1,514 research outputs found
A two-stage video coding framework with both self-adaptive redundant dictionary and adaptively orthonormalized DCT basis
In this work, we propose a two-stage video coding framework, as an extension
of our previous one-stage framework in [1]. The two-stage frameworks consists
two different dictionaries. Specifically, the first stage directly finds the
sparse representation of a block with a self-adaptive dictionary consisting of
all possible inter-prediction candidates by solving an L0-norm minimization
problem using an improved orthogonal matching pursuit with embedded
orthonormalization (eOMP) algorithm, and the second stage codes the residual
using DCT dictionary adaptively orthonormalized to the subspace spanned by the
first stage atoms. The transition of the first stage and the second stage is
determined based on both stages' quantization stepsizes and a threshold. We
further propose a complete context adaptive entropy coder to efficiently code
the locations and the coefficients of chosen first stage atoms. Simulation
results show that the proposed coder significantly improves the RD performance
over our previous one-stage coder. More importantly, the two-stage coder, using
a fixed block size and inter-prediction only, outperforms the H.264 coder
(x264) and is competitive with the HEVC reference coder (HM) over a large rate
range
Greed is good: algorithmic results for sparse approximation
This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho's basis pursuit (BP) paradigm can recover the optimal representation of an exactly sparse signal. It leverages this theory to show that both OMP and BP succeed for every sparse input signal from a wide class of dictionaries. These quasi-incoherent dictionaries offer a natural generalization of incoherent dictionaries, and the cumulative coherence function is introduced to quantify the level of incoherence. This analysis unifies all the recent results on BP and extends them to OMP. Furthermore, the paper develops a sufficient condition under which OMP can identify atoms from an optimal approximation of a nonsparse signal. From there, it argues that OMP is an approximation algorithm for the sparse problem over a quasi-incoherent dictionary. That is, for every input signal, OMP calculates a sparse approximant whose error is only a small factor worse than the minimal error that can be attained with the same number of terms
Computational Methods for Sparse Solution of Linear Inverse Problems
The goal of the sparse approximation problem is to approximate a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical engineering, statistics, and applied mathematics can be posed as sparse approximation problems, making these algorithms versatile and relevant to a plethora of applications
Analysis, Visualization, and Transformation of Audio Signals Using Dictionary-based Methods
date-added: 2014-01-07 09:15:58 +0000 date-modified: 2014-01-07 09:15:58 +0000date-added: 2014-01-07 09:15:58 +0000 date-modified: 2014-01-07 09:15:58 +000
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