The problem of estimating a sparse channel, i.e. a channel with a few non-zero taps, appears in many fields of communication including acoustic underwater or wireless transmissions. In this paper, we have developed an algorithm based on Iterative Alternating Minimization technique which iteratively detects the location and the value of the channel taps. In fact, at each iteration we use an approximate Maximum A posteriori Probability (MAP) scheme for detection of the taps, while a least square method is used for estimating the values of the taps at each iteration. For approximate MAP detection, we have proposed three different methods leading to three variants for our algorithm. Finally, we experimentally compared the new algorithms to the Cram