1. An ultrasonic image processing apparatus comprising: an inter-frame processor which applies a plurality of pattern matching processes separately per pixel between a first frame and a second frame acquired by transmitting and receiving ultrasound, and which calculates movement destinations on the second frame separately per pixel for pixels of interest in the first frame; and a re-constructing unit which re-constructs the second frame into a high-density frame using the movement destinations calculated for the pixels of interest, wherein the inter-frame processor comprises: a correlation value profile generating unit which generates a correlation value profile as a result of the pattern matching process separately per pixel for each of the pixels of interest in the first frame; and a correspondent address calculating unit which calculates a correspondent address on the second frame as the movement destination based on the correlation value profile separately per pixel for each of the pixels of interest in the first frame, wherein the correspondent address on the second frame for each of the pixels of interest in the first frame includes an integer part corresponding to an integer multiple of an original pixel spacing in the second frame and a fractional value smaller than the original pixel spacing, the correspondent address with the fractional value being identified by a sub-pixel estimation using a plurality of correlation values in the correlation value profile that correlate closest to the pixel of interest.