Unsupervised design for broadband multispectral and polarization filter array patterns

Imaging multiple wavelength and polarization components is problematic due to the complexity of equipment and the increase in the number of imaging shots, so imaging using filter arrays with various patterns has been widely reported from elemental research to practical applications. Most of them use bandpass filters with different center wavelengths for each pixel. Recently, however, filter arrays with multimodal transmission characteristics have been proposed using photonic crystals or Fabry-Perot filters. In any of these methods, the design of the filter array arrangement pattern is important to improve the quality of the captured image, as well as the improvement of the demosaicking algorithm. One way to design a filter array pattern is to minimize the mean squared error (MSE) between the ideal image and the demosaicked image. However, the more multidimensional the imaging components, the more difficult it becomes to collect training data. In such cases, it is necessary to empirically determine candidate transmission characteristics and patterns of filter arrays. In this study, we propose a method for evaluating filter array patterns without using any training data in the design of filter arrays for multispectral and polarization imaging. The proposed method estimates the MSE by approximating the autocorrelation matrix without using image data by expressing the imaging model as a linear forward problem and the demosaicking as a linear inverse problem. Since this method can be applied not only to ideal bandpass filter arrangements, but also to multispectral filter arrays with multimodal spectral transmission characteristics and even multispectral polarization filter arrays with different extinction ratios at different wavelengths, we will show that image quality can be improved over empirical arrangements by evaluating these patterns and by testing examples of optimal designs using genetic algorithms.