Channel (linear operator) estimation requires either a-priori knowledge or joint estimation of channel temporal coherence. This information serves to condition the estimation process reducing estimator variance. Kalman-like conditional expectation algorithms have exhibited success by modeling the channel response via time evolution either assuming coherence time a priori or jointly estimating it. With coherence time viewed as a ‘‘time resolution’’ property of the channel response rather than a ‘‘time evolution’’ property a new computational structure results. From this viewpoint we introduce a new channel estimation algorithm ‘‘in-scale’’ vice ‘‘in-time.’’ In such a framework detail is added, or synonymously coherence time is successively reduced, to meet a maximum a posteriori (MAP) criteria. The algorithm starts with a ‘‘mean’’ (time invariant) estimate and gradually adds detail evolving in scale until the MAP is attained. Computationally the algorithm exploits conjugate gradient directions recursing from low resolution to higher resolution until the requisite prior complexity (estimated via an empirical Bayes method) and data fidelity are met. Scale projections are computed efficiently and dimension reduction is aided via a wavelet decomposition. Explanations in terms of the minimum description length principle are also provided.