1. A liquid crystal display, comprising: an RGBW panel having a plurality of data lines, a plurality of gate lines crossing the data lines, a plurality of TFTs connected to crossings between the data lines and the gate lines, and an RGBW pixel structure; an image conversion unit for converting white luminance Y of data displaying a white background into a value satisfying any one of the following equations upon detecting a brightness contrast image including a pure color image corresponding to any one of a yellow, a cyan, and a magenta image with the white background; a data driving circuit for converting digital data converted by the image conversion unit into positive/negative analog data voltages; and a gate driving circuit for supplying gate pulses to the gate lines, wherein the image conversion unit includes a chromatic analysis part for calculating the luminance of yellow data, cyan data, or magenta data after analyzing pixel data of input RGB digital video data, and determining the pixel data as the yellow data, the cyan data, or the magenta data, the equations including: Y ⁡ ( white ) = Yref ⁡ ( white ) × MIN ⁢ { Y ⁡ ( yellow ) Yref ⁡ ( yellow ) , Y ⁡ ( cyan ) Yref ⁡ ( cyan ) , Y ⁡ ( magenta ) Yref ⁡ ( magenta ) } , ⁢ Y ⁡ ( white ) = Yref ⁡ ( white ) × Y ⁡ ( yellow ) Yref ⁡ ( yellow ) , and Y ⁡ ( white ) = Y ⁡ ( yellow ) wherein Y(X) is a luminance value of color X, Yref(X) is a luminance value of color X of a reference display device having an RGB pixel structure, and MIN Y(X, Y, Z) is the minimum luminance value among X, Y, and Z.