FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W236467976> ?p ?o ?g. }

• W236467976 abstract "The problem of selecting a basis within a redundant tree structure naturally arises in the frameworks of wavelet packet transform (WPT) and cosine packet transform (CPT) for signal representation. The tree has to be consider before performing that selection using suitable information cost functions for the branches. The redundant tree has many constraints. Among them is the bit overhead for coding explicitly the name of the resulting non redundant (prune) tree. Besides, from computational or real time constraints it is convenient to perform suboptimal top-down tree computation/search instead of the optimal bottom-up tree search after computing the complete tree. Even when a optimal coding of the tree remains an open join coding problem, a practical selection algorithm is reported here that takes the above and others considerations into account. The algorithm has been implemented an tested in the framework of a wavelet based audio coding system. Variations of the algorithm can be used in many practical situations where a subset from an redundant structure has to be chosen with the constraint of minimal bit cost. Proceedings CACIC ‘97 Procesamiento Distribuido y Paralelo. Tratamiento de Senales UNLP Departamento de Informatica Facultad de Ciencias Exactas 2 The Problem When there is a choice of bases for the representation of a signal, then it is possible to seek the best one by some criterion. If the choice algorithm is sufficiently cheap, then it is possible to assign each signal its very own adapted basis of waveforms. If this basis description is efficient, then that signal has been compressed. The problem of selecting a basis within a redundant tree structure naturally arises in the frameworks of wavelet packet transform (WPT) and cosine packet transform (CPT) or Malvaar adapted transform, for signal representation. The so called actual tree has to be consider before performing that selection using suitable information cost functions instead of the classical entropy for selecting branches or subbands. Besides, from computational or real time constraints it is convenient to perform sub-optimal topdown tree computation/search instead of the optimal bottom-up tree search after computing the complete tree. Admissible Bases The next figure is a schematic representation of the library of wavelet coefficients presenting a tree arrangement.: • The levels of the tree are u . • The branches v correspond to blocks of coefficients of dyadic sizes. • The refinement progress from top to down. • The block on top is the N -size frame of the signal itself. | | | | | u | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ||||||||||||||||||||||||||||||||| v Fig, 1 The complete tree, with all its branches, is a redundant representation of the frame. The conditions to choose a complete orthonormal basis representation are the following: 1. Every column contains exactly one element. 2. Elements in a single row appear in contiguous blocks of 2 k elements, where 0 < < k n is an integer. 3. Row blocks begin an integer multiple of their length from left edge of the array. Searching the Tree Given and additive information cost function associated to the library of bases (see [Wic1]). If that library is a tree with finite depth, then we can find the best basis by computing the information cost of a vector in each node of the tree and comparing children to parent starting from the bottom (bottom-up search). This is actually a low complexity search since the additive property of additive information cost functions Proceedings CACIC ‘97 Procesamiento Distribuido y Paralelo. Tratamiento de Senales UNLP Departamento de Informatica Facultad de Ciencias Exactas 3 means that each node is examined only twice: once as a child and once as a parent. To search an L-level decomposition of an N L = 2 sample periodic signal therefore requires just ( ) O N comparisons. Taswell (see [Tas2]) has shown that even for non additive cost function it is possible to apply a top-down search algorithm for finding a called near best basis from a redundant tree. The advantage of this approach is a reduction in computations with non practical reduction in quality of compression and distortion. This algorithm is called sub-optimal top-down tree computation/search instead of the optimal bottom-up tree search after computing the complete tree. The top-down bases are selected in the opposite direction by depth-first top-down searches with the search terminated as soon as the cost of the children blocks or branches is greater than the cost of the parent block or branch. The Actual Tree The actual redundant tree has an associated climber. There is a variable number of bits for full coding the tree (each branch has a fixed length and a coding of its coefficients using its own quantizer/s. And an a priori fixed number of bits for full coding the climber (each one coding the characteristics of each associated branch quantizer/s). There also exist a bit overhead for coding explicitly the name of the resulting prune . As a mater of fact, • the prune tree name, • the coefficients of the prune tree branches, • and the information of the prune associated climber branches, should be jointly coded/quantized [CrRa]." @default.
• W236467976 created "2016-06-24" @default.
• W236467976 creator A5070574739 @default.
• W236467976 date "1997-01-01" @default.
• W236467976 modified "2023-09-23" @default.
• W236467976 title "Practical selection of a basis from a redundant tree structure" @default.
• W236467976 hasPublicationYear "1997" @default.
• W236467976 type Work @default.
• W236467976 sameAs 236467976 @default.
• W236467976 citedByCount "0" @default.
• W236467976 crossrefType "journal-article" @default.
• W236467976 hasAuthorship W236467976A5070574739 @default.
• W236467976 hasConcept C105795698 @default.
• W236467976 hasConcept C113174947 @default.
• W236467976 hasConcept C11413529 @default.
• W236467976 hasConcept C12426560 @default.
• W236467976 hasConcept C125583679 @default.
• W236467976 hasConcept C134306372 @default.
• W236467976 hasConcept C179518139 @default.
• W236467976 hasConcept C207024777 @default.
• W236467976 hasConcept C2524010 @default.
• W236467976 hasConcept C33923547 @default.
• W236467976 hasConcept C41008148 @default.
• W236467976 hasConcept C45374587 @default.
• W236467976 hasConcept C80444323 @default.
• W236467976 hasConceptScore W236467976C105795698 @default.
• W236467976 hasConceptScore W236467976C113174947 @default.
• W236467976 hasConceptScore W236467976C11413529 @default.
• W236467976 hasConceptScore W236467976C12426560 @default.
• W236467976 hasConceptScore W236467976C125583679 @default.
• W236467976 hasConceptScore W236467976C134306372 @default.
• W236467976 hasConceptScore W236467976C179518139 @default.
• W236467976 hasConceptScore W236467976C207024777 @default.
• W236467976 hasConceptScore W236467976C2524010 @default.
• W236467976 hasConceptScore W236467976C33923547 @default.
• W236467976 hasConceptScore W236467976C41008148 @default.
• W236467976 hasConceptScore W236467976C45374587 @default.
• W236467976 hasConceptScore W236467976C80444323 @default.
• W236467976 hasLocation W2364679761 @default.
• W236467976 hasOpenAccess W236467976 @default.
• W236467976 hasPrimaryLocation W2364679761 @default.
• W236467976 hasRelatedWork W1003868381 @default.
• W236467976 hasRelatedWork W1504520068 @default.
• W236467976 hasRelatedWork W1598883216 @default.
• W236467976 hasRelatedWork W2100562604 @default.
• W236467976 hasRelatedWork W2181425632 @default.
• W236467976 hasRelatedWork W2185256534 @default.
• W236467976 hasRelatedWork W2250390514 @default.
• W236467976 hasRelatedWork W2280371997 @default.
• W236467976 hasRelatedWork W2890194927 @default.
• W236467976 hasRelatedWork W2899872869 @default.
• W236467976 hasRelatedWork W2963863610 @default.
• W236467976 hasRelatedWork W2966205006 @default.
• W236467976 hasRelatedWork W2971270287 @default.
• W236467976 hasRelatedWork W3086690391 @default.
• W236467976 hasRelatedWork W309033309 @default.
• W236467976 hasRelatedWork W3094110505 @default.
• W236467976 hasRelatedWork W3200356986 @default.
• W236467976 hasRelatedWork W2840760536 @default.
• W236467976 hasRelatedWork W3172799548 @default.
• W236467976 hasRelatedWork W944447804 @default.
• W236467976 isParatext "false" @default.
• W236467976 isRetracted "false" @default.
• W236467976 magId "236467976" @default.
• W236467976 workType "article" @default.