Information Hiding
and its Applications
Steganography and Watermarking
A detailed look at Steganography
   ◦ Text Steganography
   ◦ Hypertext Steganography
   ◦ Audio Steganography
   ◦ Image Steganography
   ◦ Steganography in Open System
Image Steganography Techniques
   ◦ Spatial Domain LSB Insertion
   ◦ Masking and Filtering
   ◦ DCT-based Steganography
   ◦ Wavelet-based Steganography
How to Detect Steganography
   ◦ Blind Detection
   ◦ Analytical Detection

Wavelet-based Steganography (JPEG2000)

In addition to DCT, images can be processed with discrete wavelet transformation DWT. Wavelet is used in JPEG2000 compression to perform the transformation. The wavelet transformation is followed by quantization and encoding stages. Various algorithms and approaches are used in embedding process which takes place after the wavelet transformation of the image in order to hide the secret message in it. After applying the discrete wavelet transform (DWT) on the original image and getting  the wavelet coefficients, the wavelet coefficients are changed according to the embedded data. Finally, inverse wavelet transform (IDWT) is applied to get the steganographed image.

we will discuss a method of steganography technique based on DWT transform whish was proposed in the reference shown below. The method has ability to hide secret message in a digital image. The secret message is embedded into the image by changing wavelet coefficients. The quality of the stego image of this method is very close to that of the original one. Embedding process contains two-dimensional discrete wavelet transformation of cover image, permutation of secret message, modification of transformation coefficients and finally inverse 2D-DWT of modified coefficients. Inputs of embedding process are cover image and secret message. Output of this process is stego image. Secret key contains information about choice of DWT transformation coefficients and permutation random vector. Before modification of coefficients, pseudorandom permutation of the secret message is used for increasing security of embedded message, see the figure shown below.

The following form expresses the embedding process, where m (x) represents the secret message’s bit and i (x) represents the DWT coefficient. Modified DWT coefficient can be expressed in the following form:

Where a is a real number.

The extraction of secret message from the steganographed image will be done by comparing the selected DWT coefficients of the steganographed and original image. The comparison operation can be expressed in the following form:

Reference:
• STEGANOGRAPHY BASED ON DWT TRANSFORM, by Rastislav Hovančák, Peter Foriš, Dušan Levický.