Sparse Hyperspectral Band Selection Based on Expectation Maximization

Hyperspectral band selection seeks to identify a compact subset of informative spectral channels that preserves task–relevant information while mitigating the storage, transmission, and computational burdens imposed by high–dimensional data. Yet prevailing techniques face two pervasive limitations: (i) scoring- or ranking-based methods assess bands independently, overlooking the joint dependency that determine their true utility; and (ii) combinatorial search approaches, though theoretically exhaustive, require prohibitive enumeration that is incompatible with the scale and end-to-end nature of modern deep-learning pipelines. We recast band selection as a combinatorial inference problem and propose a task-agnostic framework that embeds a learnable Band Selection Layer equipped with an Expectation–Maximization–driven Sparsity Loss The E-step efficiently enumerates the expected likelihood of all <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>-out-of-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> band subsets via dynamic programming, thereby making implicit dependencies explicit; the M-step optimises band importances toward a provably <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>-sparse solution without post-hoc thresholding. Comprehensive theoretical analysis proves the absence of spurious local maxima and guarantees convergence to an exact sparse optimum. Extensive experiments on three public benchmarks (KSC, HT2013, HT2018), two auxiliary tasks (anomaly and target detection), and six classifiers demonstrate that the proposed method consistently surpasses state-of-the-art baselines. The results confirm that EM-guided sparsification not only stabilises the sparsity pattern but also yields interpretable inter-band dependency structures, making the framework a robust and broadly applicable tool for hyperspectral analysis and other sparsity-oriented vision problems.