Convolutional neural networks for the reconstruction of spectra in compressive sensing spectrometers

In optical filter based compressive sensing (CS) spectrometers, an input spectrum is multiplexed and modulated by a small number of optical filters which have different sensing patterns. Then, detectors read out the modulated signals called measurements. By exploiting the CS reconstruction algorithms that utilize the measurements and the sensing patterns of optical filters, the spectrum is recovered. However, there exists a drawback on CS reconstruction algorithms. The input spectrum should be a sparse signal or be sparsely represented by a pre-determined sparsifying basis. In practice, however, the input spectrum could not be sparse or be sparsely represented by the pre-determined sparsifying basis. Therefore, the performance of spectral recovery using the CS reconstruction algorithms is varying according to the sparsity of the input spectrum and the sparsifying basis. In this paper, we implement a convolutional neural networks (CNNs) structure to reconstruct the input spectrum from the measurements of the CS spectrometers. The CNNs structure learns the way of solving the inverse problem of the underdetermined linear system. As an input of the CNNs structure, a spectrum calculated by multiplying a fixed transform matrix and the measurements is used. We investigate the reconstruction performance of the CNNs structure comparing with the CS reconstruction algorithm with different sparsifying basis. The experiment results indicate the reconstruction performance of the CNNs structure is compatible with the CS reconstruction algorithm.