In shallow water zones and at low frequency, seabed and water column properties can be estimated from the acoustic wavenumbers using inversion algorithms. When considering horizontal line arrays (HLA) and narrowband sources, the wavenumbers can be evaluated with classic spectral analysis methods. In this paper, a compressed sensing (CS) method for sparse recovery of the wavenumbers is proposed. This takes advantage of the few propagating modes and allows for spectral estimation when short HLA are used. The CS representation improves the wavenumber estimation, compared to the Fourier transform. However, for small arrays and several propagating modes, the CS generates interferences and does not allow proper wavenumber estimation. When considering broadband sources, it is possible to combine the wavenumbers estimated at several frequencies in order to build a frequency-wavenumber (f?-?k) representation. In this case, a post-processing tracking operation which improves the f?-?k resolution is presented. This relies on a general approach of waveguide physics and uses a particle filtering (PF) algorithm to track the wavenumbers. The consecutive use of CS and PF leads to a better wavenumber estimation. This methodology can be used for sources that are not at an end-fire position. It is illustrated by simulations and successfully applied on the Shallow Water 2006 data using the 32 sensor SHARK array.