Hyperspectral images (HSI) provide extensive spectral information but their high dimensionality and redundancy create substantial challenges for computation and storage while increasing energy demands. The proposed solution combines sparse dictionary learning with Field Programmable gate Array (FPGA)-accelerated Sparse matrix vector multiplication (SpMV) operations and Support Vector Machine (SVM) training to tackle these issues. Spatial patches and spectral blocks partition HSI to enable the extraction of compact discriminative sparse features through the use of a learned sub-dictionary. In contrast to deep learning frameworks which demand large training datasets and generate significant computational overhead, the SVM-based approach achieves efficient real-time training and adaptation. The FPGA accelerator executes intensive SpMV operations through dynamic load balancing. We tested our approach with four varied HSI datasets gathered from aerial and UAV systems as well as terrestrial platforms on the PYNQ-Z2 board. Our design reaches classification accuracies between 98.65% and 99.95% across datasets including Indian Pines,AVRIS-NG, Cubert-UAV, Cubert-Terrestrial with per-pixel classification times below 7 us and inference times up to 36x faster than optimized software baselines which remain under typical sensor acquisition times. The strategy requires less than 0.24 W of on-chip power at maximum load which makes it ideal for deployment on satellites or UAVs. The proposed method outperforms existing FPGA-based SVM architectures in classification accuracy and throughput while enabling on-device incremental learning which makes it ideal for analyzing hyperspectral images in real-time.