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• We impose a sparse reconstruction framework to deconvolve the underwater acoustic channel impulse response (CIR) blindly by minimizing the resulting penalty function in iterative steps using a dictionary of elements constructing from a set of potentially transmitted waveforms. • A wideband integrated dictionary is introduced in order to allow the blind deconvolution algorithm the ability to estimate frequency point in a continuous frequency sampling space, thereby reducing the effects of off grid components. • Examining real measurements, we conclude that the proposed method is able to form a sparse estimate of the CIR, enabling an efficient representation of the channel. In this paper, we propose a blind channel deconvolution method based on a sparse reconstruction framework exploiting a wideband dictionary under the (relatively weak) assumption that the transmitted signal may be assumed to be well modelled as a sum of sinusoids. Using a Toeplitz structured formulation of the received signal, we form an iterative blind deconvolution scheme, alternatively estimating the underwater impulse response and the transmitted waveform. The resulting optimization problems are convex, and we formulate a computationally efficient solver using the Alternating Direction Method of Multipliers (ADMM). We illustrate the performance of the resulting estimator using both simulated and measured underwater signals. [ABSTRACT FROM AUTHOR]