zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Variational methods on the space of functions of bounded Hessian for convexification and denoising. (English) Zbl 1098.49022
The authors study variational principles on the space of functions of bounded Hessian. First some basic properties of convex functions, functions of bounded variation and relations between convex functions and the space of bounded Hessians are recalled. Then the existence of minimizers of variational problems for denoising, approximation by convex functions, and for calculation of the convex envelope are proved. Some numerical results are given.
MSC:
49K20Optimal control problems with PDE (optimality conditions)
49J25Optimal control problems with equations with ret. arguments (exist.) (MSC2000)
65J20Improperly posed problems; regularization (numerical methods in abstract spaces)
49J40Variational methods including variational inequalities
65K10Optimization techniques (numerical methods)
References:
[1] · Zbl 0809.35151 · doi:10.1088/0266-5611/10/6/003
[2]
[3] · Zbl 0796.65009 · doi:10.1137/0731007
[4]
[5]
[6] · Zbl 0874.68299 · doi:10.1007/s002110050258
[7] · Zbl 0968.68175 · doi:10.1137/S1064827598344169
[8] · Zbl 0929.68118 · doi:10.1137/S1064827596299767
[9] · Zbl 0923.65037 · doi:10.1137/S0036142997327075
[10]Chan, T. F., Wong, C. K.: Convergence of the alternating minimization algorithm for blind deconvolution. Linear Algebra Appl. 316, 259–285 (2000). Conf. Celebrating the 60th Birthday of Robert J. Plemmons (Winston-Salem, NC, 1999).
[11]Chan, T. F., Wong, C. K.: Total variation blind deconvolution. IEEE Trans. Image Proc. 7, (1998).
[12] · Zbl 0890.49010 · doi:10.1051/cocv:1997113
[13]
[14]
[15] · Zbl 0554.73030 · doi:10.1080/01630568308816155
[16]
[17]
[18]
[19] · doi:10.1109/83.392335
[20] · Zbl 0573.62030 · doi:10.1109/TPAMI.1984.4767596
[21]Golub, G. H., Van Loan, Ch. F.: Matrix computations, 3rd ed. Baltimore: The Johns Hopkins University Press 1996.
[22]Isakov, V.: Inverse source problems. Providence, RI: American Mathematical Society, 1990.
[23]Isakov, V.: Inverse problems for partial differential equations. Appl. Math. Sci. 127, (1998).
[24] · Zbl 0918.65050 · doi:10.1051/m2an:1999102
[25] · Zbl 0971.49014 · doi:10.1016/S0362-546X(98)00299-5
[26] · Zbl 1007.90049 · doi:10.1023/A:1017591716397
[27] · Zbl 0852.90117 · doi:10.1007/BF00248008
[28] · Zbl 05453109 · doi:10.1109/TIP.2003.819229
[29]
[30]
[31] · Zbl 0914.65067 · doi:10.1080/01630569808816863
[32]Nashed, M. Z., Scherzer, O. (eds.): Interactions on inverse problems and imaging. Contemp. Math. 313, (2002).
[33] · Zbl 0991.94015 · doi:10.1137/S0036139997327794
[34] · Zbl 0996.94011 · doi:10.1109/78.887035
[35] · Zbl 0714.65096 · doi:10.1137/0727053
[36] · doi:10.1006/jvci.1999.0437
[37] · Zbl 0780.49028 · doi:10.1016/0167-2789(92)90242-F
[38] · Zbl 0919.49001 · doi:10.1006/aima.1998.1770
[39] · Zbl 0891.65103 · doi:10.1007/BF02684327
[40]Scherzer, O.: Explicit versus implicit relative error regularization on the space of functions of bounded variation. In [32], 171–198 (2002).
[41] · Zbl 0945.68183 · doi:10.1023/A:1008344608808
[42] · Zbl 0935.35087 · doi:10.1080/03605309908821476
[43]
[44]
[45] · Zbl 1011.68538 · doi:10.1006/cviu.2000.0875