MUSE-based emission-line maps of the spiral galaxy NGC 4030 reveal the existence of unresolved sources with forbidden line emission enhanced with respect to those seen in its own HII regions. This study reports our efforts to detect and isolate these objects and identify their nature. Candidates are first detected as unresolved sources on an image of the second principal component of the Hb, [OIII]5007, Ha, [NII]6584, [SII]6716, 6731 emission-line data cube, where they stand out clearly against both the dominant HII region population and the widespread diffuse emission. The intrinsic emission is then extracted accounting for the highly inhomogeneous emission-line background throughout the field of view. Collisional to recombination line ratios like [SII]/Ha, [NII]/Ha, and [OI]/Ha tend to increase when the background emission is corrected for. We find that many (but not all) sources detected with the principal component analysis have properties compatible with supernova remnants (SNRs). Applying a combined [SII]/Ha and [NII]/Ha classification criterion leads to a list of 59 sources with SNR-like emission lines. Many of them exhibit conspicuous spectral signatures of SNRs around 7300 Angs, and a stacking analysis shows that these features are also present, except weaker, in other cases. At nearly 30 Mpc, these are the most distant SNRs detected by optical means to date. We further report the serendipitous discovery of a luminous (M_V ~ -12.5), blue, and variable source, possibly associated with a supernova impostor.
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