Sorina Dumitrescu

Detection of LSB Steganography via Sample Pair Analysis

This paper introduces a new, principled approach to detecting LSB steganography in digital signals such as images and audio. It is shown that the length of hidden message embedded in the least significant bits of signal samples can be estimated with relatively high precision. The new steganalytic approach is based on some statistical measures of sample pairs that are highly sensitive to LSB embedding operations. The resulting detection algorithm is simple and fast. To evaluate the robustness of the proposed steganalytic approach, bounds on estimation errors are developed. Furthermore, the vulnerability of the new approach to possible attacks is also assessed, and counter measures are suggested.

On steganalysis of random LSB embedding in continuous-tone images

We present an LSB steganalysis technique that can detect the existence of hidden messages that are randomly embedded in the least significant bits of natural continuous-tone images. The technique is inspired by the recent work of J. Fridrich et al. (see Proc. ACM Workshop on Multimedia and Security, p.27-30, 2001) and just like their work, it can also precisely measure the length of the embedded message, even when the hidden message is very short relative to the image size. The key to our success is the formation of some subsets of pixels whose cardinalities change with LSB embedding, and such changes can be precisely quantified under the assumption that the embedded bits are randomly scattered. Interestingly, our study on steganalysis of LSB embedding sheds light on the work of Fridrich et al. on the detection of LSB embedding, and offers an analytical proof of an observation made by them.

A new framework of LSB steganalysis of digital media

We propose a general framework for the detection of the least significant bit (LSB) steganography using digital media files as cover objects. The new framework exploits high-order statistics of the samples. It can compute a robust estimate of the length of a secret message hidden in the LSBs of samples for a large class of digital media contents such as image, video, and audio, in which the underlying signals consist of correlated samples. A case study on the LSB steganalysis of natural grey-scale and color images and experimental results are reported.

On optimal multi-resolution scalar quantization

Any scalar quantizer of 2/sup h/ bins, where h is a positive integer, can be structured by a balanced binary quantizer tree T of h levels. Any pruned subtree /spl tau/ of T corresponds to an operational rate R(/spl tau/) and distortion D(/spl tau/) pair. Denote by S/sub n/ the set of all pruned subtrees of n leaf nodes, 1/spl les/n/spl les/2/sup h/. We consider the problem of designing a 2/sup h/-bin scalar quantizer that minimizes the weighted average distortion D~=/spl Sigma//sub n=1//sup 2(h)/ D(/spl tau/)W(n), where W(n) is a weighting function in the size of pruned subtrees (or the resolution of the underlying quantizer). We present an O(hN/sup 3/) algorithm to solve the underlying optimization problem (N is the number of points of the histogram that represents the source probability mass function), and call the resulting quantizer optimal multi-resolution scalar quantizer in the sense that it minimizes a global distortion measure averaged over all quantization resolutions of T. Interestingly, a similar quantizer design problem studied by Brunk et al. (1996) is a special case of our formulation, and can thus be solved exactly and efficiently using our algorithm. Furthermore, we present an algorithm to generate a sequence of 2/sup h/ nested pruned subtrees of T, from the root of T to the entire tree T itself, which minimizes an expected distortion over a range of operational rates. The resulting nested pruned subtree sequence generates an optimized embedded (rate-distortion scalable) code stream with maximum granularity of 2/sup h/ quantization stages, as opposed to existing successively refinable quantizers, such as the popular bit-plane coding scheme, which offer only h stages.

Monotonicity-based fast algorithms for MAP estimation of Markov sequences over noisy channels

In this correspondence, we study algorithmic approach to solving the problem of maximum a posteriori (MAP) estimation of Markov sequences transmitted over noisy channels, which is also known as the MAP decoding problem. For the class of memoryless binary channels that produce independent substitution and erasure errors, the MAP sequence estimation problem can be formulated and solved as one of the longest path in a weighted directed acyclic graph. But for algorithm efficiency, we transform the graph problem to one of matrix search. If the underlying matrix is totally monotone, then the complexity of MAP sequence estimation can be greatly reduced. We give a sufficient condition for the matrix induced by MAP sequence estimation to be totally monotone, which is indeed the case if the input sequence is Gaussian Markov. Under this condition, the complexity of MAP decoding can be reduced from O(N/sup 2/M) to O(NM), where N is the size of source alphabet and M is the length of input sequence. Furthermore, for Markov sequences of fixed-length code we propose a block parsing strategy to reduce the complexity of MAP sequence estimation to O(M+N/sup 2/M/logM) or to O(M+NM/logM), depending on if the total monotonicity holds. Another significance of this correspondence lies in the applicability of the presented algorithmic approach, which has been thoroughly studied in computer science literature, to many other discrete optimization problems encountered in both source and channel coding, ranging from optimal multiresolution and multiple-description quantizer design, to context quantization for minimum conditional entropy, and to optimal packetization with uneven error protection.

Algorithms for optimal multi-resolution quantization

Multi-resolution quantization is a way of constructing a progressively refinable description of a discrete random variable. The underlying discrete optimization problem is to minimize an expected distortion over all refinement levels weighted by the probability or importance of the descriptions of different resolutions. This research is motivated by the application of multimedia communications via variable-rate channels. We propose an O(rN2) time and O(N2 log N) space algorithm to design a minimum-distortion quantizer of r levels for a random variable drawn from an alphabet of size N. It is shown that for a very large class of distortion measures the objective function of optimal multi-resolution quantization satisfies the convex Monge property. The efficiency of the proposed algorithm hinges on the convex Monge property. But our algorithm is simpler (even though of the same asymptotic complexity) than the well-known SMAWK fast matrix search technique, which is the best existing solution to the quantization problem. For exponential random variables our approach leads to a solution of even lower complexity: O(rN) time and O(N log N) space, which outperforms all the known algorithms for optimal quantization in both multi- and single-resolution cases. We also generalize the multi-resolution quantization problem to a graph problem, for which our algorithm offers an efficient solution.

Globally optimal uneven error-protected packetization of scalable code streams

In this extended abstract we present a family of new algorithms for rate-fidelity optimal packetization of scalable source bit stream with uneven error protection. In the most general setting where no assumption is made on the probability function of packet loss or on the rate-fidelity function of the scalable code stream, one of our algorithms can find the globally optimal solution to the problem in O(N/sup 2/L/sup 2/) time, compared to a previously claimed O(N/sup 3/L/sup 2/) complexity, where N is the number of packets and L is the packet payload size. The time complexity can be reduced to O(NL/sup 2/) if the rate-fidelity function of the input is convex and under the reasonable assumption that the probability function of packet loss is monotonically decreasing. In the convex case the algorithm of Mohr et al. (2000) has complexity O(N/sup 2/L log N). Furthermore, our O(NL/sup 2/) algorithm for the convex case can be modified to find an approximation solution for the general case that is better than the results of other algorithms in the prior literature. All of our algorithms do away with the expediency of fractional redundancy allocation, a limitation of some existing algorithms. To our best knowledge this work offers for the first time globally optimal solutions to the important problem of optimal UEP packetization.In this paper, we present a family of new algorithms for rate-fidelity optimal packetization of scalable source bit streams with uneven error protection. In the most general setting where no assumption is made on the probability function of packet loss or on the rate-fidelity function of the scalable code stream, one of our algorithms can find the globally optimal solution to the problem in O(N/sup 2/L/sup 2/) time, compared to a previously obtained O(N/sup 3/L/sup 2/) complexity, where N is the number of packets and L is the packet payload size. If the rate-fidelity function of the input is convex, the time complexity can be reduced to O(NL/sup 2/) for a class of erasure channels, including channels for which the probability function of losing n packets is monotonically decreasing in n and independent erasure channels with packet erasure rate no larger than N/2(N + 1). Furthermore, our O(NL/sup 2/) algorithm for the convex case can be modified to rind an approximation solution for the general case. All of our algorithms do away with the expediency of fractional bit allocation, a limitation of some existing algorithms.

Layered Multicast With Inter-Layer Network Coding for Multimedia Streaming

Multirate multicast is a powerful methodology of multimedia communication in heterogenous networks. A variant of multirate multicast motivated by scalable multimedia streaming is layered multicast, where the transmitted signal is presented in successive data layers. With recent advances of network coding theory, many layered multicast schemes using network coding have been proposed to improve the performance of traditional routing-based layered multicast. They divide the network into different layers and construct a unirate multicast network code for each layer. However, these schemes do not perform network coding between data layers, and consequently cannot realize the full potential of network coding. In this paper, we propose a novel approach to layered multicast that allows network coding of data in different layers. This relaxation lends the proposed scheme greater flexibility in optimizing the data flow than previous layered solutions, and thus achieves higher throughput.

Layered Multicast with Inter-Layer Network Coding

Multirate multicast is a powerful methodology of multimedia communication in heterogenous networks. A vari- ant of multirate multicast motivated by scalable multimedia streaming is layered multicast, where the transmitted signal is presented in successive data layers. With recent advances of network coding theory, many layered multicast schemes using network coding have been proposed to improve the performance of traditional routing based layered multicast. They divide the network into different layers and construct a unirate multicast network code for each layer. However, these schemes do not perform network coding between data layers, and consequently cannot realize the full potential of network coding. In this paper, we propose a novel approach to layered multicast that allows network coding of data in different layers. This relaxation lends the proposed scheme greater flexibility in optimizing the data flow than previous layered solutions, and thus achieves higher throughput.

Energy-Efficient Full Diversity Collaborative Unitary Space-Time Block Code Designs via Unique Factorization of Signals

In this paper, a novel concept called a uniquely factorable constellation pair (UFCP) is proposed for the systematic design of a noncoherent full diversity collaborative unitary space-time block code by normalizing two Alamouti codes for a wireless communication system having two transmitter antennas and a single receiver antenna. It is proved that such a unitary UFCP code assures the unique identification of both channel coefficients and transmitted signals in a noise-free case as well as full diversity for the noncoherent maximum likelihood receiver in a noise case. To further improve error performance, an optimal unitary UFCP code is designed by appropriately and uniquely factorizing a pair of energy-efficient cross quadrature amplitude modulation (QAM) constellations to maximize the coding gain subject to a transmission bit rate constraint. After a deep investigation of the fractional coding gain function, a technical approach developed in this paper to maximizing the coding gain is to carefully design an energy scale to compress the first three largest energy points in the corner of the QAM constellations in the denominator of the objective as well as carefully design a constellation triple forming two UFCPs, with one collaborating with the other two so as to make the accumulated minimum Euclidean distance along the two transmitter antennas in the numerator of the objective as large as possible, and at the same time, to avoid as many corner points of the QAM constellations with the largest energy as possible to achieve the minimum of the numerator. In other words, the optimal coding gain is attained by intelligent constellations collaboration and efficient energy compression. Computer simulations demonstrate that error performance of the optimal unitary UFCP code presented in this paper outperforms those of the differential code and the signal-to-noise-ratio-efficient training code.