1. An ultrasonic diagnostic apparatus comprising: a probe that transmits ultrasonic waves to a heart and receives reflected waves from the heart; an image generating processor that generates an original Doppler image corresponding to a scan region including a blood flow region and a tissue region of the heart based on the reflected waves received by the probe, wherein the original Doppler image represents blood flow in the heart; a detection processor that detects a predetermined region by image processing for an ultrasonic image, wherein a position of the predetermined region depends on a position of a boundary between the blood flow region and the tissue region; and a correction processor that (a) generates a smoothed Doppler image by smoothing at least the predetermined region of the original Doppler image, (b) generates a first weighted image by weighting at least the predetermined region of the original Doppler image with a first weighting factor and generates a second weighted image by weighting at least the predetermined region of the smoothed Doppler image with a second weighting factor, and (c) generates a blended image by blending the first weighted image and the second weighted image.