Quansheng Liu

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This paper models the messages embedded by spatial least significant bit (LSB) matching as independent noises to the cover image, and reveals that the histogram of the differences between pixel gray values is smoothed by the stego bits despite a large distance between the pixels. Using the characteristic function of difference histogram (DHCF), we prove(More)
We first obtain exponential inequalities for martingales. Let (Xk)(1 ≤ k ≤ n) be a sequence of martingale differences relative to a filtration (Fk), and set Sn = X1 + ... + Xn. We prove that if for some δ > 0, Q ≥ 1, K > 0 and all k, a.s. E[ek Q |Fk−1] ≤ K, then for some constant c > 0 (depending only on δ,Q and K) and all x > 0, P [|Sn| > nx] ≤ 2e , where(More)
Patch-based sparse representation and low-rank approximation for image processing attract much attention in recent years. The minimization of the matrix rank coupled with the Frobenius norm data fidelity can be solved by the hard thresholding filter with principle component analysis (PCA) or singular value decomposition (SVD). Based on this idea, we propose(More)
We first introduce a similarity assumption to describe the similarity phenomenon in natural images, and establish a similarity principle which supplies a simple mathematical justification for the non-local means filter in removing Gaussian noises. Using the similarity principe in an adapted way, we then propose a new algorithm, called mixed noise filter(More)
We propose a new image denoising algorithm when the data is contaminated by a Poisson noise. As in the Non-Local Means filter, the proposed algorithm is based on a weighted linear combination of the observed image. But in contract to the latter where the weights are defined by a Gaussian kernel, we propose to choose them in an optimal way. First some(More)
We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The environment is supposed to be stationary and ergodic. For A ⊂ R , let Zn(A) be the number of particles of(More)
Traditional methods for sex identification are not applicable to sexually monomorphic species, leading to difficulties in the management of their breeding programs. To identify sex in sexually monomorphic birds, molecular methods have been established. Two established primer pairs (2550F/2718R and p8/p2) amplify the CHD1 gene region from both the Z and W(More)