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Hyperspectral remote sensing attempts to identify features in the surface of the Earth using sensors that generally provide large amounts of data. The data are usually collected by a satellite or an airborne instrument and sent to a ground station that processes it. The main bottleneck of this approach is the (often reduced) bandwidth connection between the satellite and the station, which drastically limits the information that can be sent and processed in real time. A possible way to overcome this problem is to include onboard computing resources able to preprocess the data, reducing its size by orders of magnitude. Reconfigurable field-programmable gate arrays (FPGAs) are a promising platform that allows hardware/software codesign and the potential to provide powerful onboard computing capability and flexibility at the same time. Since FPGAs can implement custom hardware solutions, they can reach very high performance levels. Moreover, using run-time reconfiguration, the functionality of the FPGA can be updated at run time as many times as needed to perform different computations. Hence, the FPGA can be reused for several applications reducing the number of computing resources needed. One of the most popular and widely used techniques for analyzing hyperspectral data is linear spectral unmixing, which relies on the identification of pure spectral signatures via a so-called endmember extraction algorithm. In this paper, we present the first FPGA design for N-FINDR, a widely used endmember extraction algorithm in the literature. Our system includes a direct memory access module and implements a prefetching technique to hide the latency of the input/output communications. The proposed method has been implemented on a Virtex-4 XC4VFX60 FPGA (a model that is similar to radiation-hardened FPGAs certified for space operation) and tested using real hyperspectral data collected by NASA's Earth Observing-1 Hyperion (a satellite instrument) and the Airborne Visible Infra-- ed Imaging Spectrometer over the Cuprite mining district in Nevada and the Jasper Ridge Biological Preserve in California. Experimental results demonstrate that our hardware version of the N-FINDR algorithm can significantly outperform an equivalent software version and is able to provide accurate results in near real time, which makes our reconfigurable system appealing for onboard hyperspectral data processing.