Fixed-point iteration shows promise for quantitative reconstruction of optical absorption in photoacoustic tomography. However, there are issues that prevent the technique from being practical including: non-uniqueness of scattering and absorption profiles, divergence with over-iteration, and sensitivity to noise. Multiple illumination has been proposed to deal with the first problem, and may help with the second. The issue of noise may be balanced out by increasing the regularization parameter at the expense of the exactness of the reconstruction. In a multiple-illumination setup with a circular geometry where fluence is abundant, using a patterned illumination with a decoding step may provide an alternative which will boost SNR. We present a simple sequence of patterned illuminations based on an S-sequence that serves to improve SNR. While the forward model of the iterative method may be applied directly to the patterned excitations, including the decoding step improves SNR in an individual image by a factor equal to the size of the S-sequence, thus greatly improving convergence for a given value of regularization and SNR. For example, with 15 illuminations, 50-60dB noise levels with S-sequence patterned illuminations gives similar simulated performance to the 70dB case with single-source illuminations. This technique will allow the application of fixed-point iteration techniques in a broader range of SNR conditions without resorting to averaging.