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Whithin the CG method,
the IRLS algorithm can be considered as the LS method,
but with its operator, , modified by the weight, .The only change that distinguishes the IRLS algorithm
from the LS one is the substitution of
and for and , respectively.
Instead of modifying the operator,
we can choose a way to guide the minimizing search
to find the minimum -norm in a specific model subspace
so as to obtain a solution that meets a user's specific criteria.
The specific model subspace could be
guided by a specific -norm's gradient
or constrained by an a priori model.
Such guiding of the model vector can be realized by
weighting the residual vector or gradient vector in the CG algorithm.