Abstract: In single-pixel (ghost) imaging, known illumination patterns probe an object and a detector with no spatial resolution returns one number per pattern. Each measurement costs acquisition time and photons and, for ionizing probes, contributes to delivered dose. Motivated by automated radiographic defect screening, where a class label suffices, we introduce Learning Illumination Patterns for Single-Pixel Classification (LIPS-PC). The patterns are learned end-to-end while the measurement operator remains one fixed linear matrix, identical for every input. We parameterize it as a residual correction to a two-dimensional discrete cosine transform (2D-DCT), $D=D_{\mathrm{base}}+Δ$, and jointly train the correction and a compact classifier using cross-entropy, without a reconstruction objective. This yields a task-driven linear embedding through optimization. We evaluate LIPS-PC numerically on MNIST and Fashion-MNIST under a controlled protocol, then on RIAWELC, a real industrial X-ray weld-radiograph dataset. Across five budgets, $M\in{8,16,32,64,128}$, corresponding to sampling ratios from below 1% to 12.5%, the learned operator outperforms the best tested fixed transform by 9-15 percentage points at $M=8$ on all three datasets. Its eight-measurement accuracy requires roughly 16-32 measurements with the best fixed transform, indicating a $2\times$ to $4\times$ saving at comparable accuracy. The advantage generally shrinks as $M$ increases, with a small reversal on RIAWELC at higher budgets. These results show that learning what to measure is especially valuable when measurements are scarce.