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Inversion of magnetic data has been an important tool for the interpretation of the data. The conventional inversion approaches cannot recover geologically acceptable models in the presence of remanence. Hence, some techniques have been developed for the inversion of magnetic amplitude data which is independent of magnetization direction. The conventional methods in the inversion of magnetic amplitude data give rise to blurred models with long tails. In this study, a new algorithm has been developed in favor of sparse inversion of the data that generates more focused models using the Cauchy norm. The algorithm applies a regularized conjugate gradient (RCG) method to acquire the inverse model. The new algorithm has been employed for the inversion of two data sets from synthetic examples and magnetic data sets over the Allahabad iron deposit in Iran and the Osborne copper–gold deposit in Australia. All data sets exhibit remanent magnetization. The results showed that the new algorithm generates robust solutions that are geologically acceptable. [ABSTRACT FROM AUTHOR]