Morten Nielsen's Publications

• Sorted by Date • Classified by Publication Type •

Classified by Publication Type

• Journal Article • Accepted in Journal • Refereed Conference • Technical Report • Ph.D. Thesis • Doctoral Thesis •

Journal Article

• M. Nielsen. Trigonometric bases for matrix weighted $L_p$-spaces. J. Math. Anal. Appl., 371:784–792, 2010.
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• M. Nielsen. Orthonormal bases for $\alpha$-modulation spaces. Collect. Math., 61(2):173–190, 2010.
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• M. Nielsen. On stability of finitely generated shift-invariant systems. J. Fourier Anal. Appl., 16(6):901–920, 2010.
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• M. Nielsen. Trigonometric quasi-greedy bases for $L_p([0,1])$. Rocky Mountain J. Math., 39(4):1267–1278, 2009.
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• L. Borup and M. Nielsen. On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators. J. Funct. Spaces Appl., 6(2):107–154, 2008.
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• L. Borup, R. Gribonval, and M. Nielsen. Beyond coherence: recovering structured time-frequency representations. Appl. Comput. Harmon. Anal., 24(1):120–128, 2008.
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• R. Gribonval and M. Nielsen. Beyond sparsity: recovering structured representations by $l\sp 1$ minimization and greedy algorithms. Adv. Comput. Math., 28(1):23–41, 2008.
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• M. Nielsen and H. Sikic. Quasi-greedy systems of integer translates. J. Approx. Theory, 155(1):43–51, 2008.
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• L. Borup and M. Nielsen. Frame decomposition of decomposition spaces. J. Fourier Anal. Appl., 13(1):39–70, 2007.
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• R. Gribonval and M. Nielsen. Highly sparse representations from dictionaries are unique and independent of the sparseness measure. Appl. Comput. Harmon. Anal., 22(3):335–355, 2007.
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• M. Nielsen. An example of an almost greedy uniformly bounded orthonormal basis for $L\sb p(0,1)$. J. Approx. Theory, 149(2):188–192, 2007.
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• M. Nielsen and H. Sikic. Schauder bases of integer translates. Appl. Comput. Harmon. Anal., 23(2):259–262, 2007.
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• M. Nielsen. On polynomial symbols for subdivision schemes. Adv. Comput. Math., 27(2):195–209, 2007.
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• L. Borup and M. Nielsen. Boundedness for pseudodifferential operators on multivariate $\alpha$-modulation spaces. Ark. Mat., 44(2):241–259, 2006.
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• L. Borup and M. Nielsen. Banach frames for multivariate $\alpha$-modulation spaces. J. Math. Anal. Appl., 321(2):880–895, 2006.
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• L. Borup and M. Nielsen. Nonlinear approximation in $\alpha$-modulation spaces. Math. Nachr., 279(1-2):101–120, 2006.
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• R. Gribonval and M. Nielsen. Nonlinear approximation with dictionaries. II. Inverse estimates. Constr. Approx., 24(2):157–173, 2006.
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• L. Borup and M. Nielsen. Nonlinear approximation with general wave packets. Anal. Theory Appl., 21(3):201–215, 2005.
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• L. Borup and M. Nielsen. On the equivalence of brushlet and wavelet bases. J. Math. Anal. Appl., 309(1):117–135, 2005.
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• L. Borup and M. Nielsen. Approximation with wave packets generated by a refinable function. Proc. Amer. Math. Soc., 133(8):2409–2418 (electronic), 2005.
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• L. Borup, R. Gribonval, and M. Nielsen. Tight wavelet frames in Lebesgue and Sobolev spaces. J. Funct. Spaces Appl., 2(3):227–252, 2004.
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• L. Borup, R. Gribonval, and M. Nielsen. Bi-framelet systems with few vanishing moments characterize Besov spaces. Appl. Comput. Harmon. Anal., 17(1):3–28, 2004.
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• R. Gribonval and M. Nielsen. On a problem of Gröchenig about nonlinear approximation with localized frames. J. Fourier Anal. Appl., 10(4):433–437, 2004.
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• R. Gribonval and M. Nielsen. Nonlinear approximation with dictionaries. I. Direct estimates. J. Fourier Anal. Appl., 10(1):51–71, 2004.
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• R. Gribonval and M. Nielsen. On approximation with spline generated framelets. Constr. Approx., 20(2):207–232, 2004.
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• M. Nielsen. Nonseparable Walsh-type functions on $\mathbf R\sp d$. Glas. Mat. Ser. III, 39(59)(1):111–138, 2004.
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• L. Borup and M. Nielsen. Fast Adaptive Expansions in Local Trigonometric Bases. Signal Processing, 83(2):445–451, 2003.
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• L. Borup and M. Nielsen. Approximation with brushlet systems. J. Approx. Theory, 123(1):25–51, 2003.
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• R. Gribonval and M. Nielsen. Sparse representations in unions of bases. IEEE Trans. Inform. Theory, 49(12):3320–3325, 2003.
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• M. Nielsen. Size properties of wavelet packets generated using finite filters. Rev. Mat. Iberoamericana, 18(2):249–265, 2002.
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• M. Nielsen and D.-X. Zhou. Mean size of wavelet packets. Appl. Comput. Harmon. Anal., 13(1):22–34, 2002.
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• M. Nielsen. On convergence of wavelet packet expansions. Approx. Theory Appl. (N.S.), 18(1):34–50, 2002.
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• M. Nielsen. Highly nonstationary wavelet packets. Appl. Comput. Harmon. Anal., 12(2):209–229, 2002.
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• R. Gribonval and M. Nielsen. Approximate weak greedy algorithms. Adv. Comput. Math., 14(4):361–378, 2001.
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• R. Gribonval and M. Nielsen. Some remarks on non-linear approximation with Schauder bases. East J. Approx., 7(3):267–285, 2001.
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• M. Nielsen. On the construction and frequency localization of finite orthogonal quadrature filters. J. Approx. Theory, 108(1):36–52, 2001.
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• M. Nielsen. Walsh-type wavelet packet expansions. Appl. Comput. Harmon. Anal., 9(3):265–285, 2000.
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Accepted in Journal

• M. Nielsen and K. N. Rasmussen. Compactly supported frames for decomposition spaces. J. Fourier Anal. Appl. (in press), 2011.
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• M. Nielsen. On transference of multipliers on matrix weighted $L_p$-spaces. J. Geom. Anal. (in press), 2011.
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• M. Nielsen and H. Sikic. Maximal functions, product condition and its eccentricity. Collect. Math. (in press), 2011.
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Refereed Conference

• L. Borup, R. Gribonval, and M. Nielsen. Nonlinear approximation with bi-framelets. In Approximation theory XI: Gatlinburg 2004, Mod. Methods Math., pp. 93–104, Nashboro Press, Brentwood, TN, 2005.
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• M. Nielsen, L. Borup, and R. Gribonval. Nonlinear Approximation with Redundant Dictionaries. In Proc. ICASSP' 05 (IEEE Conf. on Acoustics, Speech and Signal Proc.), pp. 261–264, IV, 2005.
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• R. Gribonval and M. Nielsen. On the strong uniqueness of highly sparse expansions from redundant dictionaries. In Proc. Int Conf. Independent Component Analysis (ICA'04), 2004.
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• R. Gribonval and M. Nielsen. Approximation with Highly Redundant Dictionaries. In Proc. SPIE'03: 'Wavelets: Applications in Signal and Image Processing', pp. 216–227, 5207, 2003.
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• M. Nielsen and R. Gribonval. Sparse decompositions in 'Incoherent' dictionaries. In Proc. IEEE Intl. Conf. on Image Proc. (ICIP'03), 2003.
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• L. Borup and M. Nielsen. Nonseparable wavelet packets. In Approximation theory, X (St. Louis, MO, 2001), Innov. Appl. Math., pp. 51–61, Vanderbilt Univ. Press, Nashville, TN, 2002.
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Technical Report

• R. Gribonval and M. Nielsen. The restricted isometry property meets nonlinear approximation with redundant frames. Technical Report INRIA-IRISA, 2011.
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• E. Hernandez, M. Nielsen, H. Sikic, and F. Soria. Democratic systems of translates. Technical Report Aalborg University, 2011.
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• M. Nielsen and K. N. Rasmussen. Compactly supported curvelet type frames. Technical Report Aalborg University, 2010.
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• L. Borup and M. Nielsen. Some remarks on shrinkage operators. Technical Report Aalborg University, 2003.
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• M. Nielsen and R. Gribonval. On the Quasi-greedy Property and Uniformly Bounded Orthonormal Systems. Technical Report Aalborg University, 2003.
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Ph.D. Thesis

• M. Nielsen. Size Properties of Wavelet Packets. Ph.D. Thesis, Washington University in St. Louis, 1999.
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Doctoral Thesis

• M. Nielsen. Aspects of Nonlinear Approximation with Dictionaries. Doctoral Thesis, Aalborg University, 2009.
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