A hybrid inversion procedure for subsoil prospecting by ground-penetrating radar (GPR) measurements is proposed and experimentally validated in this letter. The approach integrates the benefits of qualitative beamforming in an adaptive multifrequency (MF) inexact-Newton scheme formulated in Lebesgue spaces with variable exponents. After a first preprocessing step aimed at estimating the incident field, a delay-and-sum (DAS) method provides an initial image of the region of interest. Then, the inexact-Newton algorithm exploits the qualitative indicator for both setting the exponent function and selectively weighting the update of the unknown during iterations. The proposed approach is tested against experimental GPR data.

The ability to enhance the spatial resolution of measurements collected by a conical-scanning microwave radiometer (MWR) is discussed in terms of noise amplification and improvement of the spatial resolution. Simulated (and actual) brightness temperature profiles are analyzed at variance of different intrinsic spatial resolutions and adjacent beams overlapping modeling a simplified 1-D measurement configuration (MC). The actual measurements refer to Special Sensor Microwave Imager (SSM/I) data collected using the 19.35 and the 37.00 GHz channels that match the simulated configurations. The reconstruction of the brightness profile at enhanced spatial resolution is performed using an iterative gradient method which allows a fine tuning of the level of regularization. Objective metrics are introduced to quantify the enhancement of the spatial resolution and noise amplification. Numerical experiments, performed using the simplified 1-D MC, show that the regularized deconvolution results in negligible advantages when dealing with low-overlapping/fine-spatial-resolution configurations. Regularization is a mandatory step when addressing the high-overlapping/low-spatial-resolution case and the spatial resolution can be enhanced up to 2.34 with a noise amplification equal to 1.56. A more stringent requirement on the noise amplification (up to 0.6) results in an improvement of the spatial resolution up to 1.64.

An enhanced spatial resolution brightness temperature product is proposed for future conical scan microwave radiometers. The technique is developed for Copernicus Imaging Microwave Radiometer (CIMR) measurements that are simulated using the CIMR antenna pattern at the L-band and the measurement geometry proposed in the Phase A study led by Airbus. An inverse antenna pattern reconstruction method is proposed. Reconstructions are obtained using two CIMR configurations, namely, using measurements collected at L-band by the forward (FWD) scans only, and combining forward and backward (FWD+BWD) scans. Two spatial grids are adopted, namely,$3 \mathrm {\,\,km} \times 3 \mathrm {\,\,km}$and$36 \mathrm {\,\,km} \times 36 \mathrm {\,\,km}$. Simulation results, referred to synthetic and realistic reference brightness fields, demonstrate the soundness of the proposed scheme that provides brightness temperature fields reconstructed at a spatial resolution up to ~1.9 times finer than the measured field when using the FWD+BWD combination.

In this study, a new antenna pattern deconvolution method to enhance the spatial resolution of multi -channel microwave radiometer (MWR) measurements is developed. This technique, based on a conventional gradient-like iterative method, utilizes the information contained in a high-frequency channel to enhance the spatial resolution of the lower-frequency channel in a data-fusion fashion. The physical idea consists of initializing the gradient -like inversion scheme using higher frequency details that are filtered out by the system measurement function. Experiments, performed on a dataset that includes both simulated and actual radiometer measurements, show that the proposed technique allows outperforming the conventional gradient method, while being very robust with respect to artifacts that could be induced by the higher frequency channel.

In this letter, a new approach is proposed to ameliorate the performance of iterative gradient-like regularization schemes aimed at enhancing the spatial resolution of microwave radiometer measurements in the Hilbert space. The approach consists of preconditioning the ill-conditioned discrete problem to let the iterative gradient-based inversion technique be more computer-time effective. Experiments undertaken on the simulated radiometer brightness profiles demonstrate the soundness of the proposed rationale that outperforms conventional gradient-like methods in terms of both computer-time effectiveness and accuracy in reconstructing spot-like discontinuities while resulting in larger fluctuations over the background.

Although characterized by two different mathematical definitions, both the Radon and the Hough transforms ultimately take an image as input and provide, as output, functions defined on a preassigned parameter space, i.e., the so-called Radon and Hough sinograms, respectively. The parameters in these two spaces describe a family of curves, which represent either the integration domains considered in the Radon transform, or the kind of curves to be detected by the Hough transform. It is heuristically known that the Hough sinogram converges to the corresponding Radon sinogram when the discretization step in the parameter space tends to zero. However, as far as we know, no formal result has been proven so far about such convergence. Therefore, by considering generalized functions in a multidimensional setting, in this paper we give an analytical proof of this heuristic rationale when the input digital image is described as a set of grayscale points, that is, as a sum of weighted Dirac delta functions. On these grounds, we also show that this asymptotic equivalence may lead to a visualization process relying on the interpretation of the Radon sinogram as a Hough sinogram.

In this study, a method to improve the reconstruction performance of antenna-pattern deconvolution based on the gradient iterative regularization scheme is proposed. The method exploits microwave measurements acquired by a multichannel radiometer to enhance their native spatial resolution. The proposed rationale consists of using the information carried on a high-frequency (finer spatial resolution) channel to ameliorate the spatial resolution of the lowest resolution radiometer channel. Experiments performed using both synthetic and real special sensor microwave/imager (SSM/I) radiometer data demonstrate that an enhanced spatial resolution 19.35-GHz channel can be obtained by ingesting in the algorithm information coming from 37.0-GHz channel. This multichannel spatial resolution method is also shown to outperform the conventional gradient-like regularization scheme in terms of both observation of smaller targets and reduction of ringings and fluctuations.

A novel two-step inverse-scattering technique is proposed for through-the-wall microwave imaging. The approach is based on a regularization scheme developed in the framework of variable-exponent Lebesgue spaces, which enhances the quality of the reconstruction by properly tuning the exponent function that defines the adopted norm. Such a function is built directly from the available data by using a beamforming technique based on a delay-and-sum scheme. After an initial numerical assessment, the approach is validated against experimental measurements in a laboratory environment, with targets placed behind a brick wall. Measured data are collected in time domain by scanning the transmitting and receiving antennas in a multi-illumination and multi-view arrangement. The processing of experimental data is performed in the frequency domain, where data at multiple frequencies are extracted by a Fast Fourier Transform (FFT) and simultaneously processed by the imaging algorithm. The obtained imaging results confirm the good reconstruction capabilities of the developed inverse-scattering scheme in the case of both metallic and low-contrast targets.

An iterative multiscaling approach for solving the electromagnetic inverse scattering problem related to the imaging of shallow subsurface targets with the ground-penetrating radar (GPR) is proposed. The approach combines the zooming properties of the multiscaling technique with the reconstruction capabilities of an Inexact-Newton (IN) method developed in$L^{p}$spaces. It is based on multifrequency processing that allows one to face the ill-posedness of the inverse scattering problem by exploiting the regularization properties of a truncated Landweber (LW) method. Experimental data, extracted from radargrams obtained by the GPR in a real situation, are used for validation. The reconstruction results are also compared with those from competitive alternatives, such as a standard IN method or a state-of-the-art multifrequency Conjugate Gradient (CG)-based approach.

In this paper, we introduce a novel approach to enhance the spatial resolution of single-pass microwave data collected by mesoscale sensors. The proposed rationale is based on an Lp-minimization approach with a variable p exponent. The algorithm automatically adapts the p exponent to the region of the image to be reconstructed. This approach allows taking benefit of the advantages of both the regularization in Hilbert (p = 2) and Banach (1 <; p <; 2) spaces. Experiments are undertaken considering the microwave radiometer and refer to both actual and simulated data collected by the special sensor microwave imager (SSM/I). Results demonstrate the benefits of the proposed method in reconstructing abrupt discontinuities and smooth gradients with respect to conventional approaches in Hilbert or Banach spaces.

We present a novel approach to enhance the spatial resolution of microwave data collected by meso-scale sensors. The proposed rationale is based on an LP-penalization approach with a variable exponent p, ranging in the interval [1.5,2]. This allows taking benefits of the advantages of both Hilbert and Banach spaces. Preliminary experiments undertaken using simulated and actual radiometer data confirm the effective improvement in the signal reconstruction by using this approach with respect to conventional Hilbert and Banach-space methods.

In this paper, a new computer-time effective iterative method is proposed to enhance the spatial resolution of microwave radiometer data in both Hilbert and Banach spaces. The reconstruction method is based on the conjugate gradient (CG) method. CG is a well-known method in electromagnetics, where it is commonly used to address inverse problems in Hilbert spaces. However, the method has never been applied to inverse problems related to spatial resolution enhancement of microwave remotely sensed measurements. In this paper, CG is adapted to the microwave radiometer case and exploited to reconstruct the brightness field at enhanced spatial resolution. Then, CG is, for the first time, extended to Banach spaces by means of duality maps and then applied to enhance the radiometer spatial resolution. Experiments undertaken on both simulated and actual radiometer data confirm the soundness of the proposed approach in Banach spaces and demonstrate that CG is able to provide a reconstruction accuracy similar to the conventional Landweber method, but with a significantly reduced processing time.

An innovative technique, based on a generalization of the conjugate gradient (CG) method in Banach spaces, is first proposed to enhance the spatial resolution of microwave radiometer measurements. This approach allows reducing the over-smoothing effects and the oscillations that are often present in Hilbert reconstructions and it is very effective in terms of processing time. Experiments undertaken on actual SSM/I data confirm the soundness of the proposed approach and show that CG is able to provide reconstructions similar to the conventional Landweber ones but with a significantly reduced processing time.

A simple innovation that enables a faster convergence rate of iterative gradient-like descent approaches is proposed and applied to linear image reconstruction problems from irregular sampling. The key idea is to reduce the amount of regularization effects of the conventional Tikhonov functional by introducing a negative seminorm penalty term, whose role is to speed up the convergence without reducing the reconstruction accuracy. The method is employed to enhance the spatial resolution of microwave remotely sensed products. First experiments, undertaken on simulated radiometer data, demonstrate that the technique significantly increases the convergence rate, halving the number of iterations when applied to speed up the basic and widely used Landweber method.

Most of the inverse problems arising in applied electromagnetics come from an underdetermined direct problem, this is the case, for instance, of spatial resolution enhancement. This implies that no unique inverse operator exists; therefore, additional constraints must be imposed on the sought solution. When dealing with microwave remote sensing, among the possible choices, the minimum p-norm constraint, with 1preconstructions for 12ones when spot-like discontinuities are considered; when dealing with abrupt discontinuities, l2and lp reconstructions are characterized by similar performance; however, lpreconstructions exhibit oscillations when the background is not properly accounted for.

A reconstruction technique, mathematically based on a generalization of the gradient method in Banach spaces, is first proposed to enhance the spatial resolution of radiometer earth observation measurements. This approach allows reducing the over-smoothing effects and the oscillations that are often present in standard Hilbert-spaces procedures without any drawback on the numerical complexity. Experiments undertaken on a data set consisting of both simulated and actual 2-D special sensor microwave imager radiometer measurements show the accuracy and the effectiveness of the proposed technique. A typical radiometer scene is processed in few minutes by a standard PC processor. Furthermore, since the proposed approach is iterative, the processing time increases slowly with the problem's size.

The imaging of buried objects is a challenging topic in electromagnetic research. In this letter, a method previously proposed for imaging of scatterers in free-space is extended to the case of objects buried in a lossy half-space. The proposed approach is based on the solution of the underlying inverse-scattering problem within the second-order Born approximation by means of a two-step inexact-Newton algorithm. The capabilities and limitations of the method are evaluated by means of some numerical simulations. Furthermore, comparisons with the free-space approach are also reported

A new approach to noninvasive inspection of dielectric targets at microwave frequencies is proposed. Cylindrical dielectric objects are reconstructed under the second-order Born approximation. A multi-illumination configuration is considered. The continuous model is discretized by the moment method and an efficient inexact-Newton method is applied. The dielectric profile is iteratively reconstructed starting from the measured scattered data, which are related to the unknown target through the inverse scattering equations written in a variational setting. Several numerical results are reported, which are aimed at assessing the capabilities of the approach in dealing with the nonlinear ill-posed inverse problem associated to the short-range microwave imaging. Single, multilayer, and separate cylinders are reconstructed in noiseless and noisy environments.