  We present an alternative method for reconstructing a velocity-delay map in
reverberation mapping (RM) based on the pixon algorithm initially proposed for
image reconstruction by Pina & Puetter (1993). The pixon algorithm allows for a
variable pixon basis to adjust resolution of each image pixel according the
information content in that pixel, which therefore enables the algorithm to
make the best possible use of measured data. The final optimal pixon basis
functions would be those that minimize the number of pixons while still
providing acceptable descriptions to data within the accuracy allowed by
noises. We adapt the pixon algorithm to RM analysis and develop a generic
framework to implement the algorithm. Simulation tests and comparisons with the
widely used maximum entropy method demonstrate the feasibility and high
performance of our pixon-based RM analysis. This paper serves as an
introduction to the framework and the application to velocity-unresolved RM. An
extension to velocity-resolved cases will be presented in a companion paper.
