Spatially Varying Exposure with 2-by-2 Multiplexing: Optimality and
  Universality
Xiangyu Qu Yiheng Chi Stanley H. Chan
The advancement of new digital image sensors has enabled the design of
exposure multiplexing schemes where a single image capture can have multiple
exposures and conversion gains in an interlaced format, similar to that of a
Bayer color filter array. In this paper, we ask the question of how to design
such multiplexing schemes for adaptive high-dynamic range (HDR) imaging where
the multiplexing scheme can be updated according to the scenes. We present two
new findings.
  (i) We address the problem of design optimality. We show that given a
multiplex pattern, the conventional optimality criteria based on the
input/output-referred signal-to-noise ratio (SNR) of the independently measured
pixels can lead to flawed decisions because it cannot encapsulate the location
of the saturated pixels. We overcome the issue by proposing a new concept known
as the spatially varying exposure risk (SVE-Risk) which is a pseudo-idealistic
quantification of the amount of recoverable pixels. We present an efficient
enumeration algorithm to select the optimal multiplex patterns.
  (ii) We report a design universality observation that the design of the
multiplex pattern can be decoupled from the image reconstruction algorithm.
This is a significant departure from the recent literature that the multiplex
pattern should be jointly optimized with the reconstruction algorithm. Our
finding suggests that in the context of exposure multiplexing, an end-to-end
training may not be necessary.