  Energy consumption and hardware cost of signal digitization together with the
management of the resulting data volume form serious issues for high-rate
measurement systems with multiple sensors. Switching to binary sensing
front-ends results in a resource-efficient layout but is commonly associated
with significant distortion due to the nonlinear signal acquisition. In
particular, for applications that require to solve high-resolution processing
tasks under extreme conditions, it is a widely held belief that low-complexity
$1$-bit analog-to-digital conversion leads to unacceptable performance
degradation. In the Big Science context of low-frequency radio astronomy, we
propose a telescope architecture based on simplistic binary sampling, precise
probabilistic modeling, and likelihood-oriented data processing. The main
principles, building blocks, and advantages of such a radio telescope system,
which we refer to as The Massive Binary Radio Lenses, are sketched. The open
engineering science questions which have to be answered before building a
prototype are outlined. We set sail for the academic technology study by
deriving a statistical algorithm for interferometric imaging from binary array
measurements. The method aims at extracting the full discriminative information
about the spatial power distribution embedded in a binary sensor data stream
without bias. Radio measurements obtained with LOFAR are used to test the
developed imaging technique and discuss visual and quantitative results. These
assessments shed light on the fact that binary radio telescopes are suited for
surveying the universe.
