  The ability to automatically detect certain types of cells or cellular
subunits in microscopy images is of significant interest to a wide range of
biomedical research and clinical practices. Cell detection methods have evolved
from employing hand-crafted features to deep learning-based techniques. The
essential idea of these methods is that their cell classifiers or detectors are
trained in the pixel space, where the locations of target cells are labeled. In
this paper, we seek a different route and propose a convolutional neural
network (CNN)-based cell detection method that uses encoding of the output
pixel space. For the cell detection problem, the output space is the sparsely
labeled pixel locations indicating cell centers. We employ random projections
to encode the output space to a compressed vector of fixed dimension. Then, CNN
regresses this compressed vector from the input pixels. Furthermore, it is
possible to stably recover sparse cell locations on the output pixel space from
the predicted compressed vector using $L_1$-norm optimization. In the past,
output space encoding using compressed sensing (CS) has been used in
conjunction with linear and non-linear predictors. To the best of our
knowledge, this is the first successful use of CNN with CS-based output space
encoding. We made substantial experiments on several benchmark datasets, where
the proposed CNN + CS framework (referred to as CNNCS) achieved the highest or
at least top-3 performance in terms of F1-score, compared with other
state-of-the-art methods.
