Frequency hopping (FH) signals have well-documented merits for commercial and military applications due to their near-far resistance and robustness to jamming. Estimating FH signal parameters (e.g., hopping instants, carriers, and amplitudes) is an important and challenging problem, but optimum estimation incurs an unrealistic computational burden. The spectrogram has long been the nonparametric estimation workhorse in this context, followed by line spectra refinement. The problem is that hop timing estimates derived from the spectrogram are coarse and unreliable, thus severely limiting performance. In this paper we take a fresh look at this problem, based on sparse linear regression (SLR). At any point in time, there are only few active carriers; and carrier hopping is rare for slow FH. Using a dense frequency grid, we formulate the problem as under-determined linear regression with a dual sparsity penalty, and develop an exact solution using the alternating direction method of multipliers (ADMoM). Simulations demonstrate that the developed technique outperforms spectrogram-based methods, especially with regards to hop timing estimation, which is the crux of the problem.