uDAS: An Untied Denoising Autoencoder With Sparsity for Spectral Unmixing

Linear spectral unmixing is the practice of decomposing the mixed pixel into a linear combination of the constituent endmembers and the estimated abundances. This paper focuses on unsupervised spectral unmixing where the endmembers are unknown a priori. Conventional approaches use either geometrical- or statistical-based approaches. In this paper, we address the challenges of spectral unmixing with unsupervised deep learning models, in specific, the autoencoder models, where the decoder serves as the endmembers and the hidden layer output serves as the abundances. In several recent attempts, part-based autoencoders have been designed to solve the unsupervised spectral unmixing problem. However, the performance has not been satisfactory. In this paper, we first discuss some important findings we make on issues with part-based autoencoders. By proof of counterexample, we show that all existing part-based autoencoder networks with nonnegative and tied encoder and decoder are inherently defective by making these inappropriate assumptions on the network structure. As a result, they are not suitable for solving the spectral unmixing problem. We propose a so-called untied denoising autoencoder with sparsity, in which the encoder and decoder of the network are independent, and only the decoder of the network is enforced to be nonnegative. Furthermore, we make two critical additions to the network design. First, since denoising is an essential step for spectral unmixing, we propose to incorporate the denoising capacity into the network optimization in the format of a denoising constraint rather than cascading another denoising preprocessor in order to avoid the introduction of additional reconstruction error. Second, to be more robust to the inaccurate estimation of a number of endmembers, we adopt an $l_{21}$ -norm on the encoder of the network to reduce the redundant endmembers while decreasing the reconstruction error simultaneously. The experimental results demonstrate that the proposed approach outperforms several state-of-the-art methods, especially for highly noisy data.