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This paper considers the microwave imaging reconstruction problem, based on additive penalization and gradient-based optimization. Each evaluation of the cost function and of its gradient requires the resolution of as many high-dimensional linear systems as the number of incident fields, which represents a large amount of computations. Since all such systems involve the same matrix, we propose a block inversion strategy, based on the block-biconjugate gradient stabilized (BiCGStab) algorithm,doi:10.3390/s20216282 pmid:33158198 pmcid:PMC7663225 fatcat:xmqwyx6bqnfafhkw2wuszlhnfy