One appealing aspect that compressive sensing offers is the possibility of retrieving a signal’s spectral information using a bucket detector and a characterized measurement matrix. Demonstrations of CS applied to optical coherence tomography (OCT) were performed, however, in the final signal-processing instead of the acquisition end. Here we propose a novel OCT system with a broadband superluminescent excitation and a bucket photodetector where the interferogram is obtained by spectral reconstruction. In particular, this system assumes the same interferometric setup as typical swept-source OCT systems except the excitation is replaced by a broadband source. The interferogram then passes through an off-the-shelf, fast tunable Fabry-Perot filter (FPF) of modest finesse whose free spectral range is designed to be much less than the excitation bandwidth. The spectral response is characterized a priori, before the filtered output is integrated by the photodetector. The spectral sampling measurement is repeated by altering the FPF’s resonant conditions multiple times through the cavity length. Having acquired the integrated photodetector values and the corresponding spectral filter functions, we reconstruct the original interferogram whose Fourier transform generates the tomogram. The sensitivity of this OCT technique is evaluated and compared using simulations with synthetic data. Moreover, B-scan reconstruction of the interferogram due to a fingertip was simulated using our scheme and the resultant image shows excellent reconstruction fidelity compared to the original OCT B-scan. These illustrations point towards a promising future of a new class of tomographic system which combines the respective strengths of swept-source and spectral-domain OCT.