1. An apparatus for estimating a scale ratio and noise strength of an encoded image, the apparatus comprising: a data storage devise; an edge detection unit generating an edge map including edge pixels selected based on sizes and consistency of high frequency components extracted from an input image, from among pixels of the input image obtained by encoding and decoding an original image via a block-based image compression technique; a projection histogram calculation unit calculating a horizontal histogram that indicates the number of edge pixels included in each column of the edge map, and a vertical histogram that indicates the number of edge pixels included in each row of the edge map; a distance histogram calculation unit calculating a distance histogram that is represented as the number of frequencies with respect to each of the horizontal histogram and the vertical histogram according to a size of a column distance that is a distance between two adjacent columns in which the column values are not 0 on a horizontal axis; a scale ratio estimation unit estimating a horizontal scale ratio and a vertical scale ratio of the input image with respect to the original image from the distance histogram calculated from each of the horizontal histogram and the vertical histogram based on the value of the column distance corresponding to the maximum number of frequencies; a block boundary determination unit determining a group including the maximum number of edge pixels from among a plurality of groups obtained by classifying a plurality of columns that constitute the edge map based on the horizontal scale ratio, and a group including the maximum number of edge pixels from among a plurality of groups obtained by classifying a plurality of rows that constitute the edge map based on the vertical scale ratio as a block boundary of the input image; and a noise strength estimation unit estimating strength of noise included in the input image based on edge information calculated from the group determined as the block boundary.