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To effectively utilize the storage capacity, digital image compression has been applied to numerous science and engineering problems. There are two fundamental image compression techniques, either lossless or lossy. The former employs probabilistic models for lossless storage on a basis of statistical redundancy occurred in digital images. However, it has limitation in the compression ratio and bit per pixel ratio. Hence, the latter has also been widely implemented to further improve the storage capacities, covering various fundamental digital image processing approaches. It has been well documented that most lossy compression schemes will provide perfect visual perception under an exceptional compression ratio, among which discrete wavelet transform, discrete Fourier transform and some statistical optimization compression schemes (e.g., principal component analysis and independent component analysis) are the dominant approaches. It is necessary to evaluate these compression and reconstruction schemes objectively in addition to the visual appealing. Using a well defined set of the quantitative metrics from Information Theory, a comparative study on several typical digital image compression and reconstruction schemes will be conducted in this research.