{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T06:53:17Z","timestamp":1759042397975},"reference-count":36,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"4","license":[{"start":{"date-parts":[[1998,4,1]],"date-time":"1998-04-01T00:00:00Z","timestamp":891388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Signal Process."],"published-print":{"date-parts":[[1998,4]]},"DOI":"10.1109\/78.668541","type":"journal-article","created":{"date-parts":[[2002,8,24]],"date-time":"2002-08-24T19:31:03Z","timestamp":1030217463000},"page":"845-856","source":"Crossref","is-referenced-by-count":19,"title":["Design of regular nonseparable bidimensional wavelets using Grobner basis techniques"],"prefix":"10.1109","volume":"46","author":[{"family":"Jean-Charles Faugere","sequence":"first","affiliation":[]},{"given":"F.M.","family":"de Saint-Martin","sequence":"additional","affiliation":[]},{"given":"F.","family":"Rouillier","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/82.404083"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/82.281843"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/ICIP.1994.413832"},{"key":"ref30","author":"becker","year":"1993","journal-title":"Gro&#x00A8 bner Bases A Computationnal Approach to Commutative Algebra"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/31.101301"},{"key":"ref35","first-page":"243","article-title":"sobolev regularity of wavelets and stability of iterated filter banks","author":"villemoes","year":"0","journal-title":"Progress in Wavelet Analysis and Applications"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1994.1005"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160410705"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"ref12","first-page":"7","article-title":"universal variable length coding for an integrated approach to image coding","volume":"46","author":"delogne","year":"1991","journal-title":"Ann Te&#x00B4 le&#x00B4 commun"},{"key":"ref13","author":"fauge`re","year":"1994","journal-title":"Re&#x00B4 solution des syste&#x00B4 mes d e&#x00B4 quations polynomiales"},{"key":"ref14","article-title":"efficient computation of zero-dimensional groebner basis by change of ordering","author":"fauge`re","year":"1994","journal-title":"J Symbolic Comput"},{"key":"ref15","author":"fauge`re","year":"1997","journal-title":"A new efficient algorithm for computing Gro&#x00A8 bner basis (F4)"},{"key":"ref16","author":"davenport","year":"1993","journal-title":"Calcul Formel"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/18.119722"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/78.382414"},{"key":"ref19","author":"moreno maza","year":"1997","journal-title":"Calculs de pgcd au-dessus des tours d extensions simples et re&#x00B4 solution des syste&#x00B4 mes d e&#x00B4 quations alge&#x00B4 briques"},{"key":"ref28","author":"stanhill","year":"1995","journal-title":"Two-dimensional linear-phase orthogonal filter-banks and wavelets"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-5225-6_6"},{"key":"ref27","doi-asserted-by":"crossref","DOI":"10.1109\/29.90373","article-title":"efficient bit allocation for an arbitrairy set of quantizers","volume":"36","author":"shoham","year":"1988","journal-title":"IEEE Trans Acoustic Speech and Signal Processing"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01844169"},{"key":"ref6","author":"cohen","year":"1995","journal-title":"A new technique to estimate the regularity of refinable functions"},{"key":"ref29","author":"stanhill","year":"1995","journal-title":"Two-dimensional orthogonal wavelets with vanishing moments"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.4171\/RMI\/133"},{"key":"ref8","author":"cox","year":"1992","journal-title":"Ideals Varieties and Algorithms An Introduction to Computational Algebraic Geometry and Commuataive Algebra"},{"key":"ref7","author":"cohen","year":"1995","journal-title":"Regularity of multi-variate refinable functions"},{"key":"ref2","author":"buchberger","year":"1965","journal-title":"Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal"},{"key":"ref9","article-title":"systems of algebraic equations (algorithms and complexity)","author":"lazard","year":"1993","journal-title":"Comput Algebraic Geom Commutative Algebra Proc Cortona Conf"},{"key":"ref1","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/978-3-0348-6303-2_2","article-title":"an elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations","volume":"86","author":"auzinger","year":"1998","journal-title":"Int Series Numer Math"},{"key":"ref20","author":"moreau de saint-martin","year":"1997","journal-title":"Bancs de filtres et ondelettes Synthe&#x00B4 ses adaptations et applications"},{"key":"ref22","article-title":"groebner bases and multidimensional fir multirate systems","author":"park","year":"1996","journal-title":"J Multidimensional Syst Signal"},{"key":"ref21","author":"onno","year":"1996","journal-title":"Bancs de filtres et quantification vectorielle sur re&#x00B4 seau E&#x00B4 tude conjointe pour la compression d images"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/83.217221"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2752-6_15"},{"key":"ref26","author":"rouillier","year":"1996","journal-title":"Algorithmes efficaces pour l e&#x00B4 tude des ze&#x00B4 ros re&#x00B4 els des syste&#x00B4 mes polynomiaux"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/0523086"}],"container-title":["IEEE Transactions on Signal Processing"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx4\/78\/14620\/00668541.pdf?arnumber=668541","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T20:15:20Z","timestamp":1638216920000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/668541\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,4]]},"references-count":36,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.1109\/78.668541","relation":{},"ISSN":["1053-587X"],"issn-type":[{"value":"1053-587X","type":"print"}],"subject":[],"published":{"date-parts":[[1998,4]]}}}