  We introduce a novel multichannel blind deconvolution (BD) method that
extracts sparse and front-loaded impulse responses from the channel outputs,
i.e., their convolutions with a single arbitrary source. A crucial feature of
this formulation is that it doesn't encode support restrictions on the
unknowns, unlike most prior work on BD. The indeterminacy inherent to BD, which
is difficult to resolve with a traditional L1 penalty on the impulse responses,
is resolved in our method because it seeks a first approximation where the
impulse responses are: "maximally white" -- encoded as the energy focusing near
zero lag of the impulse-response auto-correlations; and "maximally
front-loaded" -- encoded as the energy focusing near zero time of the impulse
responses. Hence we call the method focused blind deconvolution (FBD). The
focusing constraints are relaxed as the iterations progress. Note that FBD
requires the duration of the channel outputs to be longer than that of the
unknown impulse responses.
  A multichannel blind deconvolution problem that is appropriately formulated
by sparse and front-loaded impulse responses arises in seismic inversion, where
the impulse responses are the Green's function evaluations at different
receiver locations, and the operation of a drill bit inputs the noisy and
correlated source signature into the subsurface. We demonstrate the benefits of
FBD using seismic-while-drilling numerical experiments, where the noisy data
recorded at the receivers are hard to interpret, but FBD can provide the
processing essential to separate the drill-bit (source) signature from the
interpretable Green's function.
