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The problem of restoring images degraded by blur and corrupted by noise is considered in this report. A discretization of the Fredholm integral equation of the first kind in a two dimensional form is performed. The overdetermined and underdetermined regression models are examined in detail, with particular attention to the problem of ill conditioning. The results of the restoration of simulated pictures under atmospheric turbulence and diffraction limited point spread functions are presented. A priori information in the form of deterministic constraints is proposed as a means to solve the ill conditioning problem. With linear equality constraints, a combination of estimation and hypothesis testing is used to decide if a reduction of the mean square error occurs upon the imposition of the restrictions. Experimental results show that more acceptable results are obtained in the restoration. Linear inequality constraints are incorporated by a quadratic programming formulation. The use of low (nonnegativeness) and upper bounds indicate a substantial improvement in the restoration, even for the ill conditioned situation.

Photographic images degraded by linear, spatially-invariant blurs can often be restored using an inverse or estimation filter in a coherent optical processor. In this procedure the degraded image is input to the processor as a photographic transparency. The spatial spectrum of the image is modified by a spatial filter and inverse transformed to obtain the restored image. The dynamic range of the spatial filter places an upper bound on the performance that can be achieved. This thesis demonstrates a new method for generating spatial filters with large dynamic ranges, and derives limitations inherent in the application of such filters to image restoration. (Modified author abstract), Sponsored in part by Sandia Labs., Livermore, Calif. and Army Electronics Command, Fort Monmouth, N.J.

The following subjects are presented: (1) discussion of the merits of available techniques that may be considered for use in each stage of the process of screening aerial reconnaissance photographs for purposes of detecting objects of military significance; (2) description and com parison of alternative hardware realizations of the techniques of (1) above; (3) summary of the application of the principles of statistical de cision theory to the reconnaissance photoscreen ing problem; (4) description of the conceptual design of an imagery screening device; and (5) detaiscription of a computer simulation problem on the detection of tanks in aerial photographs. The simulation, to be carried out during the next six months, is expected to provide design details to extend the conceptual design of item (4).

The mathematical relationships for filtering in a space domain are developed in a general analogy with temporal filtering. Cases in which the ele ments of the filtering system are continuous crete are discussed. General examples of spatial filtering and the realization of such filters are shown., Report on Guidance and Sensing Techniques for Advanced Vehicles.

This paper deals with the design and analysis of an adaptive array processor for use in passive detection of directional stochastic signals such as are found in sonar. The processor consists of a set of tapped delay-line filters, one for each array element. The algorithm used for adjusting the tap gains is a modification of the stochastic approximation method of Robbins and Monro, and it utilizes knowledge of the signal autocorrelation function and spatial direction of the target. It is shown that the final form approached by the processor is that of a space-time filter optimized in the direction corresponding to assumed target location. The system performance is analyzed by considering a noise field consisting of a spatially isotropic component and a single directional component referred to as an interference. It is shown that although the system initially cannot discriminate between the target and the interference, it eventually acts to eliminate the effect of the interference almost completely. It is also shown how the useful signal to noise ratio increases during adaptation. (Author), Prepared in cooperation with Yale Univ., New Haven, CT. Dept. of Engineering and Applied Science.

During this period the analysis of the listener detection behavior has been completed. The results are reported in Appendix I included with this report. The comparison between the efficiencies of the spatial correlator and the replica correlator has continued. The number of echo cycles included in the study has been extended. The determination of coincidence of false alarms in the spatial correlator processor and the replica correlator processor has been run on the computer. Results are being assembled and were to have been presented at the Conference on Signal Processing and Recognition Differential scheduled at Raytheon, Portsmouth, for 28 January 1965. A number of complete echo cycle correlograms have been passed through a symmetrical AGC. The resulting output has been passed through the false alarm rate program and this output will be used to construct detection curves for comparison with the spatial correlator detection curves. (Author)

The coherence between two points of the received acoustic waveform after reflection from a time varying random surface is evaluated for the far field case. A Neumann-Pierson spectrum and an isotropic sea is considered. For the low roughness case, the coherence is computed for wind speeds from 2 to 10 knots. For the specular and non-specular direction, the coherent region is on the order of the pattern resulting from the insonified surface area. (Author)

Two new techniques for making computer generated spatial filters with high dynamic range and high light efficiency are described, and a general treatment of computer generated holograms is given. Examples of single-channel (continuous phase control) phase-only filters, binary phase-only filters, as well as the absorption-type filters have been realized experimentally. Experiments have been carried out for correcting blurred images and for character recognition. Finally, a ternary hologram (binary absorption and binary phase), which preserves advantages of both types of binary holograms but is capable of a higher dynamic range than either individually, has been realized experimentally using color film. (Modified author abstract)

A new tracking optical processor which uses a computer generated matched filter to process the synthetic aperture radar data is described. The general consideration in generating the matched filter is discussed in detail and some experimental results are presented. (Author)

The book discusses problems of theory of primary data processing in optical-electronic direction-finding systems for detecting a small object on a non-uniform random background. A theory is developed for moving image analyzers, and analysis is made of characteristics of spatial filtering carried out by optical elements, and scanning, modulating and photo-receiving devices of various kinds. Effect of parameters of emission sources and system elements on signal-to-noise ratio is studied. (Modified author abstract), Trans. from Sovetskoe Radio, Moscow, 1971.

Matched spatial filters are constructed for various modes of a spherical Fabry-Perot interferometer. The cross-correlation between many of these modes are obtained experimentally as well as theoretically. The orthogonality between various modes are demonstrated and used in order to discriminate against all but the desired mode. The Fabry-Perot interferometer with a zero-order mode filter could be used as a scanning interferometer over a full free range without spurious signal and over a large range of cavity spacings. (Author)

A method of producing spatial filters by recording straight line fringe patterns produced by interferring two laser beams on spectroscopic plates is discussed. Techniques used to obtain maximum modulation, maximum transmission, and extremely straight fringes are included. (Author), Master's thesis.

BLUE BELL PA SCIENTIFIC SYSTEMS DIVImage Motion Detector for Handheld Photographic System.Final technical rept. 21 Apr 71-13 Dec 72,FShin,Ihsuk ;DCR-340F30602-71-C-0234AF-5534553401RADCTR-73-45(*cameras, image motion compensation), photoelectric cells(semiconductor), integrated circuits, wiring diagrams, photointerpretation, test methodsperformance evaluation, spatial filteringThe feasibility of a technique for detecting the image motion rate at the focal plane of a handheld camera by monitoring the time variation of a photocell output whose input is the spatially filtered optical image was determined. A breadboard model of a device which detects the image motion rate and triggers the camera shutter only when the detected rate is equal to or below a preselected value was fabricated and tested. (Author)

The properties of the Fourier Transforms of Titanium alloy photomicrographs are investigated. The characteristics of the discrete Fourier Transforms are outlined, and the principles of pattern recognition by spatial filtering and matched filter correlation are discussed. The technique of data preparation is described, and the results from both spatial filtering and correlation methods are presented and discussed. The conclusion is reached that texture patterns such as metal microstructure are too noisy for successful pattern recognition by spatial filtering, but matched filter correlation techniques show some promise for accurate measurement of defined object populations in noisy samples. (Author)

A spatial filtering technique for observing several different moire patterns in the same image of superposed gratings and for separating them at will, is described. In addition to the commonly observed moire pattern, and the equivalent patterns obtained by fringe sharpening or multiplication, patterns can be observed that correspond to different forms of the indicial equation describing the parametric properties of moire phenomena. In particular both the additive and subtractive moires are obtained individually, over the field. This method, combined with a previously developed method for obtaining spatial partial derivatives from deformed gratings (as a direct moire rather than moire of moire), permits the experimental determination of the whole field of Cartesian shears and rigid rotations. The method is applied to a circular ring subjected to diametral compression. (Author)

The holographic stereogram, a hologram synthesized from ordinary stereoscopic component photographs, is investigated as an alternative to classical holograms and to previous types of stereograms for three-dimensional perfect imagery. The process is partly holographic in nature, but it provides images of naturally illuminated objects, and its application is not limited by the technology of laser illumination. The pinhole camera stereogram and the fly's eye lens stereogram are also analyzed, since the principles of their operation are similar. Pinhole camera stereogram imagery is shown to have several deficiencies, among which is the necessity for small camera-object distances. The fly's eye lens is much superior, but is limited in practice by aberrations, a difficulty which the holographic stereogram overcomes. Also treated are the full-color, the focused-type, and the distortionless-scaled holographic stereogram, and optical spatial filtering of holographic stereogram images. The achromatically imaged Fresnel zone plate is analyzed as a technique of very general applicability which compensates for source incoherency in two-beam type holographic arrangements. The emphasis is on physical interpretation rather than mathematical formulation. Two simple graphical mnemonics are developed for rapid analytical inspection of the effects of, respectively, temporal and spatial incoherence of the source in any achromatically imaged zone plate or Gabor in-line type holographic system. The scalar wave function approximation of physical optics is used throughout. (Author)

This report concerns some applications of coherent optical techniques to imagery of the earth sciences. Four typical problems are included: (1) the determination of the two-dimensional wave spectrum of water waves by use of a coherent optical Fourier analyzer; (2) the detection of linear geological features from aerial photographs by optical spatial filtering; (3) the measurement of water motion by use of optical correlation techniques; and (4) image distortion correction by partitioned-field spatial filtering. (Author)

Several spatial filters are discussed whose input comes from the image plane of an optical imaging system. These filters are for the purpose of detecting a localized intensity source imbedded in a confusing background of similar sources. Three of the filters have two-dimensional static pictures as both input and output. Two of these are called polynomial filters while the third is of a general type. A fourth filter, called a decision filter, has a yes or no output with regard to the presence or absence of the localized intensity source. A remarkable connection between the decision filter and the general type is shown. (Author)

Several experiments were performed on a two channel, electrooptical device, whose design and construction is described in Volume I: Image Integration for the purpose of averaging random noise, integration of optically filtered images, and penetration of foliage using parallax information. (Author), See also Volume 1, AD-804 093L.

The patent describes an electrostatically cooled spatial filter for high powered pulsed lasers. The filter comprises a first lens which focuses a laser beam on a pinhole, and a second lens positioned behind the pinhole to receive the beam. To prevent the laser beam from destroying the pinhole an electric field is applied across the pinhole. This field cools the pinhole and as a result the size of the pinhole is preserved.

The patent describes an electrostatically cooled spatial filter for high powered pulsed lasers. The filter comprises a first lens which focuses a laser beam on a pinhole, and a second lens positioned behind the pinhole to receive the beam. To prevent the laser beam from destroying the pinhole an electric field is applied across the pinhole. This field cools the pinhole and as a result the size of the pinhole is preserved.

Three methods of spatial filtration of image-orthicon pictures are considered: (1) two independently produced images - a high-definition positive and a blurred negative - are algebraically combined on the storing target of the orthicon. An additional grid in the image-transfer section is introduced. Such a spatial-frequency filter can be adjusted by varying the potentials of electrodes and the exposure time; (2) by selecting the potential of the target irradiated by slow electrons, a compensation of relatively uniform background noise (suppression of lower spatial frequencies) can be achieved. An additional 1-f filtration can be obtained, in the process of readout, by applying a negative feedback from the video-amplifier output - via a 1-f filter - to the target grid. Such a method may find application in astronomic TV; (3) a modification of the preceding method permits obtaining a two-side restriction of electronic images. The target potential can be reduced as soon as the storage has been completed. As this operation is performed on the target before the image readout, only the desirable picture (not noise) is accentuated., Edited machine trans. of Tekhniko Kino i Televideniya (USSR) v12 n4 p51-57 1968.