We propose an algorithm that deals with broadband ultrasonic signals acquired in the near-field domain using probes close to the skin. This technique is designed for diffraction tomography of compact support objects interrogated by spherical waves (small transducers). It is an approximate inversion procedure in the Born approximation based on elliptical backprojection. Near-field imaging is enhanced by reducing the geometrical distortion observed on standard tomography. Numerical tests based on finite difference time domain (FDTD) simulations of data scattered by a tissue-like phantom are given.