Owing to the stochastic nature of discrete processes such as photon counts in imaging, real-world data measurements
often exhibit heteroscedastic behavior. In particular, time series components and other measurements
may frequently be assumed to be non-iid Poisson random variables, whose rate parameter is proportional to the
underlying signal of interest-witness literature in digital communications, signal processing, astronomy, and
magnetic resonance imaging applications. In this work, we show that certain wavelet and filterbank transform
coefficients corresponding to vector-valued measurements of this type are distributed as sums and differences
of independent Poisson counts, taking the so-called Skellam distribution. While exact estimates rarely admit
analytical forms, we present Skellam mean estimators under both frequentist and Bayes models, as well as
computationally efficient approximations and shrinkage rules, that may be interpreted as Poisson rate estimation
method performed in certain wavelet/filterbank transform domains. This indicates a promising potential
approach for denoising of Poisson counts in the above-mentioned applications.
Recent developments in spatio-spectral sampling theory for color imaging devices show that the choice of color
filter array largely determines the spatial resolution of color images achievable by subsequent processing schemes
such as demosaicking and image denoising. This paper highlights the cost-effectiveness of a new breed of color
filter array patterns based on this sampling theory by detailing an implementation of the demosaicking method
consisting of entirely linear elements and comprising a total of only ten add operations per full-pixel reconstruction.
With color fidelity that rivals the state-of-the-art interpolation methods and an order of complexity near
to that of the bilinear interpolation, this joint sensor-demosaicking solution to digital camera architectures can
fulfill the image quality and complexity needs of future digital multimedia simultaneously.