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image compression is basically to make use of human perception model. (where higher frequencies r not noticed)
dct helps u to represent the spatial signal as sum of spatial frequencies. using which you could quantize each spatial frequency by different quant level.
one important property is its one to one mapping(i.e. mainly the idct(dct(spatial signal)) = spatial signal and dct and idct dontleed to any loss )
In general all the transforms are orthoganal transforms. After applying the transform (1-D or 2-D) the energy is compacted into few samples. The DCT is the most optimum compared to other transforms in the sense of energy compaction. Since the energy distribution in the high frequency coefficients are neglible and hence can be discarded without significant loss in the image quality (exploiting the human psychovisual redundancy). Only the selected low frequency coefficients having significant energy distribution may be quantised and coded to reduce the bit rate for transmission or the size of the coded image for storage requiring less space.
Since the DCT is the real-part of the FFT, the computionally effiicient algorithm can implemented to realise the hardware.
Theoretically the most optimum transform is the K-L transform.
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