zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Projection filter, Wiener filter, and Karhunen-Loève subspaces in digital image restoration. (English) Zbl 0588.94005
In image processing by computer, the transformation from the original continuous-domain image to the degraded and sampled discrete observation image is usually modelled as a linear transformation with additive noise. The relation between two types of filters, the Wiener filter (WF) and the projection filter (PF), for the restoration of the original image from the observation is discussed. The latter is based on the same principle as pseudoinverse filtering but also suppresses the additive noise. The PF and the WF are shown to be closely related under a condition depending on the degradation-sampling operator and the Karhunen-Loève expansion for the family of original images. The relation between the PF and the Gauss-Markov estimator is also clarified.

94A08Image processing (compression, reconstruction, etc.)
68T10Pattern recognition, speech recognition
Full Text: DOI
[1] Albert, A.: Regression and the Moore-Penrose pseudoinverse. (1972) · Zbl 0253.62030
[2] Andrews, H. C.; Hunt, B. R.: Digital image restoration. (1977) · Zbl 0379.62098
[3] Campbell, S. L.; Meyer Jr., C. D.: Generalized inverses of linear transformations. (1979) · Zbl 0417.15002
[4] Freiberger, W.; Grenander, U.: A method in pattern theory. Proc. 2nd scand. Conf. on image analysis, 11-17 (June 15--17, 1981)
[5] Groetsch, C. W.: Generalized inverses of linear operators. (1977) · Zbl 0358.47001
[6] Nakamura, N.; Ogawa, H.: Optimum digital image restoration under additive noises. Trans. IECE Japan 67-D, No. No. 5, 563-570 (1984)
[7] Ogawa, H.: Optimum digital image restoration. Proc. int. Conf. on advances in information science and technology, 8.1-8.7 (Jan. 11--14, 1982)
[8] Ogawa, H.; Nakamura, N.: Projection filter restoration of degraded images. Proc. 7th int. Conf. on pattern recognition (July 30--Aug. 2, 1984)
[9] Oja, E.: Subspace methods of pattern recognition. Research stud., letchworth (1983)
[10] Oja, E.; Ogawa, H.: Parametric projection filter for image and signal restoration. (1984)
[11] Zyskind, G.: On canonical forms, nonnegative covariance matrices, and best and simple least squares estimators in linear models. Ann. of math. Statist. 38, 1092-1109 (1967) · Zbl 0171.17103