Mohamed Ali Ben Ayed

A nonexistence result for Yamabe type problems on thin annuli

Abstract Given any constant C>0, we show that there exists e0>0 such that for any e P e : −Δu e =u e (n+2)/(n−2) , u e >0 in A e ;u e =0 on ∂A e , has no solution ue, whose energy, ∫Ae|∇ue|2, is less than C, where Ae is a ringshaped open set in R n and n⩾4.

TZSearch pattern search improvement for HEVC motion estimation modules

Motion estimation (ME) is a key operation for video compression. In fact, it contributes heavily to the compression efficiency by removing temporal redundancies. This process is the most critical part in a video encoder and can consume itself more than 50% of coding complexity or computational coding time. To reduce the computational time, many fast ME algorithms were proposed and implemented. The present paper proposes a fast ME algorithm that improves the basic Test Zone Search (TZS) ME algorithm which is considered to be one of the fastest ME algorithms and was implemented in HEVC reference software HM8.0. Experimental results show an improvement that can reach 8% up to 49% compared to the basic TZSearch.

A Morse lemma at infinity for Yamabe type problems on domains

Abstract In this paper we consider the following nonlinear elliptic problem (P): −Δu=up, u>0 in Ω , u=0 on ∂ Ω , where Ω is a bounded and smooth domain in R n , n⩾4, p+1=2n/(n−2) is the critical Sobolev exponent. We prove a version of Morse lemmas at infinity for this problem. As application of these lemmas we will give a characterization of the critical points at infinity of the functional corresponding to (P).

Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

Abstract.In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the n-sphere, with n ≥ 5. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given positive function under which we prove the existence of a metric, conformally equivalent to the standard metric, with prescribed Paneitz curvature.

Prescribing the Scalar Curvature under Minimal Boundary Conditions on the Half Sphere

Abstract This paper is devoted to the problem of prescribing the scalar curvature under zero boundary conditions. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results on the standard half sphere.

Fast Intra Mode Decision Algorithm for H264/AVC HD Baseline Profile Encoder

The high performance of H.264/AVC video encoder is accompanied with a wide computation complexity especially for high definition (HD) video sequences. One of the major H.264/AVC features to be optimized is the mode decision for both inter and intra prediction. Thus, based on high correlation observed between selected inter prediction mode and intra mode decision, a fast intra mode decision algorithm based on the best inter prediction mode for H264 high definition (HD) baseline profile encoder is proposed. The evaluation of the proposed approach was based on the rate distortion and PSNR variation, execution time and percentage of skipping intra4x4 and intra16x16. The proposed scheme is performed on 720p (1280x720) and 1080p (1920x1088) HD video sequences. Experimental results show that the proposed algorithm can save up to 60% of intra prediction computation time, 16% of skipping intra16x16 and up to 83% for intra4x4 without inducing PSNR degradation and bit-rate increase. General Terms Video compression techniques and signal processing

Topological Tools in Prescribing the Scalar Curvature on the Half Sphere

Abstract Using a topological invariant, due to Bahri [4], and dynamical methods, we prove some existence results for the problem prescribing the scalar curvature under zero boundary conditions on the standard half sphere.

TOWARD AN OPTIMAL BLOCK MOTION ESTIMATION ALGORITHM FOR H.264/AVC

A merging procedure joining search pattern and variable block size motion estimation for H.264/AVC is proposed in this paper. The principal purpose of the proposed methods is the reduction of the computational complexity for block matching module. In fact, there are numerous contributions in the literature aiming the reduction of the computational cost needed for motion estimation. The best solution from a qualitative point of view is the full search that considers every possible detail. The computational effort required is enormous and this makes motion estimation by far the most important computational bottleneck in video coding systems. Our approach invests and exploits the center-biased characteristics of the real world video sequences, aiming to achieve an acceptable image quality while independently targeting the reduction of the computational complexity. The simulations results demonstrated that the proposal performs well.

A fast coding algorithm based on fast mode decision for HEVC standard

As the new generation standard of video coding, the High Efficiency Video Coding (HEVC) is intended to provide significantly better coding efficiency than all existing video coding standards. One of his improvements is the encoding process of the structure block. It was established that this process requires high computing power because it is performed using all the possible depth levels and prediction modes to find the one with the least rate distortion (RD) cost using Lagrange multiplier. To reduce the computational complexity, fast coding unit size decision algorithms were proposed and implemented in HM. These algorithms can significantly reduce computational complexity while maintaining almost the same performance as the original HEVC encoder.

PROFILE AND EXISTENCE OF SIGN-CHANGING SOLUTIONS TO AN ELLIPTIC SUBCRITICAL EQUATION

In this paper, we study the nonlinear elliptic problem involving nearly critical exponent (Pe) : Δ2 u = |u|(8/(n-4))-eu, in Ω, Δu = u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝn, n ≥ 5. We characterize the low energy sign-changing solutions (ue) of (Pe). We prove that (ue) are close to two bubbles with different signs and they have to blow up either at two different points with the same speed or at a critical point of the Robin function. Furthermore, we construct families of each kind of these solutions and we prove that the bubble-tower solutions exist in our case.