Research On The Design Of Color Filter Arrays

In digital color imaging, a raw image is typically obtained via a single sensor cov-ered by a color filter array (CFA), which allows only one color component to be measured at each pixel. The procedure to reconstruct a full color image from the raw image is called demosaicking. Since the CFA may cause irreversible visual artifacts, the CFA as well as the demosaicking algorithm is crucial to the quality of demosaicked images. The Bayer CFA dominates the consumer market, but it has two fundamental limitations. First, it has spectral overlap in the frequency domain, making it prone to have aliasing artifacts. The second is that it blocks much of the incident light, which limits its performance in high-speed imaging and low-light imaging. Over the past decades, many new CFAs have been proposed to overcome the two limitations of Bayer CFA. However, there are still some crucial issues, which are unsolved and worth studying. Frist, some researchers have pointed out the advantages of the irregular layout of animal retina in reducing aliasing artifacts. But all the retina-inspired CFAs simplify the irregular retina to square pixels in regular layouts. Second, the design of CFAs in the frequency domain provided a theoret-ical approach to minimizing the spectral overlap. However, almost all the existing design methods in the frequency domain involve considerable human effort. Third, high light sensitivity color cameras are highly expected, but this issue only received surprisingly little attention in the existing literature.In this dissertation, I focus on the above crucial problems, and the main contributions include:(1) I propose using the Penrose pixel layout for capturing color images. Due to the uniform three-colorability of Penrose layout, the quality of color images can be guaranteed. Moreover, since the Penrose pixel layout uses only two shapes of pix-els, its manufacturing is relatively easy (although not as easy as square and hexag-onal pixel layouts). It should be the first choice if an irregular layout is considered for color imaging. In order to testify the performance of Penrose pixel layout, we propose a sparse representation based method for Penrose demosaicking, which is more challenging than regular demosaicking. Extensive experiments show that the Penrose pixel layout outperforms regular pixel layouts.(2) I present a new method to automatically design CFAs in the frequency domain. Our method is based on the frequency structure representation of CFAs. We utilize a multi-objective optimization approach to propose frequency structure candidates, in which the overlap among the frequency components of raw images with the CFA is minimized. Then we optimize parameters for each candidate, which is formulat-ed as a constrained optimization problem. We use the alternating direction method (ADM) to solve it. Our parameter optimization method is applicable to arbitrary frequency structures, including those with conjugate replicas of chrominance com-ponents. Experiments on benchmark images confirm the advantage of the proposed method.(3) We propose a theoretical approach to design high light-sensitive CFAs in the fre-quency domain. Our method is also based on the frequency structure representation of CFAs. We first propose frequency structure candidates, which could produce C-FAs with or beyond a desired percentage of panchromatic pixels. Then for each candidate, we optimize parameters to obtain the CFA, which achieves or exceeds the desired percentage of panchromatic pixels and is also robust to aliasing artifact-s. We formulate this procedure as a constrained optimization problem and solve it using ADM. Extensive experiments confirm the advantage of the proposed method and CFA, especially in the low-light conditions.