The present invention provides a method and a system for producing an image using an imaging system by weighting: i) the signals transmitted from at least one element of a transducer array to form limited diffraction transmitted beams or the transmitted beams are steered with linear time delay over transducer aperture; and, ii) weighting the echo signals received at the separate elements to form limited diffraction receive beams or doing Fourier transformations of the echo signals over the transducer aperture. Fourier transformations of the weighted or Fourier transformed signals form multi-dimensional k-space data sets which are used to interpolate into a rectilinear k-space of the object to be imaged. Inverse Fourier transformation along each dimension of the rectilinear k-space to produce an image.