Arthur Alaniz, Tina Mantaring

Introduction

As the use of digital cameras becomes more and more widespread, the imaging algorithms that go into these cameras have also become more sophisticated. The typical digital camera uses a processing pipeline to convert raw sensor values to a final image, and the different parts of the pipeline may involve correcting for hardware defects, interpolating color filter array values, removing noise, and performing color space transformations. As more and more focus is being given to this field, the pipeline algorithms are also becoming more and more complex. However, one must ask the question: do these complex algorithms really outperform their simpler, more straightforward counterparts?

Methods

Denoising and Demosaicking

For our project, the primary algorithm we chose for our imaging pipeline was the one presented in the paper “Denoising and Interpolation of Noisy Bayer Data with Adaptive Cross-Color Filters”, by D. Paliy, A. Foi, R. Bilcu, and V. Katkovnik. Their technique performs simultaneous denoising and demosaicking using directional adaptive filters that are based on the concepts of local polynomial approximation (LPA) and intersection of confidence intervals (ICI).

Local Polynomial Approximation

Local polynomial approximation, or LPA, works on the assumption that the data in some local region can be fitted to a polynomial function. The cross-color filters used in the algorithm are linear combinations of LPA smoothing and difference filters that operate on complimentary color channels. The above figure shows an example of an LPA smoothing filter (left) and an LPA difference filter (right). The combined LPA cross-color filter is shown below, where the differing colors illustrate that the smoothing and difference components work on different color channels. File:LPAcombined.png

If we let $g_{m,s,\theta }^{(k)}$ denote a directional 1D convolution kernel, where $m$ is the polynomial order, $k$ is the order of the derivative, and $\theta$ is the direction, then we can write the interpolation kernels ${\overline{g}}_{s,\theta }$ and the denoising kernels ${\tilde{g}}_{s,\theta }$ as follows:

${\overline{g}}_{s,\theta }=(1-\alpha )g_{0,s,\theta }^{(0)}+\alpha g_{1,s,\theta }^{(0)}+\beta g_{1,s,\theta }^{(1)}$

<math>\tilde{g}_{s,\theta} = (1 - \alpha) g_{0,s,\theta}^{(0)} + \alpha g_{1,s,\theta}^{(0)} + \beta g_{1,s,\theta}^{(1)}</math?