Direct Imaging Algorithm Research Articles

Near-Field 3D Sparse SAR Direct Imaging with Irregular Samples

Sparse imaging is widely used in synthetic aperture radar (SAR) imaging. Compared with the traditional matched filtering (MF) methods, sparse SAR imaging can directly image the scattered points of a target and effectively reduce the sidelobes and clutter in irregular samples. However, in view of the large-scale computational complexity of sparse reconstruction with raw echo data, traditional sparse reconstruction algorithms often require huge computational expense. To solve the above problems, in this paper, we propose a 3D near-field sparse SAR direct imaging algorithm for irregular trajectories, adopting a piece of preliminary information in the SAR image to update the dictionary matrix dimension, using the Gaussian iterative method, and optimizing the signal-processing techniques, which can achieve 3D sparse reconstruction in a more direct and rapid manner. The proposed algorithm was validated through simulations and empirical study of irregular scanning scenarios and compared with traditional MF and sparse reconstruction methods, and was shown to significantly reduce the computation time and effectively preserve the complex information of the scenes to achieve high-resolution image reconstruction.

Imaging of buried obstacles in a two-layered medium with phaseless far-field data

This paper is concerned with the inverse problem of reconstructing the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. Similarly to the homogenous background medium case, for this problem it is also true that the modulus of the far-field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, and thus it is impossible to determine the location of the obstacle from such phaseless far-field data. Based on the idea of using superpositions of two plane waves with different directions as the incident fields, a direct imaging algorithm is developed in this paper to locate the position of small anomalies with the intensity of the far-field pattern measured in the upper half-space. This is a nontrivial extension of our previous work (2018 Inverse Problems 34 104005) from the homogenous background medium case to the two-layered background medium case. Both the limited aperture measurement data and the presence of the two-layered background medium lead to difficulties in the theoretical analysis of the proposed imaging algorithm. To overcome the difficulties we employ the theory of oscillatory integrals. Further, with the aid of the imaging algorithm, a recursive Newton-type iteration algorithm in frequencies is proposed to reconstruct both the location and shape of extended obstacles. Finally, numerical experiments are presented to illustrate the feasibility of our algorithms.

Fast imaging of scattering obstacles from phaseless far-field measurements at a fixed frequency

This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field pattern or the phaseless far-field pattern generated by one plane wave as the incident field, which means that the location of the obstacle cannot be recovered from such phaseless far-field data at a fixed frequency. It was recently proved in our previous work Xu et al 2018 (SIAM J. Appl. Math. 78 1737–53) that the obstacle can be uniquely determined by the phaseless far-field patterns generated by infinitely many sets of superpositions of two plane waves with different directions at a fixed frequency if the obstacle is a priori known to be a sound-soft or an impedance obstacle with real-valued impedance function. The purpose of this paper is to develop a direct imaging algorithm to reconstruct the location and shape of the obstacle from the phaseless far-field data corresponding to infinitely many sets of superpositions of two plane waves with a fixed frequency as the incident fields. Our imaging algorithm only involves the calculation of the products of the measurement data with two exponential functions at each sampling point and is thus fast and easy to implement. Further, the proposed imaging algorithm does not need to know the type of boundary conditions on the obstacle in advance and is capable to reconstruct multiple obstacles with different boundary conditions. Numerical experiments are also carried out to illustrate that our imaging method is stable, accurate and robust to noise.

A Generic and Efficient E-field Parallel Imaging Correlator for Next-Generation Radio Telescopes

Modern radio telescopes are favouring densely packed array layouts with large numbers of antennas ($N_\textrm{A}\gtrsim 1000$). Since the complexity of traditional correlators scales as $\mathcal{O}(N_\textrm{A}^2)$, there will be a steep cost for realizing the full imaging potential of these powerful instruments. Through our generic and efficient E-field Parallel Imaging Correlator (EPIC), we present the first software demonstration of a generalized direct imaging algorithm, namely, the Modular Optimal Frequency Fourier (MOFF) imager. Not only does it bring down the cost for dense layouts to $\mathcal{O}(N_\textrm{A}\log_2 N_\textrm{A})$ but can also image from irregular layouts and heterogeneous arrays of antennas. EPIC is highly modular, parallelizable, implemented in object-oriented Python, and publicly available. We have verified the images produced to be equivalent to those from traditional techniques to within a precision set by gridding coarseness. We have also validated our implementation on data observed with the Long Wavelength Array (LWA1). We provide a detailed framework for imaging with heterogeneous arrays and show that EPIC robustly estimates the input sky model for such arrays. Antenna layouts with dense filling factors consisting of a large number of antennas such as LWA, the Square Kilometre Array, Hydrogen Epoch of Reionization Array, and Canadian Hydrogen Intensity Mapping Experiment will gain significant computational advantage by deploying an optimized version of EPIC. The algorithm is a strong candidate for instruments targeting transient searches of Fast Radio Bursts (FRB) as well as planetary and exoplanetary phenomena due to the availability of high-speed calibrated time-domain images and low output bandwidth relative to visibility-based systems.

A phase and space coherent direct imaging method

A direct imaging algorithm for point and extended targets is presented. The algorithm is based on a physical factorization of the response matrix of a transducer array. The factorization is used to transform a passive target problem to an active source problem and to extract principal components (tones) in a phase consistent way. The multitone imaging function can superpose multiple tones (spatial diversity/aperture of the array) and frequencies (bandwidth of the probing signal) based on phase coherence. The method is a direct imaging algorithm that is simple and efficient since no forward solver or iteration is needed. Robustness of the algorithm with respect to noise is demonstrated via numerical examples.

Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm

A novel continuation method is presented for solving the inverse medium scattering problem of the Helmholtz equation, which is to reconstruct the shape of the inhomogeneous medium from boundary measurements of the scattered field. The boundary data is assumed to be available at multiple frequencies. Initial guesses are chosen from a direct imaging algorithm, multiple signal classification (MUSIC), along with a level set representation at a certain wavenumber, where the Born approximation may not be valid. Each update via recursive linearization on the wavenumbers is obtained by solving one forward and one adjoint problem of the Helmholtz equation.

A direct imaging method using far-field data**This research is partially supported by ONR grant N00014-02-1-0090, DARPA grant N00014-02-1-0603, NSF grant 0307011 and the Sloan Foundation.

We present a direct imaging algorithm for extended targets using far-field data generated by incident plane waves. The algorithm uses a factorization of the response matrix for far-field data that is derived from physical considerations and a resolution-analysis-based regularization. The algorithm is simple and efficient since no forward solver or iteration is needed. Efficiency and robustness of the algorithm with respect to measurement noise are demonstrated.

A direct imaging algorithm for extended targets

We present a direct imaging algorithm for extended targets. The algorithm is based on a physical factorization of the response matrix of a transducer array. The multi-signal classification imaging function is used to visualize the results. A resolution and noise level-based thresholding strategy is developed for regularization. The algorithm is simple and efficient since no forward solver or iteration is needed. Multiple-frequency information improves both resolution and stability of the algorithm. Efficiency and robustness of the algorithm with respect to measurement noise and random medium fluctuations are demonstrated.

A cell‐transverse display algorithm for regular and rectilinear 3D grid data

AbstractThis paper proposes an efficient direct imaging algorithm for constructing iso‐surfaces from regular and rectilinear 3D grid data in scientific and engineering visualization. The basic idea is to generate and draw polygons simultaneously by processing the cells spanned by grids in decreasing order of distance from the current viewpoint. Iso‐surfaces are generated in five or six tetrahedrons into which the cells are subdivided, and are sent to a graphics device or drawn into a frame buffer on the fly. The execution order of each of the tetrahedrons is identical and is determined by the current viewpoint. Since the algorithm does not need to store intermediate polyhedral data and does not require a depth buffer memory for hidden surface removal, it is applicable to a large quantity of data on a 3D grid, such as computed tomography (CT) data. It is also particularly powerful for semi‐transparent display, because transparency calculation can be reduced to image compositing operations if the polygons are drawn in order of their z‐depth from the current viewpoint.