^{1}

^{1}

^{2}

^{1}

^{2}

A new robust technique for high-resolution reconstructive imaging is developed as required for enhanced remote sensing (RS) with imaging array radar or/and synthetic aperture radar (SAR) operating in an uncertain RS environment. The operational scenario uncertainties are associated with the unknown statistics of perturbations of the signal formation operator (SFO) in turbulent medium, imperfect array calibration, finite dimensionality of measurements, uncontrolled antenna vibrations, and random carrier trajectory deviations in the case of SAR. We propose new descriptive experiment design regularization (DEDR) approach to treat the uncertain radar image enhancement/reconstruction problems. The proposed DEDR incorporates into the minimum risk (MR) nonparametric estimation strategy the experiment design-motivated operational constraints algorithmically coupled with the worst-case statistical performance (WCSP) optimization-based regularization. The MR objective functional is constrained by the WCSP information, and the robust DEDR image reconstruction operator applicable to the scenarios with the low-rank uncertain estimated data correlation matrices is found. We report and discuss some simulation results related to enhancement of the uncertain SAR imagery indicative of the significantly increased performance efficiency gained with the developed approach.

Modern applied theory of reconstructive
radar imaging is now a mature and well-developed research field, presented and
detailed in many works (see, e.g., [

The predominant challenge of this study is
to solve the SSP reconstruction problem in context of the uncertain environment. Thus, the problem of enhanced imaging of the extended large-scale scenes
remotely sensed with an array radar/SAR operating in the

Consider a coherent RS experiment in a
random medium and the narrowband assumption [

The random functional kernel

We assume an
incoherent nature of the backscattered field

Viewing it as an approximation problem leads one to a projection concept
for a reduction of the data field

In analogy to (

The descriptive experiment design (DED) aspects of the SSP
reconstruction problem involving the analysis of how to choose the basis
functions

In the DED
formalism, an imperfect calibration of the array (due to displacements of some
array elements with respect to the presumed nominal positions, as well as
distorted antennas shapes [

In (

Now, we proceed from the stochastic integral-form EO (

We refer to the estimate,

In the descriptive statistical formalism, the desired SSP vector

To optimize
the search for the desired SO

To proceed with the
derivation of the estimator (

Routinely solving the minimization problem (

Note, that the derived robust
SO (

The general-form DEDR-optimal SO (

A family of the DEDR-related algorithms for estimating
the SSP can be derived now from (

Consider the white zero-mean noise in
observations and no preference to any prior model information, that is, putting

Consider the model from the previous
example for an assumption,

Consider the case of an arbitrary
zero-mean noise with the composed correlation matrix

The three SSP reconstruction
techniques that employ the SOs (

The conventional MVDR beamformer [

For the purposes of establishing a relationship between the MVDR
beamformer and the DEDR-related SSP estimators (

Examining the formulae (

We simulated
a conventional side-looking SAR with the fractionally synthesized aperture, that
is, the array was synthesized by the moving antenna. The regular SFO of such
SAR is factored along two axes in the image plane [

For the
purpose of objectively testing the performances of different DEDR-related SSP
estimation algorithms, a quantitative evaluation of the improvement in the SSP
estimates (gained due to applying the DEDR-related reconstructive solution
operators

IOSNR gained with different DEDR-related reconstruction algorithms (results are reported for the first uncertain operational scenario and second scene).

Scenario 1: | ||||
---|---|---|---|---|

Nonconstrained RSF | Constrained RSF | Nonconstrained RASF | Constrained RASF (WCSP-optimized) | |

5 | 1.85 | 2.158 | 2.2 | 2.45 |

10 | 2.4 | 2.68 | 2.32 | 2.89 |

15 | 2.56 | 2.76 | 2.67 | 3.4 |

20 | 2.73 | 3.37 | 3.02 | 4.2 |

25 | 3.47 | 4.23 | 3.1 | 5.32 |

30 | 3.85 | 4.95 | 3.64 | 5.46 |

IOSNR gained with different DEDR-related reconstruction algorithms (results are reported for the second uncertain operational scenario and second scene).

Scenario 2: | ||||
---|---|---|---|---|

Nonconstrained RSF | Constrained RSF | Nonconstrained RASF | Constrained RASF (WCSP-optimized) | |

5 | 1.71 | 2.17 | 1.9 | 2.41 |

10 | 1.85 | 2.61 | 1.92 | 2.88 |

15 | 1.9 | 2.9 | 2.2 | 3.45 |

20 | 1.93 | 3.4 | 2.18 | 4.16 |

25 | 2.01 | 3.78 | 2.6 | 4.56 |

30 | 2.11 | 4.3 | 3.08 | 5.32 |

In this section, we report
the qualitative simulation results and the relevant quantitative performances
evaluated via the IOSNRs (

First uncertain operational scenario
(simulation experiment specifications):

fractional azimuth AF width,

(at the 0.5 from the peak value of
the “sinc-type” AF,

range AF
width,

SNRs range,

SFO uncertainty factor,

Second uncertain operational scenario
(simulation experiment specifications):

fractional
azimuth AF width,

(at the 0.5 from the peak value of the
“bell-type” AF,

range AF
width,

SNRs range,

SFO uncertainty factor,

Figures

First operational scenario, first scene (

Second operational scenario, first scene (

First operational scenario, second scene (

Second operational scenario, second scene (

From the presented simulation results, the advantage of the well-designed
imaging experiments (constrained RSF and WCSP-optimized RASF) over the case of
badly designed experiment (nonrobust MSF and unconstrained RSF) is evident. Due
to the performed regularized inversions, the resolution was substantially
improved in all simulated scenarios (as reported in Tables

New descriptive experiment design regularization (DEDR) approach for estimation of the spatial spectrum pattern (SSP) of the wavefield power distribution in the uncertain remotely sensed environment has been proposed as required for the conventional array imaging radar, side-looking airborne radar, and SAR. Unifying the DEDR and the worst-case statistical performance (WCSP) optimization into the aggregated WCSP-constrained minimum risk technique, the inverse problem ill-posedness has been alleviated in a statistically grounded fashion. The derived general-form DEDR estimator does not involve the inversion of the estimated data correlation matrix. This principal algorithmic-level result of the undertaken study constitutes the crucial advantage of the developed family of the DEDR-related estimators that makes them applicable to the uncertain operational scenarios with ill-conditioned (e.g., low-rank) estimates of the array data correlation matrices, in particular, to the SAR imaging scenarios where only one realization of the trajectory data signal degraded due to the uncontrolled random carrier trajectory deviation and antenna vibration is available for further processing. Being nonlinear and solution-dependent, the DEDR-optimal robust adaptive spatial filtering (RASF) estimator requires rather complex signal processing. The computational complexity arises due to the necessity to perform simultaneously the solution-dependent operator inversion operations and adaptive adjustments of the degrees of freedom of the overall RASF technique. To reduce the computational load, the simplified constrained robust spatial filtering (RSF) algorithm was proposed and employed, which manifests almost the same reconstruction performances as the RASF in typical uncertain operational scenarios that was verified in the simulation experiment.