A highly constrained image processing method is used to improve the quality, including spatial resolution and signal-to-noise ratio (SNR), of ultrasound image frames. Ultrasound image frames are accumulated to form a composite image that contains a priori information about the subject being imaged. This composite image is used in a HYPR processing method to improve the quality of the ultrasound image frame. For example, the SNR of the composite image is increased as a function of the number of ultrasound image frames used to produce it, and this increased SNR is passed on to each highly constrained image frame. Additionally, high spatial resolution ultrasound images are produced using an undersampled sampling density, and the quality of these images is restored to substantially the same level as a fully sampled image.