## Fractal image compression thesis

The most efficient algorithm in the area of image compression is the Set Partitioning in Hierarchical Trees (SPIHT) [20]. It uses a sub-band coder which produces a pyramid structure where an image is decomposed sequentially by applying power complementary low pass and high pass filters and then decimating the resulting images. These filters are one- dimensional filters that are applied in cascade (row then col- umn) to an image whereby creating the four-way decomposi- tion such as LL (low-pass then another low pass), LH (low pass then high pass), HL (high and low pass) and finally HH (high pass then another high pass). Such resulting LL version is again four-way decomposed. This procedure is repeated until the top of the pyramid is reached.

And each of them recursively maintains a spatial similarity to its corresponding four off-spring. The structure of pyramid is commonly known as spatial orientation tree. The Figure shows the similarity among sub-bands within levels in the

wavelet space If a given coefficient at location (i,j) is signifi-

cant in magnitude then some of its descendants will also

probably be significant in magnitude. It takes advantage of the

spatial similarity present in the wavelet space to optimally

find the location of the wavelet coefficient that is significant by

means of a binary search algorithm.

The SPIHT algorithm sends the top coefficients in the pyr- amid structure using a progressive transmission method. This method allows obtaining a high quality version of the original image from the minimal amount of transmitted data. The pyr- amid wavelet coefficients are ordered by magnitude and then the most significant bits are transmitted first and then are fol- lowed by the next bit plane and so on until the lowest bit plane is reached. This progressive transmission can signifi- cantly reduce the Mean Square Error (MSE) distortion for eve- ry bit-plane sent.

To take advantage of the spatial relationship among the coefficients at different levels and frequency bands. This algo- rithm orders the wavelets coefficient according to the signifi- cance test defined as:

The Adaptive SPIHT compression scheme provides selective compression on medical images by compressing the ROI using JPEG2000 and the rest of the image by standard SPIHT, making it energy efficient. SPIHT displays exceptional characteristics over several properties all at once including [15]:

has to be transmitted to the decoder as shown in fig. unlike the max -shift ROI coding. Therefore, in this case, by discarding all of the background, object can be exactly decoded .But unfortunately, near the object there is some unwanted effect looking at the background. This is because of additional coefficients at an early stage of progressive coding.

## IMAGE COMPRESSION THESIS - OchDownloader

[3] A. S. Lewis and G. Knowles, "Image Compression Using the 2-D Wavelet Transform" IEEE Trans. on Image Processing, Vol. I . NO. 2, PP. 244 - 250, APRIL 1992.