  Modern radio telescopes are favouring densely packed array layouts with large
numbers of antennas ($N_\textrm{A}\gtrsim 1000$). Since the complexity of
traditional correlators scales as $\mathcal{O}(N_\textrm{A}^2)$, there will be
a steep cost for realizing the full imaging potential of these powerful
instruments. Through our generic and efficient E-field Parallel Imaging
Correlator (EPIC), we present the first software demonstration of a generalized
direct imaging algorithm, namely, the Modular Optimal Frequency Fourier (MOFF)
imager. Not only does it bring down the cost for dense layouts to
$\mathcal{O}(N_\textrm{A}\log_2 N_\textrm{A})$ but can also image from
irregular layouts and heterogeneous arrays of antennas. EPIC is highly modular,
parallelizable, implemented in object-oriented Python, and publicly available.
We have verified the images produced to be equivalent to those from traditional
techniques to within a precision set by gridding coarseness. We have also
validated our implementation on data observed with the Long Wavelength Array
(LWA1). We provide a detailed framework for imaging with heterogeneous arrays
and show that EPIC robustly estimates the input sky model for such arrays.
Antenna layouts with dense filling factors consisting of a large number of
antennas such as LWA, the Square Kilometre Array, Hydrogen Epoch of
Reionization Array, and Canadian Hydrogen Intensity Mapping Experiment will
gain significant computational advantage by deploying an optimized version of
EPIC. The algorithm is a strong candidate for instruments targeting transient
searches of Fast Radio Bursts (FRB) as well as planetary and exoplanetary
phenomena due to the availability of high-speed calibrated time-domain images
and low output bandwidth relative to visibility-based systems.
