Multispectral filter array design without training images

Multispectral images (MSIs) have been studied for many applications; however, limitations persist in techniques to capture them due to the complexity of assembling one or more prisms and multiple sensor arrays in order to detect signals. Inspired by the application of color filter arrays to commercial digital RGB cameras, a number of researchers have studied multispectral filter arrays (MSFAs) to solve this problem. Determining the measurement wavelength and pattern of an MSFA is important for improving the quality of the demosaicked image. Some conventional studies for designing MSFAs have used training data and have optimized the measurement wavelengths and the pattern by iteratively minimizing the error between the training data and the demosaicked images. We propose a metric to evaluate an MSFA without MSIs, and optimize the measurement wavelengths and the pattern of the MSFA by minimizing the metric. The proposed metric measures the sampling distance between filters in a spatial–spectral domain and quantifies the dispersion of the sampling points by average nearest-neighbor distance (ANND) under a given arbitrary MSFA. Since the quality of the demosaicked image is assumed to be proportional to the degree of dispersion of the sampling points in the spatial–spectral domain, we optimize the MSFA by minimizing the ANND in a nested simulated annealing process. Experimental results show that the optimized MSFA obtained using our method attained a higher peak signal-to-noise ratio (PSNR) than conventional untrained MSFAs in many cases. In addition, the performance difference between some trained MSFAs and the proposed MSFA was small. We also confirmed the validity of the proposed ANND by a comparison with the mean square error obtained from MSI datasets.