1. An image processing device to convert a first image data into a second image data having a higher image quality, said image processing device comprising: predicted tap extracting means to extract from said first image data a plurality of pixels existing in the periphery of a corresponding pixel, including the corresponding pixel of said first image data that corresponds to a pixel of interest, as a predicted tap to be used for prediction computing to predict such pixel of interest which is a pixel of said second image data on which to focus interest; level limit class tap extracting means to extract from said first image data a plurality of pixels existing in the periphery of said corresponding pixel, including said corresponding pixel, as a level limit class tap to be used for level limit classifying processing that classifies said pixel of interest into one of a plurality of level limit classes; waveform class tap extracting means to extract from said first image data a plurality of pixels existing in the periphery of said corresponding pixel, including said corresponding pixel, as a waveform class tap to be used for waveform pattern classifying processing that classifies said pixel of interest into one of a plurality of waveform pattern classes; level limit classifying means to perform said level limit classifying processing to classify said pixel of interest into one of a plurality of level limit classes, based on a ratio between a level width which expresses the size of a range wherein said pixel of interest can be taken and a dynamic range of the plurality of pixels making up said level limit class tap, which is obtained according to a maximum value or minimum value of the pixel values of the plurality of pixels making up said level limit class tap; waveform pattern classifying means to perform said waveform pattern classifying processing to classify said pixel of interest into one of a plurality of waveform pattern classes, based on a waveform expressing change to the plurality of pixels making up said waveform class tap; prediction coefficient output means to output a prediction coefficient corresponding to a combination of a level limit class of said pixel of interest and a waveform pattern class of said pixel of interest, from among prediction coefficients corresponding respectively to a plurality of combinations of said level limit class and said waveform pattern class which are obtained and held beforehand by learning which minimizes the error difference between the result of said prediction computing using said first image data for learning and said second image data for learning which corresponds to said first image data for learning; and prediction computing means to predict said pixel of interest of said second image data by said prediction computing using said prediction coefficient output by said prediction coefficient output means and the plurality of pixels making up said prediction tap extracted by said prediction tap extracting means.