1. An image data compression apparatus, comprising: a compression circuit, for applying a plurality of compression approaches to a first block, and accordingly generating a plurality of first candidate compression results of the first block; a characteristic value extracting circuit, coupled to the compression circuit, for deriving a plurality of first characteristic values from the first candidate compression results, respectively; and a selecting circuit, coupled to the compression circuit and the characteristic value extracting circuit, for selecting a target compression result of the first block from the first candidate compression results according to the first characteristic values and at least one characteristic value threshold.