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Band selection (BS) algorithms are an effective means of reducing the high volume of redundant data produced by the hundreds of contiguous spectral bands of Hyperspectral images (HSI). However, BS is a feature selection optimization problem and can be a computationally intensive to solve. Compressive sensing (CS) is a new minimally lossy data reduction (DR) technique used to acquire sparse signals using global, incoherent, and random projections. This new sampling paradigm can be implemented directly in the sensor acquiring undersampled, sparse images without further compression hardware. In addition, CS can be simulated as a DR technique after an HSI has been collected. This paper proposes a new combination of CS and BS using band clustering in the compressively sensed sample domain (CSSD). The new technique exploits the incoherent CS acquisition to develop BS via a CS transform utilizing inter-band similarity matrices and hierarchical clustering. It is shown that the CS principles of the restricted isometric property (RIP) and restricted conformal property (RCP) can be exploited in the novel algorithm coined compressive sensing band clustering (CSBC) which converges to the results computed using the original data space (ODS) given a sufficient compressive sensing sampling ratio (CSSR). The experimental results show the effectiveness of CSBC over traditional BS algorithms by saving significant computational space and time while maintaining accuracy.
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