Fast Thumbnail Extraction for H.264/AVC, HEVC and VP9

In this paper, we propose a partial decoding method with limited memory usage for high-speed thumbnail extraction. The proposed method performs a partial inverse transform and a partial intra prediction in order to reconstruct pixels for intra prediction and thumbnails. Thereafter, the reconstructed pixels at the bottom and right line of the block are stored in the line buffer and the thumbnail buffer without being stored in the decoded picture buffer with full resolution. H.264/AVC, HEVC and VP9 video codecs have different coding structures, prediction and transforms; however, the proposed algorithm can be applied to the corresponding codecs in the same manner. In order to evaluate the performance of the proposed method, we implemented the proposed algorithm for H.264/AVC, HEVC and VP9. We found that the thumbnail extraction time of the proposed method decreased by 66% in H.264/AVC, 52% in HEVC and 48% in VP9 as compared to the full decoding method.

MPI+OpenMP parallel implementation of conjugate gradient method with preconditioner of block partial inverse triangular decomposition of IC2S and IC1

The paper proposes a new preconditioner for solving systems of linear algebraic equations with a symmetric positively defined matrix by the method of conjugate gradients – Block Incomplete Inverse Cholesky BIIC preconditioner in combination with a triangular first-order decomposition "by value" - BIIC-IC1. The algorithm based on MPI+OpenMP techniques is proposed for the construction and application of the BIIC preconditioner combined with stabilized triangular decomposition of the second order "by value" (BIIC-IS2S). In this case, the BIIC-IC2S preconditioner uses the number of blocks multiple of the number of processors used and the number of threads used. Two algorithms based on MPI+OpenMP techniques are proposed for the construction and application of the BIIC-IC1 preconditioner. Comparative timing results for the MPI+OpenMP and MPI implementations of the proposed preconditioning used with the conjugate gradient method for a model problem and the sparse matrix collections SuiteSparse are presented.

A partial inverse problem for quantum graphs with a loop

We consider the Sturm–Liouville operator on quantum graphs with a loop with the standard matching conditions in the internal vertex and the jump conditions at the boundary vertex. Given the potential on the loop, we try to recover the potential on the boundary edge from the subspectrum. The uniqueness theorem and a constructive algorithm for the solution of this partial inverse problem are provided.