This paper presents an original way to perform wave number inversion from simulated data obtained in a noisy shallow-water environment. In the studied configuration an acoustic source is horizontally towed with respect to a vertical hydrophone array. The inversion is achieved from the combination of three ingredients. First, a modified version of the Prony algorithm is presented and numerical comparison is made to another high-resolution wave number inversion algorithm based on the matrix-pencil technique. Second, knowing that these high-resolution algorithms are classically sensitive to noise, the use of a holographic array processing enables improvement of the signal-to-noise ratio before the inversion is performed. Last, particular care is taken in the representations of the solutions in the wave number space to improve resolution without suffering from aliasing. The dependence of this wave number inversion algorithm on the relevant parameters of the problem is discussed.