The primary goal of any image compression technique is to reduce the number of bits needed to represent the image with little perceptible distortion. Subband coding using wavelets is one of the best performing techniques among different transform based image compression techniques. Figure 2 shows the block diagram of a wavelet based image compression system. The first three blocks (DWT, quantizer and entropy coder) compress the image data whereas the last two blocks (entropy decoder, inverse discrete wavelet transform (IDWT))reconstruct the image from the compressed data.

The DWT performs an octave frequency subband decomposition of the image information. In its subband representation, an image is more compactly represented since most of its energy is concentrated in relatively few DWT coeficients.

The quantizer then performs quantization by representing the transform coeficients with a limited number of bits. Quantization represents lossy compression some image information is irretrievably lost. A quantizer in a DWT-based coder exploits the spatial correlation in a wavelet-based, hierarchical scale-space decomposition.

The entropy coder follows the quantization stage in a wavelet based image compression system. Entropy coding is lossless; it removes the redundancy from the compressed bit stream. However, the typical performance improvement of 0.4-0.6 dB achieved by entropy coding is accompanied by higher computational complexity. We concentrate on the DWT and quantizer blocks.

The channel is the stored or transmitted compressed bitstream. We consider the channel to be noiseless|the received DWT coeficients are free from errors. The synthesis stage reconstructs the image from the compressed data. The entropy decoder and IDWT invert the operations performed by the entropy encoder and DWT, respectively.

**Figure 2 :** *Block diagram of a wavelet based lossy compression system (a) Wavelet decomposition structure
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Figure 3 shows the structure of a 1-level 2-D wavelet decomposition of an image. For multiple levels of decomposition, the LL band is iteratively decomposed; This results in a pyramid structure for the subbands with the coarsest subband at the top and the finest subband at the bottom. Figure 4 illustrates the pyramid structure obtained after two-level

**Figure 3 :** *3-level 2-D decomposition
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**Figure 4**:

*2-level 2-D decomposition*

**Figure 5****:** 3-level 2-D decomposition of the image; It is noticed that the LL subband from the first stage has been transformed into 4 subbands- the three other subbands remain unchanged. Color gray in the figure corresponds to the value zero.

The multiresolution nature of the wavelet decomposition compacts the energy in the signal into a small number of wavelet coeficients. For natural images, much of the image energy is concentrated in the LL band that corresponds to the coarsest scale. This can be noticed in Figure 4. The LL band is not only a coarse approximation of the image but also contains most of the image’s energy. In addition to this, it is also statistically observed that the energy in the finer subbands is also concentrated into a relatively small number of wavelet coefficients. The significant coeficients in the finer subbands do not occur at random, but rather tend to occur in clusters in the same relative spatial location in each of the higher frequency subbands. This self-similar, hierarchical nature of the wavelet transform can be used to make interband predictions; the location of the significant coeficients in the coarser bands is used to predict the location and magnitude of significant coeficients in finer subbands.