We present a method for subtracting point sources from interferometric radio images via forward modeling of the instrument response and involving an algebraic nonlinear 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 % .
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 .