We present a method for subtracting point sources from interferometric radio images via forward modelling of the instrument response and involving an algebraic non-linear minimization. The method is applied to simulated maps of the Murchison Wide-field Array but is generally useful in cases where only image data are available. After source subtraction, the residual maps have no statistical difference to the expected thermal noise distribution at all angular scales, indicating high effectiveness in the subtraction. Simulations indicate that the errors in recovering the source parameters decrease with increasing signal-to-noise ratio, which is consistent with the theoretical measurement errors. In applying the technique to simulated snapshot observations with the Murchison Wide-field Array, we found that all 101 sources present in the simulation were recovered with an average position error of 10 arcsec and an average flux density error of 0.15 per cent. This led to a dynamic range increase of approximately 3 orders of magnitude. Since all the sources were deconvolved jointly, the subtraction was not limited by source sidelobes but by thermal noise. This technique is a promising deconvolution method for upcoming radio arrays with a huge number of elements and a candidate for the difficult task of subtracting foreground sources from observations of the 21-cm neutral hydrogen signal from the epoch of reionization.
