A method for determining at least one property of a subterranean formation, the method, comprising: rotating, in a drilling operation, a bottom hole assembly including a drill bit and a logging while drilling module including an electromagnetic logging tool in a borehole penetrating the subterranean formation, wherein the electromagnetic logging tool includes a plurality of axially spaced transmitters (T1-T6) and axially spaced receivers (R1-R4); using the electromagnetic tool to acquire electromagnetic measurements of the subterranean formation while rotating the bottom hole assembly in the borehole ; and causing a processor to process the acquired electromagnetic measurements using a pixel-based inversion to determine at least one formation property of the subterranean formation, wherein said pixel-based inversion processing comprises minimizing a cost function in an iterative manner, the cost function including a data term residual and an additive regularization term; the method being characterized in that : at least one of the transmitters and at least one of the receivers of the electromagnetic logging tool includes a transverse (T6) or tilted (R3, R4) antenna; and the regularization term includes a standard regularization term and an additive gradient penalization term having a gradient penalization constant, wherein an optimum gradient penalization constant value is selected using an adaptive regularization routine that optimizes the gradient penalization constant values. rotating, in a drilling operation, a bottom hole assembly including a drill bit and a logging while drilling module including an electromagnetic logging tool in a borehole penetrating the subterranean formation, wherein the electromagnetic logging tool includes a plurality of axially spaced transmitters (T1-T6) and axially spaced receivers (R1-R4); using the electromagnetic tool to acquire electromagnetic measurements of the subterranean formation while rotating the bottom hole assembly in the borehole ; and causing a processor to process the acquired electromagnetic measurements using a pixel-based inversion to determine at least one formation property of the subterranean formation, wherein said pixel-based inversion processing comprises minimizing a cost function in an iterative manner, the cost function including a data term residual and an additive regularization term; the method being characterized in that : at least one of the transmitters and at least one of the receivers of the electromagnetic logging tool includes a transverse (T6) or tilted (R3, R4) antenna; and the regularization term includes a standard regularization term and an additive gradient penalization term having a gradient penalization constant, wherein an optimum gradient penalization constant value is selected using an adaptive regularization routine that optimizes the gradient penalization constant values. at least one of the transmitters and at least one of the receivers of the electromagnetic logging tool includes a transverse (T6) or tilted (R3, R4) antenna; and the regularization term includes a standard regularization term and an additive gradient penalization term having a gradient penalization constant, wherein an optimum gradient penalization constant value is selected using an adaptive regularization routine that optimizes the gradient penalization constant values. <EOS>