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In this paper, we present new adaptive and robust methods of reconstruction (ARMOR) for thermoacoustic tomography (TAT), and study their performances for breast cancer detection. TAT is an emerging medical imaging technique that combines the merits of high contrast due to electromagnetic or laser stimulation and high resolution offered by thermal acoustic imaging. The current image reconstruction methods used for TAT, such as the delay-and-sum (DAS) approach, are data-independent and suffer from low-resolution, high sidelobe levels, and poor interference rejection capabilities. The data-adaptive ARMOR can have much better resolution and much better interference rejection capabilities than their data-independent counterparts. By allowing certain uncertainties, ARMOR can be used to mitigate the amplitude and phase distortion problems encountered in TAT. The excellent performance of ARMOR is demonstrated using both simulated and experimentally measured data.