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Assessing soil organic carbon (SOC) stocks is crucial for understanding the carbon sequestration potential of agroecosystems and for mitigating climate change. This study presents a novel method for assessing SOC and mineral content at various soil depths in sorghum crops using hyperspectral remote sensing. Conducted at Planthaven Farms, MO, the research encompassed ten genotypes across 30 plots, yielding 180 soil samples from six depth intervals (0–150 cm) of bare soil. Chemical analyses determined the SOC and mineral levels, which were then compared to spectral data from HySpex indoor sensors. We utilized time-frequency analysis methods, including discrete wavelet transformation (DWT), continuous wavelet transformation (CWT), and frame transformation along with traditional spectral transformations, specifically fractional derivatives and continuum removal. The analysis revealed the shortwave infrared (SWIR) region, particularly the 1800–2000 nm range, as having the strongest correlations with SOC content (with R2 exceeding 0.8). The visible near-infrared (VNIR) region also provided valuable insights. Models incorporating CWT achieved high accuracy (test R2 exceeding 0.9), while frame transformation achieved strong accuracy (test R2 between 0.7 and 0.8) with fewer features. The random forest regressor (RFR) proved to be most robust, demonstrating superior accuracy and reduced overfitting compared to support vector regression (SVR), partial least squares regression (PLSR), and deep neural network (DNN) models. The models demonstrated the efficacy of hyperspectral data for SOC estimation, suggesting potential for future applications that integrate this data with above-ground biomass to improve SOC mapping across larger scales. This research offers a promising spectral transformation approach for effective carbon management and sustainable agriculture in a changing climate. 

A frame $(x_j{)}_{j\in <\#comment/>J}$for a Hilbert space $H$is said to do phase retrieval if for all distinct vectors $x,y\in <\#comment/>H$the magnitudes of the frame coefficients $(|⟨<\#comment/>x,x_j⟩<\#comment/>|{)}_{j\in <\#comment/>J}$and $(|⟨<\#comment/>y,x_j⟩<\#comment/>|{)}_{j\in <\#comment/>J}$distinguish $x$from $y$(up to a unimodular scalar). A frame which does phase retrieval is said to do $C$-stable phase retrieval if the recovery of any vector $x\in <\#comment/>H$from the magnitude of the frame coefficients is $C$-Lipschitz. It is known that if a frame does stable phase retrieval then any sufficiently small perturbation of the frame vectors will do stable phase retrieval, though with a slightly worse stability constant. We provide new quantitative bounds on how the stability constant for phase retrieval is affected by a small perturbation of the frame vectors. These bounds are significant in that they are independent of the dimension of the Hilbert space and the number of vectors in the frame.