Ioana Firoiu

Image Denoising Using a New Implementation of the Hyperanalytic Wavelet Transform

Shift invariance associated with good directional selectivity is important for the use of a wavelet transform (WT) in many fields of image processing. Generally, complex wavelet transforms, e.g., the double-tree complex WT (DTCWT), have these useful properties. In this paper, we propose the use of a recently introduced implementation of such a WT, namely, the hyperanalytic WT (HWT), in association with filtering techniques already used with the discrete WT (DWT). The result is a very simple and fast image denoising algorithm. Some simulation results and comparisons prove the performance obtained using the new method.

Bayesian Hyperanalytic Denoising of SONAR Images

The SOund Navigation And Ranging (SONAR) images are perturbed by speckle noise. This paper presents a new denoising method in the wavelet domain, which tends to reduce the speckle, preserving the structural features and the textural information of the scene. Shift invariance associated with good directional selectivity is important for the use of a wavelet transform (WT) in denoising of SONAR images. In this paper, we propose the use of a variant of hyperanalytic WT, which is quasi-shift invariant and has good directional selectivity in association with a maximum a posteriori filter named bishrink. This filter makes a very good treatment of the contours. The corresponding denoising algorithm is simple and fast. Its performance was proved on images perturbed by synthesized speckle noise and on real SONAR images.

Anomaly detection of network traffic based on Analytical Discrete Wavelet Transform

Signal processing techniques have attracted a lot of attention recently in the networking security technology, because of their capability of detecting novel intrusions or attacks. In this paper, we propose a new detection mechanism of network traffic anomaly based on Analytical Discrete Wavelet Transform (ADWT) and high-order statistical analysis. In order to describe the network traffic information, we use a set of features based on different metrics. We evaluate our technique with the 1999 DARPA intrusion detection dataset. The test results show that the proposed approach accurately detects a wide range of anomalies.

An improved version of the inverse Hyperanalytic Wavelet Transform

The success of wavelet techniques in many fields of signal and image processing was proved to be highly influenced by the properties of the wavelet transform used, mainly the shift-invariance and the directional selectivity. In the present paper we propose an improved version of the inverse Hyperanalytic Wavelet Transform (HWT), which uses hyperanalytic mother wavelets. We have already proposed implementations of the HWT and of its inverse (IHWT). The implementation supposes the computation of the discrete wavelet transform (DWT) of the hyperanalytic signal associated to the input signal. Our old computation method of the IHWT extracts the real part of the signal at the output of the inverse discrete wavelet transform (IDWT). The aim of this paper is a new implementation of the IHWT, which permits a better shift invariance. We will compare this implementation with our previous one, with the DWT and with Kingsburys Double-Tree Complex Wavelet Transform (DT CWT).

A second order statistical analysis of the Hyperanalytic Wavelet Transform

We present a second order statistical analysis of the Hyperanalytic Wavelet Transform (HWT). The results are useful to design signal processing systems based on the wavelet theory.

Hyperanalytic wavelet packets

We introduce the hyperanalytic wavelet packets concept and we prove some of their properties: good frequency localization, quasi shift-invariance, quasi analyticity and quasi rotational invariance.

A second order statistical analysis of the 2D Discrete Wavelet Transform

We present a general second order statistical analysis of the 2D Discrete Wavelet Transform (DWT) resulted after the computation of the correlation functions in all possible cases: inter-scale and inter-band dependency, inter-scale and intra-band dependency and intra-scale and intra-band dependency. The expected value and the variance of the wavelet coefficients are also computed. The resulting equations are useful for the design of different signal processing systems based on the wavelet theory.

A new watermarking method based on the use of the hyperanalytic wavelet transform

Watermarking using pixel-wise masking in the wavelet domain proves to be quite robust against common signal processing attacks. Initially, in a system proposed by Barni et al., embedding is made only in the highest resolution level; there are two disadvantages to this technique: the watermark information can be easily erased by a potential attacker and embedding in the DWT is susceptible to geometric attacks, such as shifting. To enhance this watermarking method, we use a modified perceptual mask that models the human visual system behavior in a better way, previously proposed by the authors. The texture content is appreciated with the local standard deviation of the original image, which is further compressed in the wavelet domain. Since the approximation image of the coarsest level contains too little information, we appreciate the luminance content using a higher resolution level approximation sub-image. To increase the capacity of the watermarking scheme the embedding is made in the HWT domain, using two strategies: in the real parts of the HWT coefficients and in the absolute value of the HWT coefficients of the original image. The implementation of the HWT is made using a new technique, recently proposed by the authors. Moreover, we make use of all the levels except the coarsest one, for attack resilience. We use three types of detectors that take advantage of the hierarchical decomposition. Tests were made for different attacks (JPEG compression, median filtering, resizing, cropping, gamma correction, blurring, shifting and addition of white Gaussian noise), that prove the effectiveness of perceptual watermarking in the HWT domain.