Gonzalo R. Arce

A multiresolution watermark for digital images

We introduce a new multiresolution watermarking method for digital images. The method is based on the discrete wavelet transform (DWT). Pseudo-random codes are added to the large coefficients at the high and middle frequency bands of the DWT of an image. It is shown that this method is more robust to often proposed methods to some common image distortions, such as the wavelet transform based image compression, and image halftoning. Moreover, the method is hierarchical. The computation load needed to detect the watermark depends on the noise level in an image.

Ultra-Wideband Compressed Sensing: Channel Estimation

In this paper, ultra-wideband (UWB) channel estimation based on the theory of compressive sensing (CS) is developed. The proposed approach relies on the fact that transmitting an ultra-short pulse through a multipath UWB channel leads to a received UWB signal that can be approximated by a linear combination of a few atoms from a pre-defined dictionary, yielding thus a sparse representation of the received UWB signal. The key in the proposed approach is in the design of a dictionary of parameterized waveforms (atoms) that closely matches the information-carrying pulseshape leading thus to higher energy compaction and sparse representation, and, therefore higher probability for CS reconstruction. Two approaches for UWB channel estimation are developed under a data-aided framework. In the first approach, the CS reconstruction capabilities are exploited to recover the composite pulse-multipath channel from a reduced set of random projections. This reconstructed signal is subsequently used as a referent template in a correlator-based detector. In the second approach, from a set of random projections of the received pilot signal, the Matching Pursuit algorithm is used to identify the strongest atoms in the projected signal that, in turn, are related to the strongest propagation paths that composite the multipath UWB channel. A Rake like receiver uses those atoms as templates for the bank of correlators in the detection stage. The bit error rate performances of the proposed approaches are analyzed and compared to that of traditional correlator-based detector. Extensive simulations show that for different propagation scenarios and UWB communication channels, detectors based on CS channel estimation outperform traditional correlator using just 1/3 of the sampling rate leading thus to a reduced use of analog-to-digital resources in the channel estimation stage.

Detail-preserving ranked-order based filters for image processing

The theoretical analysis of multistage median filters is developed. It is shown that multistage median filters are a combination of max/median and min/median filters. Since multistage median filters belong to the class of two-dimensional stack filters, they have threshold decomposition attributes making their theoretical analysis simple. Statistical threshold decomposition is applied to derive the statistical characteristics of these filters, and the results are used to evaluate the performance of these two types of multistage filters. Finally, a quantitative and qualitative comparison of the multistage filters and of other efficient detail-preserving filters is presented. The comparisons are made using the mean-squared-error and the mean-absolute-error criteria. >

Halftone Visual Cryptography Via Error Diffusion

Halftone visual cryptography (HVC) enlarges the area of visual cryptography by the addition of digital halftoning techniques. In particular, in visual secret sharing schemes, a secret image can be encoded into halftone shares taking meaningful visual information. In this paper, HVC construction methods based on error diffusion are proposed. The secret image is concurrently embedded into binary valued shares while these shares are halftoned by error diffusion-the workhorse standard of halftoning algorithms. Error diffusion has low complexity and provides halftone shares with good image quality. A reconstructed secret image, obtained by stacking qualified shares together, does not suffer from cross interference of share images. Factors affecting the share image quality and the contrast of the reconstructed image are discussed. Simulation results show several illustrative examples.

Wavelet transform based watermark for digital images

In this paper, we introduce a new multiresolution watermarking method for digital images. The method is based on the discrete wavelet transform (DWT). Pseudo-random codes are added to the large coefficients at the high and middle frequency bands of the DWT of an image. It is shown that this method is more robust to proposed methods to some common image distortions, such as the wavelet transform based image compression, image rescaling/stretching and image halftoning. Moreover, the method is hierarchical.

A general weighted median filter structure admitting negative weights

Weighted median smoothers, which were introduced by Edgemore in the context of least absolute regression over 100 years ago, have received considerable attention in signal processing during the past two decades. Although weighted median smoothers offer advantages over traditional linear finite impulse response (FIR) filters, it is shown in this paper that they lack the flexibility to adequately address a number of signal processing problems. In fact, weighted median smoothers are analogous to normalized FIR linear filters constrained to have only positive weights. It is also shown that much like the mean is generalized to the rich class of linear FIR filters, the median can be generalized to a richer class of filters admitting positive and negative weights. The generalization follows naturally and is surprisingly simple. In order to analyze and design this class of filters, a new threshold decomposition theory admitting real-valued input signals is developed. The new threshold decomposition framework is then used to develop fast adaptive algorithms to optimally design the real-valued filter coefficients. The new weighted median filter formulation leads to significantly more powerful estimators capable of effectively addressing a number of fundamental problems in signal processing that could not adequately be addressed by prior weighted median smoother structures.

Theoretical analysis of the max/Median filter

Median filtering has been used successfully for extracting features from noisy one-dimensional signals; however, the extension of the one-dimensional case to higher dimensions has not always yielded satisfactory results. Although noise suppression is obtained, too much signal distortion is introduced and many features of interest are lost. In this paper, we introduce a multidimensional filter based on a combination of one-dimensional median estimates. It is shown that threshold decomposition holds for this class of filters, making the deterministic analysis simpler. Invariant signals to the filter, called root signals, consist of very low resolution features making this filter much more attractive than conventional median filters.

Joint wavelet compression and authentication watermarking

A blind watermarking technique embedding a digital image signature for authentication is developed. The signature algorithm is first implemented in the discrete wavelet transform (DWT) domain and is later coupled within the SPIHT compression algorithm. The capacity of the watermarking method is determined by the upper bound on the attainable information bit rate that can be hidden in the image using two methods: binary engraving and multi-bit engraving.

Morphological filters: Statistics and further syntactic properties

Mathematical morphology has recently been introduced as a powerful tool for studying the geometrical properties of signals and systems. These techniques have been applied very successfully to the smoothing of noisy data. In this paper, we first derive some new mathematical morphology results for function and set processing (FSP) systems. Using these results we derive several statistical results for the (FSP) morphological filtering of random signals, by deriving probabilistic mappings between input and output signals. Finally, we introduce a two-dimensional filter for image restoration which has desirable structure preserving properties.

Multistage order statistic filters for image sequence processing

The application of multistage order statistic filters (MOS) to the task of noise suppression in time-varying imagery is studied. It is shown that MOS filters efficiently preserve image structures under motion without motion compensation preprocessing. In particular, the families of multistage median and weighted median filters are considered. Motion preservation and statistical smoothing measures are derived. It is shown that spatiotemporal filtering allows for a significant improvement over both spatial and temporal filtering in terms of output image resolution and noise suppression. >