The minimum-norm least-squares (MNLS) solution to reconstructing a photoacoustic image is given by the pseudoinverse of the system matrix, which relates the initial pressure distribution to the measured pressure wave. In this paper, we calculate the pseudoinverse using a singular-value decomposition (SVD). The pseudoinverse calculation involves dividing by the nonzero singular values of the system matrix. In practice, we have to regularize the problem by throwing out small singular values that would otherwise amplify the noise. Where to set the regularization threshold depends on the specific signal and noise levels. The noise in an imaging system can generally be divided into object-dependent and object-independent noise. In many imaging systems, such as x-ray CT, the object-dependent noise varies strongly across detectors. In photoacoustics, however, the object-dependent noise is relatively uniform across transducer elements (as long as the object is not too close to the transducer). The object-independent noise (such as electronic noise) is also uniform across the transducer elements. The regularization level still depends on the relative strength of the signal and noise, but it is possible to calculate a few pseudoinverse matrices based on different singular-value truncations, store these in memory, and then decide in real time which one to use based on image quality. Due to the more uniform noise properties, we expect this method to work relatively better in photoacoustics than, say, x-ray CT, which would benefit from a more advanced regularization. Using this method the reconstruction step consists only of a matrix-vector multiplication, which is very fast. In a recent publication, the system matrix of a photoacoustic imaging system was measured experimentally, and the corresponding pseudoinverse was calculated ahead of time and used for real-time imaging.^{8} This method has the advantage of including all the relevant acoustic properties in the system matrix, but the disadvantages of requiring the experimental measurement of the system matrix and the inevitable inclusion of system noise in the measurement. In this paper we develop a model for a two-dimensional (2-D) system matrix and use that to calculate the pseudoinverse. We also develop a three-dimensional (3-D) forward model to simulate a photoacoustic imaging system.