Subband decomposition and fractal image compression based steganography

This thesis proposes a novel steganographic algorithm for embedding secret image data into digital cover images. The proposed method consists of two stages. The first phase is the embedding. We start by calculating the entropy for cover image and secret image to assess the amount of information that is not compressible. We use discrete wavelet transform for cover image, and via a certain threshold value many coefficients are set to zero. We used the threshold in the wavelet domain to identify insignificant coefficients, so thresholding will be used as a method to determine the hiding map. We use Fractal Image Compression (FIC) for secret image which yields the outcome as a group of affine transformations, and then take Huffman code the result. After compressing the secret image information with Huffman code, it's necessary to store the data in a special way, because the output of the encoder is a stream of 1's and 0's, hence the stream must be converted into 8-bit-long chunks and stored. In addition, the code dictionary which is needed for the decoding process, must also be stored. Again, the dictionary is a group of 1's and 0's changing in length depending on the code generated, which, in turn, is a representation of the probability of the data symbols in the secret image as affine transformations. In the embedding stage, a secret vector is synthesized from the secret image. In other words, the group of information that is output from secret image makes up the so called "secret vector". A necessary piece of information is the length of the stream and whether it is divisible by 8. If so, another byte (8 bit) is added to the secret vector. The secret vector contains the binary stream which specifies the number of zero bits added to complete the stream to make the length of the code a multiple of 8. If there is no remainder, this byte contains the zero value. The byte is added after encoded data and the dictionary. Then secret vector is rescaled to get the highest PSNR for the cover image versus the stego image. The second phase is the extraction. The cover image is decomposed by using wavelet transform. Threshold value is calculated for the wavelet coefficients. Then a search for insignificant coefficients (less than threshold value) is initiated. The same threshold value should be guaranteed to find the same locations where we stored our secret vector. When the secret vector is found, it is rescaled back to its normal value by dividing it with the threshold value then multiply it with maximum value which is followed by Huffman decoding. Then just after this step, the fractal image iterations are carried out to rebuild the secret image as close as possible to the original image. The proposed algorithm of steganography to embedding secret image in cover image was tested over different cover images and secret images. The scheme performs well in terms of compression ratio, resolution and security. The threshold value was used as a method to determine the hiding map and to extraction. And by using the threshold value, the process becomes more secure. PSNR values for Cover image and Stego image for different secret images were ranging from 39 to 62, and the correlation was ranging from 0.995914 to 1.0000. The compression ratio was ranging between 29% to 35.6%. Results of extracted images were of high quality. Disadvantages associated with this method is that the time, due to a lot of from processing be made to obtain high quality. Results demonstrate its effectiveness, robustness and security.