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Conjugate Guided Gradient(CGG) method

Whithin the CG method, the IRLS algorithm can be considered as the LS method, but with its operator, $\bold L$, modified by the weight, $\bold W$.The only change that distinguishes the IRLS algorithm from the LS one is the substitution of $\bold L\bold W$ and $\bold W^T\bold L^T$ for $\bold L$ and $\bold L^T$, respectively. Instead of modifying the operator, we can choose a way to guide the minimizing search to find the minimum $\bold L^2$-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 $\bold L^p$-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.