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Glow discharge optical emission spectroscopy elemental mapping (GDOES EM), enabled by spectral imaging strategies, is an advantageous technique for direct multi-elemental analysis of solid samples in rapid timeframes. Here, a single-pixel, or point scan, spectral imaging system based on compressed sensing image sampling, is developed and optimized in terms of matrix density, compression factor, sparsifying basis, and reconstruction algorithm for coupling with GDOES EM. It is shown that a 512 matrix density at a compression factor of 30% provides the highest spatial fidelity in terms of the peak signal-to-noise ratio (PSNR) and complex wavelet structural similarity index measure (cw-SSIM) while maintaining fast measurement times. The background equivalent concentration (BEC) of Cu I at 510.5 nm is improved when implementing the discrete wavelet transform (DWT) sparsifying basis and Two-step Iterative Shrinking/Thresholding Algorithm for Linear Inverse Problems (TwIST) reconstruction algorithm. Utilizing these optimum conditions, a GDOES EM of a flexible, etched-copper circuit board was then successfully demonstrated with the compressed sensing single-pixel spectral imaging system (CSSPIS). The newly developed CSSPIS allows taking advantage of the significant cost-efficiency of point-scanning approaches (>10× vs. intensified array detector systems), while overcoming (up to several orders of magnitude) their inherent and substantial throughput limitations. Ultimately, it has the potential to be implemented on readily available commercial GDOES instruments by adapting the collection optics.