established and three numerically experiments are conducted to verify the performance of the model. The results demonstrate that the proposed method can avoid diffraction field loss and distortions in the field calculations, and provides excellent imaging performance for both static and moving targets.