Color Filter Arrays for Quanta Image Sensors

Quanta image sensor (QIS) is to be the next generation image sensor after CCD and CMOS. To enable such technology, significant progress was made over the past five years to advance both the device and image reconstruction algorithms. In this paper, we discuss color imaging using QIS, in particular how to design color filter arrays. Designing color filter arrays for QIS is challenging because at the pixel pitch of 1.1$\mu$m, maximizing the light efficiency while suppressing aliasing and crosstalk are conflicting tasks. We present an optimization-based framework to design color filter arrays for very small pixels. The new framework unifies several mainstream color filter array design frameworks by offering generality and flexibility. Compared to the existing frameworks which can only handle one or two design criteria, the new framework can simultaneously handle luminance gain, chrominance gain, cross-talk, anti-aliasing, manufacturability and orthogonality. Extensive experimental comparisons demonstrate the effectiveness and generality of the framework.

Optimal Threshold Design for Quanta Image Sensor

Quanta Image Sensor (QIS) is a binary imaging device envisioned to be the next generation image sensor after CCD and CMOS. Equipped with a massive number of single photon detectors, the sensor has a threshold $q$ above which the number of arriving photons will trigger a binary response "1", or "0" otherwise. Existing methods in the device literature typically assume that $q=1$ uniformly. We argue that a spatially varying threshold can significantly improve the signal-to-noise ratio of the reconstructed image. In this paper, we present an optimal threshold design framework. We make two contributions. First, we derive a set of oracle results to theoretically inform the maximally achievable performance. We show that the oracle threshold should match exactly with the underlying pixel intensity. Second, we show that around the oracle threshold there exists a set of thresholds that give asymptotically unbiased reconstructions. The asymptotic unbiasedness has a phase transition behavior which allows us to develop a practical threshold update scheme using a bisection method. Experimentally, the new threshold design method achieves better rate of convergence than existing methods.

Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications

Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure which allows one to plug in any off-the-shelf image denoising algorithm for a subproblem in the ADMM algorithm. Because of the plug-in nature, this type of ADMM algorithms is coined the name "Plug-and-Play ADMM". Plug-and-Play ADMM has demonstrated promising empirical results in a number of recent papers. However, it is unclear under what conditions and by using what denoising algorithms would it guarantee convergence. Also, since Plug-and-Play ADMM uses a specific way to split the variables, it is unclear if fast implementation can be made for common Gaussian and Poissonian image restoration problems. In this paper, we propose a Plug-and-Play ADMM algorithm with provable fixed point convergence. We show that for any denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges to a fixed point under a continuation scheme. We also present fast implementations for two image restoration problems on super-resolution and single-photon imaging. We compare Plug-and-Play ADMM with state-of-the-art algorithms in each problem type, and demonstrate promising experimental results of the algorithm.