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Microwave imaging has been proposed as an alternative to X-ray mammography for early-stage breast cancer detection. We investigate a method of microwave imaging via space-time (MIST) beamforming for detecting backscattered energy from small malignant breast tumors. The beamformer weights are designed to optimally compensate for frequency-dependent propagation effects and minimize clutter by solving a set of penalized least-squares problems that are formulated in the frequency domain. We demonstrate the efficacy of our space-time beamforming approach using backscatter data acquired from two types of breast phantoms: a realistic numerical breast model and a simple experimental breast phantom. The numerical model is derived from a magnetic resonance image of the breast and the backscatter waveforms are computed using the finite-difference time-domain method for solving Maxwell's equations. The experimental phantom consists of a synthetic tumor suspended in a homogeneous liquid. The dielectric-properties contrast between the liquid and synthetic tumor is similar to the contrast between normal and malignant breast tissue. Our images exhibit high signal-to-clutter ratios and good tumor localization even under various challenging conditions.