Recently, Moudafi and Maingé [2] studied the VI (1.2) by regularizing the mapping and defined as the unique fixed point of the equation (1.3).
Very recently, Lu et al. [3] studied the VI (1.2) by regularizing the mapping and defined as the unique fixed point of the equation (1.4).
So Lu et al. [2] defined {xs,t} as follows by regularizing the mapping S: x s, t = s [ t f ( x s, t ) + ( 1 - t ) S x s, t ] + ( 1 - s ) T x s, t, s, t ∈ ( 0, 1 ).
Very recently, Lu et al. [1] studied VI (2) by regularizing the mapping S and defined { x s, t } as the unique fixed point of the equation x s, t = s [ t f ( x s, t ) + ( 1 − t ) S ( x s, t ) ] + ( 1 − s ) T ( x s, t ), s, t ∈ ( 0, 1 ).
Recently, Moudafi and Mainge [3] studied VI (2) by regularizing the mapping t S + ( 1 − t ) T and defined { x s, t } as the unique fixed point of the equation x s, t = s f ( x s, t ) + ( 1 − s ) [ t S ( x s, t ) + ( 1 − t ) T ( x s, t ) ], s, t ∈ ( 0, 1 ).
In 2006, Moudafi and Mainge [5] studied the VI(1.2) by regularizing the mapping tS + (1 - t)T and defined {xs,t} as follows: x s, t = s f ( x s, t ) + ( 1 - s ) [ t S x s, t + ( 1 - t ) T x s, t ], s, t ∈ ( 0, 1 ).
They proved two strong convergence results by regularizing the nonexpansive mapping T using contractions.
By regularizing the complex filter function, phase degradation by noise amplification is suppressed as anticipated from intensity deconvolution [ 14].
We achieve this by regularizing the L2-norm of the model parameters using a regularization factor.
Specifically, this is achieved by regularizing the wavelength dependant Jacobian matrix prior to mixing with the spectral coefficients, a completely new method where the regularization does not affect the mapping of absorption changes onto chromophore concentrations, thereby providing a much more accurate spectral inversion technique.
