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. It takes advantage of the multiplication-convolution theorem of Fourier transforms. 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 irregularly arranged heterogeneous antenna. EPIC is highly modular and parallelizable, implemented in object oriented Python, and publicly available. We have verified the images produced to be equivalent to those produced using traditional techniques to within a precision determined by coarseness of gridding. We have also validated our implementation on data observed with the Long Wavelength Array (LWA). Antenna layouts with a dense filling factor 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 EPIC. Inherent availability of calibrated time-domain images on digitizer writeout time-scales and vastly lower I/O bandwidth relative to visibility-based systems will make it a prime candidate for transient searches of Fast Radio Bursts (FRB) as well as planetary and exoplanetary phenomena.
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