One of the main topics in synthetic aperture radar (SAR) tomography (TomoSAR) is the estimation of the vertical structures‚ location, which scatter the field back towards the sensor, constrained to a reduced number of passes. Moreover, the introduction of artifacts and the increase of the ambiguity levels due to irregular sampling, consequence of non-uniform acquisition constellations, complicate the accurate estimation of the source parameters. Pursuing the alleviation of such drawbacks, the use of statistical regularization approaches, based on the maximum-likelihood (ML) estimation theory, have been successfully demonstrated in the previous related studies. However, these techniques are constrained to the assumption that the probability density function (pdf) of the observed data is Gaussian. In this paper, in order to solve the ill-posed non-linear TomoSAR inverse problem, we relax this assumption and apply the weighted covariance fitting (WCF) criterion instead. The latter alleviates the previously mentioned drawbacks, and retrieves a power spectrum pattern (PSP) with an outline more similar to the expected one, i.e., recovered using matched spatial filtering (MSF) with a higher number of tracks. First, we present the mathematical background of the related regularization methods, adapted to solve the TomoSAR inverse problem, from which we derive our novel technique, named WISE (WCF-based Iterative Spectral Estimator). Then, the differences and similarities between the addressed regularization approaches are discussed, besides their main advantages and disadvantages. Finally, the implementation details of WISE are treated, along with simulated examples and experimental results gotten from a forested test site.

One of the main objectives of the upcoming space missions, such as Tandem-L and BIOMASS, is to map, on a global scale, the forest structure by means of synthetic aperture radar (SAR) tomography (TomoSAR). On one hand, the number of baselines is constrained to the revisit time that avoids temporal decorrelation issues. On the other hand, enhanced resolution is desired, since the forest structure is characterized from the vegetation layers that compose it, reflected in the tomographic profiles as local maxima. The TomoSAR nonlinear ill-conditioned inverse problem is conventionally tackled within the direction-of-arrival (DOA) estimation framework. The DOA-inspired nonparametric techniques are well suited to cope with distributed targets; nonetheless, the achievable resolution highly depends on the span of the tomographic aperture. Alternatively, superresolved parametric approaches have the main drawback related to the white noise model assumption that guaranties the separation of the signal and noise subspaces. Overcoming the disadvantages of the aforementioned techniques, in this letter, we address a novel maximum-likelihood (ML) inspired adaptive robust iterative approach (MARIA) for feature-enhanced TomoSAR reconstruction. MARIA performs resolution enhancement, with suppression of artifacts and ambiguity levels reduction, to an initial estimate of the continuous power spectrum pattern. After convergence, an accurate location of the closely spaced phase centers is achieved, easing the characterization of the forest structure. The feature-enhancing capabilities of the proposed approach are corroborated using airborne F-SAR data of the German Aerospace Center (DLR).

The synthetic aperture radar (SAR) tomography (TomoSAR) inverse problem is commonly tackled in the context of the direction-of-arrival estimation theory. The latter allows achieving super-resolution, along with ambiguity levels reduction, thanks to the use of parametric focusing methods, as multiple signal classification (MUSIC), and statistical regularization techniques, like the maximum-likelihood inspired adaptive robust iterative approach (MARIA). Nevertheless, in order to correctly suit the considered signal model, MUSIC and most regu-larization approaches require an appropriate setting of the involved parameters. In both cases, the accuracy of the retrieved solutions depends on the right selection of the assigned values. Thus, with the aim of dealing with such an issue, this article addresses several parameter selection strategies, adapted specifically to the TomoSAR scenario. Parametric techniques as MUSIC solve the TomoSAR problem in a different manner as the regularization methods do, hence, each approach demands different methodologies for the proper estimation of their parameters. Consequently, we refer to the Kullback-Leibler information criterion for the model order selection of parametric techniques as MUSIC, whereas we rather explore the Morozov's discrepancy principle, the L-Curve, the Stein's unbiased risk estimate and the generalized cross-validation, to choose the regularization parameters. After the incorporation of these criteria to MUSIC and MARIA, respectively, their capabilities are first analyzed through simulations, and later on, utilizing real data acquired from an urban area.

Among the objectives of the upcoming space missions Tandem-L and BIOMASS, is the 3-D representation of the global forest structure via synthetic aperture radar (SAR) tomography (TomoSAR). To achieve such a goal, modern approaches suggest solving the TomoSAR inverse problems by exploiting polarimetric diversity and structural model properties of the different scattering mechanisms. This way, the related tomographic imaging problems are treated in descriptive regularization settings, applying modern non-parametric spatial spectral analysis (SSA) techniques. Nonetheless, the achievable resolution of the commonly performed SSA-based estimators highly depends on the span of the tomographic aperture; furthermore, irregular sampling and non-uniform constellations sacrifice the attainable resolution, introduce artifacts and increase ambiguity. Overcoming these drawbacks, in this paper, we address a new multi-stage iterative technique for feature-enhanced TomoSAR imaging that aggregates the virtual adaptive beamforming (VAB)-based SSA approach, with the wavelet domain thresholding (WDT) regularization framework, which we refer to as WAVAB (WDT-refined VAB). First, high resolution imagery is recovered applying the descriptive experiment design regularization (DEDR)-inspired reconstructive processing. Next, the additional resolution enhancement with suppression of artifacts is performed, via the WDT-based sparsity promoting refinement in the wavelet transform (WT) domain. Additionally, incorporation of the sum of Kronecker products (SKP) decomposition technique at the pre-processing stage, improves ground and canopy separation and allows for the utilization of different better adapted TomoSAR imaging techniques, on the ground and canopy structural components, separately. The feature enhancing capabilities of the novel robust WAVAB TomoSAR imaging technique are corroborated through the processing of airborne data of the German Aerospace Center (DLR), providing detailed volume height profiles reconstruction, as an alternative to the competing non-parametric SSA-based methods.

Synthetic aperture radar (SAR) tomography (TomoSAR) is a multibaseline interferometric technique that estimates the power spectrum pattern (PSP) along the perpendicular to the line-of-sight (PLOS) direction. TomoSAR achieves the separation of individual scatterers in layover areas, allowing for the 3D representation of urban zones. These scenes are typically characterized by buildings of different heights, with layover between the facades of the higher structures, the rooftop of the smaller edifices and the ground surface. Multilooking, as required by most spectral estimation techniques, reduces the azimuth-range spatial resolution, since it is accomplished through the averaging of adjacent values, e.g., via Boxcar filtering. Consequently, with the aim of avoiding the spatial mixture of sources due to multilooking, this article proposes a novel methodology to perform single-look TomoSAR over urban areas. First, a robust version of Capon is applied to focus the TomoSAR data, being robust against the rank-deficiencies of the data covariance matrices. Afterward, the recovered PSP is refined using statistical regularization, attaining resolution enhancement, suppression of artifacts and reduction of the ambiguity levels. The capabilities of the proposed methodology are demonstrated by means of strip-map airborne data of the Jet Propulsion Laboratory (JPL) and the National Aeronautics and Space Administration (NASA), acquired by the uninhabited aerial vehicle SAR (UAVSAR) system over the urban area of Munich, Germany in 2015. Making use of multipolarization data [horizontal/horizontal (HH), horizontal/vertical (HV) and vertical/vertical (VV)], a comparative analysis against popular focusing techniques for urban monitoring (i.e., matched filtering, Capon and compressive sensing (CS)) is addressed.

Background/Objectives: Estimating energy and macronutrients from food images is clinically relevant yet challenging, and rigorous evaluation requires transparent accuracy metrics with uncertainty and clear acknowledgement of reference data limitations across heterogeneous sources. This study assessed ChatGPT-5, a general-purpose vision-language model, across four scenarios differing in the amount and type of contextual information provided, using a composite dataset to quantify accuracy for calories and macronutrients. Methods: A total of 195 dishes were evaluated, sourced from Allrecipes.com, the SNAPMe dataset, and Home-prepared, weighed meals. Each dish was evaluated under Case 1 (image only), Case 2 (image plus standardized non-visual descriptors), Case 3 (image plus ingredient lists with amounts), and Case 4 (replicates Case 3 but excluding the image). The primary endpoint was kcal Mean Absolute Error (MAE); secondary endpoints included Median Absolute Error (MedAE) and Root Mean Square Error (RMSE) for kcal and macronutrients (protein, carbohydrates, and lipids), all reported with 95% Confidence Intervals (CIs) via dish-level bootstrap resampling and accompanied by absolute differences (Δ) between scenarios. Inference settings were standardized to support reproducibility and variance estimation. Source stratified analyses and quartile summaries were conducted to examine heterogeneity by curation level and nutrient ranges, with additional robustness checks for error complexity relationships. Results and Discussion: Accuracy improved from Case 1 to Case 2 and further in Case 3 for energy and all macronutrients when summarized by MAE, MedAE, and RMSE with 95% CIs, with absolute reductions (Δ) indicating material gains as contextual information increased. In contrast to Case 3, estimation accuracy declined in Case 4, underscoring the contribution of visual cues. Gains were largest in the Home-prepared dietitian-weighed subset and smaller yet consistent for Allrecipes.com and SNAPMe, reflecting differences in reference curation and measurement fidelity across sources. Scenario-level trends were concordant across sources, and stratified and quartile analyses showed coherent patterns of decreasing absolute errors with the provision of structured non-visual information and detailed ingredient data. Conclusions: ChatGPT-5 can deliver practically useful calorie and macronutrient estimates from food images, particularly when augmented with standardized nonvisual descriptors and detailed ingredients, as evidenced by reductions in MAE, MedAE, and RMSE with 95% CIs across scenarios. The decline in accuracy observed when the image was omitted, despite providing detailed ingredient information, indicates that visual cues contribute meaningfully to estimation performance and that improvements are not solely attributable to arithmetic from ingredient lists. Finally, to promote generalizability, it is recommended that future studies include repeated evaluations across diverse datasets, ensure public availability of prompts and outputs, and incorporate systematic comparisons with non-artificial-intelligence baselines.