This paper presents a technique for hyperspectral image classification and dimensionality reduction using orthogonal subspace projection (OSP). The method simultaneously reduces data dimensionality, suppresses interfering spectral signatures, and detects the presence of a target spectral signature. The core idea is to project each pixel vector onto a subspace orthogonal to the interfering signatures, which optimally suppresses interference in the least squares sense. After nulling the interference, projecting the residual onto the target signature maximizes the signal-to-noise ratio (SNR), resulting in a single component image that represents the classification of the target signature. The OSP operator can be extended to multiple target signatures, enabling simultaneous classification of multiple spectral signatures. The approach is applicable to both spectrally pure and mixed pixels, where mixed pixels contain multiple spectral classes. The method is based on the theory of least squares and has been developed in the sensor array processing community. It is also related to simultaneous diagonalization (SD) filtering. The technique is applied to both simulated and real hyperspectral data. In simulations, the OSP method successfully detects target signatures at low abundance levels (as low as a few percent) with reasonable signal-to-noise ratios (≤50:1) and spectral resolution (10 nm). When applied to AVIRIS data from the Lunar Crater Volcanic Field, the method produces component images that represent class maps of various materials, consistent with field observations and published geological maps. The OSP technique is a combination of two linear operators: one for optimal interference rejection in the least squares sense and another for optimal detection in the maximum SNR sense. It is effective in both mixed and spectrally pure pixels and does not suffer from the limitations of standard statistical classifiers and matched filtering techniques. The method provides a significant reduction in data volume, transforming a high-dimensional hyperspectral image cube into a set of lower-dimensional component images that represent the classification of target signatures. The technique is useful for analyzing sensor capabilities required for detection and classification tasks in hyperspectral imaging.This paper presents a technique for hyperspectral image classification and dimensionality reduction using orthogonal subspace projection (OSP). The method simultaneously reduces data dimensionality, suppresses interfering spectral signatures, and detects the presence of a target spectral signature. The core idea is to project each pixel vector onto a subspace orthogonal to the interfering signatures, which optimally suppresses interference in the least squares sense. After nulling the interference, projecting the residual onto the target signature maximizes the signal-to-noise ratio (SNR), resulting in a single component image that represents the classification of the target signature. The OSP operator can be extended to multiple target signatures, enabling simultaneous classification of multiple spectral signatures. The approach is applicable to both spectrally pure and mixed pixels, where mixed pixels contain multiple spectral classes. The method is based on the theory of least squares and has been developed in the sensor array processing community. It is also related to simultaneous diagonalization (SD) filtering. The technique is applied to both simulated and real hyperspectral data. In simulations, the OSP method successfully detects target signatures at low abundance levels (as low as a few percent) with reasonable signal-to-noise ratios (≤50:1) and spectral resolution (10 nm). When applied to AVIRIS data from the Lunar Crater Volcanic Field, the method produces component images that represent class maps of various materials, consistent with field observations and published geological maps. The OSP technique is a combination of two linear operators: one for optimal interference rejection in the least squares sense and another for optimal detection in the maximum SNR sense. It is effective in both mixed and spectrally pure pixels and does not suffer from the limitations of standard statistical classifiers and matched filtering techniques. The method provides a significant reduction in data volume, transforming a high-dimensional hyperspectral image cube into a set of lower-dimensional component images that represent the classification of target signatures. The technique is useful for analyzing sensor capabilities required for detection and classification tasks in hyperspectral imaging.