Generalized consistent sampling in abstract Hilbert spaces

被引：2
|
作者：
Kwon, Kil Hyun [1 ]
Lee, Dae Gwan [2 ]
机构：
[1] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon 305701, South Korea
[2] Seoul Natl Univ, PLUS SNU Math Sci Div BK21, Seoul 151747, South Korea
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 433卷 / 01期
基金：
新加坡国家研究基金会;
关键词：
Consistent sampling; Frame; Oblique projection; RECONSTRUCTION; FRAMEWORK;
D O I：
10.1016/j.jmaa.2015.07.070
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider generalized consistent sampling and reconstruction processes in an abstract Hilbert space H. We first study the consistent sampling in H together with its performance analysis. We then study its generalization: partial consistency and quasi-consistency. We give complete characterizations for both of them. We also provide an iterative algorithm to compute the quasi-consistent approximation. An illustrative example is also included. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：375 / 391
页数：17
相关论文
共 50 条
  • [1] Consistent Sampling Approximations in Abstract Hilbert Spaces
    Kang, Sinuk
    Kwon, Kil Hyun
    Lee, Dae Gwan
    AXIOMS, 2024, 13 (07)
  • [2] General framework for consistent sampling in Hilbert spaces
    Eldar, YC
    Werther, T
    INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2005, 3 (03) : 347 - 359
  • [3] General framework for consistent sampling in Hilbert spaces
    Eldar, YC
    Werther, T
    INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2005, 3 (04) : 497 - 509
  • [4] Generalized frame multiresolution analysis of abstract Hilbert spaces and its applications
    Papadakis, M
    WAVELET APPLICATIONS IN SIGNAL AND IMAGE PROCESSING VIII PTS 1 AND 2, 2000, 4119 : 165 - 175
  • [5] Tomography in abstract Hilbert spaces
    Man'ko, V. I.
    Marmo, G.
    Simoni, A.
    Ventriglia, F.
    OPEN SYSTEMS & INFORMATION DYNAMICS, 2006, 13 (03): : 239 - 253
  • [6] GENERALIZED FRAMES IN HILBERT SPACES
    Najati, A.
    Rahimi, A.
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2009, 35 (01) : 97 - 109
  • [7] On the meaning and interpretation of tomography in abstract Hilbert spaces
    Man'ko, VI
    Marmo, G
    Simoni, A
    Stern, A
    Sudarshan, ECG
    Ventriglia, F
    PHYSICS LETTERS A, 2006, 351 (1-2) : 1 - 12
  • [8] Functional inequalities on abstract Hilbert spaces and applications
    Feng-Yu Wang
    Mathematische Zeitschrift, 2004, 246 : 359 - 371
  • [9] RETARDED ABSTRACT EQUATIONS IN HILBERT-SPACES
    DIBLASIO, G
    KUNISCH, K
    SINESTRARI, E
    LECTURE NOTES IN MATHEMATICS, 1984, 1076 : 71 - 77
  • [10] Consistency of logistic classifier in abstract Hilbert spaces
    Kazakeviciute, Agne
    Olivo, Malini
    ELECTRONIC JOURNAL OF STATISTICS, 2018, 12 (02): : 4487 - 4516
12345