Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Greedy sparse decompositions: a comparative study | Dymarski et al. EURASIP Journal on Advances in Signal Processing 2011 2011 34 http content 2011 1 34 o EURASIP Journal on Advances in Signal Processing a SpringerOpen Journal REVIEW Open Access Greedy sparse decompositions a comparative study Przemyslaw Dymarski1 Nicolas Moreau2 and Gael Richard2 Abstract The purpose of this article is to present a comparative study of sparse greedy algorithms that were separately introduced in speech and audio research communities. It is particularly shown that the Matching Pursuit MP family of algorithms MP OMP and OOMP are equivalent to multi-stage gain-shape vector quantization algorithms previously designed for speech signals coding. These algorithms are comparatively evaluated and their merits in terms of trade-off between complexity and performances are discussed. This article is completed by the introduction of the novel methods that take their inspiration from this unified view and recent study in audio sparse decomposition. Keywords greedy sparse decomposition matching pursuit orthogonal matching pursuit speech and audio coding 1 Introduction Sparse signal decomposition and models are used in a large number of signal processing applications such as speech and audio compression denoising source separation or automatic indexing. Many approaches aim at decomposing the signal on a set of constituent elements that are termed atoms basis or simply dictionary elements to obtain an exact representation of the signal or in most cases an approximative but parsimonious representation. For a given observation vector x of dimension N and a dictionary F of dimension N X L the objective of such decompositions is to find a vector g of dimension L which satisfies F g x. In most cases we have L N which a priori leads to an infinite number of solutions. In many applications we are however interested in finding an approximate solution which would lead to a vector g with the smallest number K of non-zero components. .
