Showing papers on "Kernel (image processing) published in 1970"
TL;DR: The fundamental identity between the operations of vector convolution and polynomial multiplication is exploited to provide a general-purpose alternative to the method of spatial filtering for digitally deconvolving noisy, degraded images of incoherently illuminated objects.
Abstract: The fundamental identity between the operations of vector convolution and polynomial multiplication is exploited to provide a general-purpose alternative to the method of spatial filtering for digitally deconvolving noisy, degraded images of incoherently illuminated objects. The method is remotely related to those of linear programming, but differs significantly from them in its exploitation of the special properties of convolution. Sampled image arrays are treated as points in euclidean n space. The convolution relation, together with bounds on individual recorded and point-spread image irradiance values, defines a set of linear constraints on the restored image-irradiance values. These constraints define a convex region of possible restorations in n space. A method is described for selecting a point (i.e., an estimate of the restored image) from near the center of this region. The human viewer may then readjust the original constraints to reflect the new information revealed by his interpretation of the restored-image estimate. The deconvolution calculations can then be repeated with the readjusted constraints, to yield a possibly better estimate. The method is applicable to restoration problems in which both the recorded image and the point-spread image contain noise. Furthermore, it is applicable to any problem requiring the numerical solution of a convolution equation involving measured data. The connection with Fourier-transform theory and comparison with spatial-filtering methods are touched upon briefly. A few computer restorations are shown, to illustrate the practicality and potential of the method.
55 citations
Patent•
21 Aug 1970
TL;DR: In this paper, a generalized convolution of values from two matrices of complex values Ao through Am and Bo through Bn respectively is presented. But this method is not suitable for vector and matrix algebra, linear programming, and transformation weighting and skirting operations.
Abstract: Method and apparatus of computing a generalized convolution of values from two matrices of complex values Ao through Am and Bo through Bn respectively. The formula used in the computation of each complex vector element Ck of the generalized convolution is WHERE P and U specify the increment for each succeeding element involved in a single convolution from each sequence respectively, Q and V specify the increments between first elements of successive convolution coefficients, in each sequence, respectively, and R and W specify the first pair of elements used in forming Co. PC specifies the number of Ck's to be computed. This computation has wide applicability to such allied mathematical operations as vector and matrix algebra, linear programming and a wide variety of transformation weighting and skirting operations such as Bessel function weighting, Hanning windows, complex Kernal transformations, and fast Fourier transforms. In addition, the apparatus described has capability to compute various special cases of the generalized equation involving vectors of real values only.
40 citations
TL;DR: In this article, a decomposition of the field at the aperture of an optical system in terms of the eigenfunctions of a certain integral equation is used in analyzing the detectability of incoherent objects.
Abstract: A decomposition of the field at the aperture of an optical system in terms of the eigenfunctions of a certain integral equation is useful in analyzing the detectability of incoherent objects. The kernel of the integral equation is the mutual coherence function of the light from the object. The decomposition permits specification of the number of degrees of freedom in the aperture field contributing to detection of the object. Quantum mechanically the coefficients of the modal decomposition become operators similar to the usual creation and annihilation operators for field modes. The optimum detector of the object is derived in terms of these operators. Specific detection probabilities are calculated for a uniform circular object whose light is observed at a circular aperture. The modal decomposition is also applied to estimating the radiance distribution of the object plane.
21 citations
TL;DR: In this article, a necessary and sufficient condition for a function to have a factorization such that both factors are bounded from above and from below by power functions is given, and an easily verifiable sufficient condition is also given.
Abstract: In this paper a necessary and sufficient condition is found for a function to have a factorization such that both factors are bounded from above and from below by power functions; an easily verifiable sufficient condition is also given. Further, the limits of validity of the Wiener-Hopf method are shown for equations in a halfspace with kernel depending on the difference of the arguments.Bibliography: 14 items.
1 citations