\section{Introduction}
\label{sec:intro}

 Earth observation (EO) - Satellite imagery offers a rich multimodal view of Earth. %yet supervised learning is hindered by limited labels, sensor heterogeneity, and inconsistent cross-sensor characteristics.% 
 Traditional remote sensing relied on handcrafted spectral indices such as NDVI \cite{xue2017significant} and classical machine learning methods such as SVMs \cite{suthaharan2016support} and random forests \cite{breiman2001random}. However, RS (Remote Sensing) and ML (Machine Learning) pipelines exhibit substantial degradation when exposed to spatial and temporal variability \cite{ranjan2024evaluating,ranjan2024prediction,shikhar2024evaluation,ranjan2024yield,singh20243d,ranjan2024stubble}. Deep learning methods, particularly CNNs \cite{o2015introduction}, improved representation learning for land cover classification and flood detection, but they remain data-hungry and fully supervised. Masked image modeling (MIM) \cite{hondru2025masked} methods, such as MAE \cite{lin2023ss,he2022masked,feichtenhofer2022masked}, alleviate the need for paired samples by reconstructing masked inputs, but most remote-sensing variants operate on a single modality or fixed spectral groupings, lacking multi-sensor integration. 
 
 Self-supervised learning (SSL) \cite{gui2024survey,wang2022self} has emerged as a powerful paradigm, demonstrating that large models can be pretrained on vast unlabeled datasets and then adapted to diverse downstream tasks. Recent remote sensing foundation models \cite{huo2025remote,huang2025survey} such as Presto \cite{tseng2023lightweight}, SatMAE \cite{cong2022satmae}, and S2MAE \cite{li2024s2mae} represent early progress towards general-purpose EO models. However, major gaps remain. Most existing approaches lack sensor diversity, focusing primarily on optical imagery or simply stacking multispectral bands without exploiting their physical and spectral distinctions. They rarely address pixel-level pretraining, which is critical for dense prediction tasks such as classification and crop type mapping. %Many also struggle under missing-modality conditions (e.g., clouds or radar unavailability) and neglect physics and geography aware priors, relying instead on architectures developed for natural images.%


To address these challenges, we introduce SPEAR a Self-Supervised Pixel-level Multi-Modal Spectral fusion framework that learns sensor-adaptive, and wavelength-continuous representations. Each modality optical, radar, and climate is modeled by a dedicated SSL learner tailored to its physical characteristics, while a flexible fusion head unifies them into per-pixel embeddings. Unlike prior patch-level approaches, SPEAR operates directly on pixel-wise spectra, enabling scalable cross-sensor learning and robust inference under missing-modality conditions through learned zero-slot tokens.

\textbf{Key Contributions and Novelty.}  
The proposed SPEAR framework is a unified, sensor-awared, self-supervised foundation model for multimodal Earth observation. It jointly pretrains optical, radar, and climate modalities at the pixel level using wavelength and geo-aware encodings to learn compact, interpretable embeddings.

\begin{itemize}[nosep,leftmargin=*]
\item \textbf{Spectral-MAE:} A wavelength-conditioned masked autoencoder for multispectral imagery (Sentinel-2~\cite{gascon2014copernicus}, PlanetScope~\cite{basheer2024comparative}) that incorporates center wavelength ($\lambda$) and bandwidth ($\Delta\lambda$) metadata to produce 32-D continuous spectral embeddings.
\item \textbf{Climate-MAE:} A geophysical autoencoder leveraging sinusoidal latitude-longitude encodings to capture spatial and climatological continuity from LST-day/night \cite{marzban2018influence}, precipitation, and elevation data.  
\item \textbf{BYOL-Denoise:} A radar-specific Bootstrap-Your-Own-Latent \cite{grill2020bootstrap} variant with physics-based augmentations (speckle noise, polarization dropout, intensity jitter) and a denoising head for noise-invariant SAR features.  
\item \textbf{Sensor- and scale-aware fusion:}A flexible head for concatenation and cross-attention integration, conditioned on sensor identity and ground-sampling distance (GSD), ensuring robustness to spatial misalignment and missing modalities.  
\item \textbf{Scalability and efficiency:} Using lightweight 32-D embeddings and only $\sim$1M parameters, SPEAR achieves competitive performance.
\end{itemize}

In summary, SPEAR is the first sensor- and scale-aware, pixel-level self-supervised framework that unifies optical, radar, and climate modalities within a compact, physically grounded embedding space, able to understand under any modality combination. The following section reviews related advances in SSL and EO that motivate our design choices.