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In this work, a multi-exposure method is proposed to increase the dynamic range (DR) of hyperspectral imaging using an InGaAs-based short-wave infrared (SWIR) hyperspectral line camera. Spectral signatures of materials were captured for scenarios in which the DR of a scene was greater than the DR of a line camera. To demonstrate the problem and test the proposed multi-exposure method, plastic detection in food waste and polymer sorting were chosen as the test application cases. The DR of the hyperspectral camera and the test samples were calculated experimentally. A multi-exposure method is proposed to create high-dynamic-range (HDR) images of food waste and plastic samples. Using the proposed method, the DR of SWIR imaging was increased from 43 dB to 73 dB, with the lowest allowable signal-to-noise ratio (SNR) set to 20 dB. Principal Component Analysis (PCA) was performed on both HDR and non-HDR image data from each test case to prepare the training and testing data sets. Finally, two support vector machine (SVM) classifiers were trained for each test case to compare the classification performance of the proposed multi-exposure HDR method against the single-exposure non-HDR method. The HDR method was found to outperform the non-HDR method in both test cases, with the classification accuracies of 98% and 90% respectively, for the food waste classification, and with 95% and 35% for the polymer classification.