Upper left panel: image of the original point source when the PSF is a bivariate, circularly symmetric, Gaussian PSF with dispersion σ_G = 3 pixels. Upper right panel: original point source added with a white noise with standard deviation equal to half the peak value of the source itself. Bottom left panel: noisy image filtered with an improper matched filter (MF) that has a Gaussian shape and σ_G = 4 pixels. Bottom right panel: noisy image filtered with the correct MF.