1. An ultrasonic measurement apparatus comprising: an image processing unit that generates an image based on a reception signal obtained by an ultrasonic echo of an ultrasonic wave transmitted toward an object from an ultrasonic element array provided with a plurality of channels being received by the ultrasonic element array; and an area-of-interest setting unit that sets an area of interest within a display area in which the generated image is to be displayed, the area of interest being smaller than the display area, in response to setting of the area of interest, for reception signals of respective channels among the plurality of channels, the image processing unit performing a high resolution image generation with respect to first data forming a basis of an image to be displayed in the area of interest, and performing a non-high resolution image generation with respect to second data forming a basis of an image to be displayed in a different area other than the area of interest in the display area, the image processing unit, as the performing of the high resolution image generation, receiving reception signals for the area of interest, performing a weight calculation to calculate an adaptive weight according to the reception signals, adding by performing phasing output using the adaptive weight and the reception signals, and performing image generation based on the phasing output, the image processing unit, as the performing of the non-high resolution image generation, receiving reception signals for the different area, which have been added together with a predetermined weight that is computed in advance and does not vary based on the reception signals before the image processing unit receives the reception signals for the different area, and performing image generation based on the reception signals which have been added together with the predetermined weight, the image processing unit including an image combining unit that combines the image generated by the performing of the high resolution image generation and the image generated by the performing of the non-high image generation.