1. A noise reducer for reducing noise in a video signal, comprising: a sum of absolute differences calculation circuit that sequentially selects each pixel in an input video signal as a pixel of interest and calculates sums of absolute differences between a central block of a predetermined size centered on the pixel of interest and neighboring blocks of the predetermined size centered on pixels adjacent the pixel of interest above, below, and to the left, right, upper right, lower right, upper left, and lower left, each sum of absolute differences being calculated as a sum of absolute differences between values of pixels in corresponding positions in the central block and in one of the neighboring blocks; a correlation direction decision circuit that selects a correlation direction indicated by a line extending from the pixel of interest through a center of one of the neighboring blocks having a minimum sum of absolute differences; and a variable-direction one-dimensional filter circuit that calculates a first weighted average of the pixel of interest and at least one pixel located in the correlation direction from the pixel of interest, and generates a first output signal having the first weighted average as a value for the pixel of interest.