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Due to the spatial-resolution limitation, mixed pixels containing energy reflected from more than one type of ground objects are widely present in remote sensing images, which often results in inefficient quantitative analysis. To effectively decompose such mixtures, a fully constrained linear unmixing algorithm based on a multichannel Hopfield neural network (MHNN) is proposed in this letter. The proposed MHNN algorithm is actually a Hopfield-based architecture which handles all the pixels in an image synchronously, instead of considering a per-pixel procedure. Due to the synchronous unmixing property of MHNN, a noise energy percentage (NEP) stopping criterion which utilizes the signal-to-noise ratio is proposed to obtain optimal results for different applications automatically. Experimental results demonstrate that the proposed multichannel structure makes the Hopfield-based mixture analysis feasible for real-world applications with acceptable time cost. It has also been observed that the proposed MHNN-based mixture-analysis algorithm outperforms the other two popular linear mixture-analysis algorithms and that the NEP stopping criterion can approach optimal unmixing results adaptively and accurately.