Adaptive noise smoothing filter for images with signal-dependent noise.

In this paper, we consider the restoration of images with signal-dependent noise. The filter is noise smoothing and adapts to local changes in image statistics based on a nonstationary mean, nonstationary variance (NMNV) image model. For images degraded by a class of uncorrelated, signal-dependent noise without blur, the adaptive noise smoothing filter becomes a point processor and is similar to Lee's local statistics algorithm [16]. The filter is able to adapt itself to the nonstationary local image statistics in the presence of different types of signal-dependent noise. For multiplicative noise, the adaptive noise smoothing filter is a systematic derivation of Lee's algorithm with some extensions that allow different estimators for the local image variance. The advantage of the derivation is its easy extension to deal with various types of signal-dependent noise. Film-grain and Poisson signal-dependent restoration problems are also considered as examples. All the nonstationary image statistical parameters needed for the filter can be estimated from the noisy image and no a priori information about the original image is required.

Artificial stereo.

A technique of artificially creating stereo image pairs from a single monocular image by digital processing is presented. Stereo information perceived as height by the human observer is obtained by extracting features from natural scenes. The features include pixel brightness, edge information, texture, or multispectral information used singly or in combination. The artificial stereo images are intended as an enhancement aid for human perception, and no attempt is made to reproduce reality. Algorithms for obtaining the stereo pair are described, and some experimental results and examples are given.

Optical crossbar interconnections using variable grating mode devices.

In this paper we propose a system design for an optical crossbar interconnection network utilizing variable grating mode liquid crystal devices (VGM LCDs) which are optical transducers capable of performing intensity-to-spatial-frequency conversion. The proposed system performs real-time, reconfigurable, and nonblocking, but nonbroadcasting, optical crossbar interconnections. The fundamental limitations and the performance of the system are discussed.

Diffractive optical element design with memory-matrix-based identification methodology.

We present a new technique for the design of diffractive optical elements (DOE's) that is based on previous nonlinear least squares (NLS) and phase-shifting quantization methods [Appl. Opt. 36, 7297-7306 (1997)]. The technique uses a memory-matrix-based identification (MMBI) optimization procedure. We compare results from the MMBI method with those from iterative Fourier transform and NLS methods. In comparison, the MMBI DOE designs produce better-quality reconstructions for DOE's with eight or more fabrication phase levels and generally have a higher signal-to-noise ratio and better uniformity.

Design of diffractive optical elements with optimization of the signal-to-noise ratio and without a dummy area.

We describe a new approach to suppress undesired diffraction orders in the signal area of a Fourier plane diffractive optical element (DOE). We implement this new approach for the DOE design by a two-stage iterative Fourier transform algorithm that incorporates an adaptive optimization of the signal-to-noise ratio and does not require the introduction of a dummy output area outside the field of view. A comparison among this approach and three other approaches are presented on the basis of numerical results from several sample diffraction patterns.

Nonlinear least-squares and phase-shifting quantization methods for diffractive optical element design.

A new, to our knowledge, design method for diffractive optical elements (DOE's) is described and compared with existing methods. The technique applies a nonlinear least-squares algorithm to design two-dimensional pure phase DOE's that reconstruct a desired diffraction pattern with high uniformity, efficiency, and signal-to-noise ratio. The technique also uses a phase-shifting quantization procedure that greatly reduces the quantization error for DOE's to a minimum level. In this paper, we compare simulated reconstruction results of DOE's designed by use of these methods with results obtained by the commonly used two-stage iterative Fourier transform design algorithm of Wyrowski. [J. Opt. Soc. Am. A 7, 961, (1990)].

Three-dimensional Omega networks for optical implementation.

We discuss a class of volume three-dimensional multistage interconnection networks suitable for optical implementation. The networks are based on perfect shuffles defined on two-dimensional arrays of signal channels combined with various types of dynamic switch elements in two-dimensional arrays. A mathematical description of the two-dimensional shuffles and these switch elements is presented. The relationship between the networks in this class (three-dimensional Omega networks) is studied. Optical or optoelectronic versions of these networks can perform high-speed parallel signal processing operations.

Time multiplexing and control for optical cellular-hypercube arrays.

We discuss the cellular-hypercube optical free-space interconnection architecture and its implementation by two-dimensional smart-pixel optoelectronic cellular arrays. We emphasize the behavior of the cellular hypercube in performing shift-invariant parallel shifts of data, a basic requirement of most single-instruction multiple-data algorithms. We present a time-multiplexing scheme for realizing the cellular hypercube, showing that the communication time is inversely proportional to the number of optical detectors per cell. We also present an improved hybrid interconnection network with improved performance that combines the cellular hypercube and mesh, using optics for the longer-distance connections and electronics for nearest-neighbor connections.

Nonlinear optical processing: analysis and synthesis.

Coherent optical systems are of interest in image or data processing because of their ability to handle rapidly large bandwidth data in parallel. They have been restricted to performing linear operations such as Fourier transformation and convolution due to the inherent linear nature of an optical system at low power levels. In this paper, the combination of a nonlinear halftoning step followed by bandpass spatial filtering to yield a specific nonlinear intensity transfer function is explored. A general analysis of the problem assuming infinite copy film gamma and saturation density is made. A constructive algorithm for designing a halftone cell shape and selecting the diffraction order to yield very general types of nonmonotonic nonlinearities is presented. Numerous examples of the synthesis procedure are given. Experimental results with general halftone screens made on a plotting flatbed microdensitometer are presented. Logarithmic, exponential, and level slice characteristics are achieved with monotonic cells.

Nonlinear optical processing: nonmonotonic halftone cells and phase halftones.

The halftone screen process has proven to be a useful, flexible technique for achieving general nonlinear functions in coherent optical systems. The two steps to the process involve making a binary pulse-width modulated copy of the continuous-level input using a halftone screen and spatial filtering of single diffraction orders of the image to produce the nonlinearly transformed output. The halftone screens are usually monotonic nondecreasing functions; thus the fundamental sampling periodicity of the screen is maintained. This paper describes some generalizations of the process using nonmonotonic periodic halftone screens. With this new type of screen, functions with an arbitrary number of slope changes can be obtained in the first diffraction order. A detailed synthesis algorithm for specifying the screen shape is given, along with examples and experimental realization of irradiance notch filter and quantization functions. A technique for making the halftone process more resistant to line blooming is descr bed, and a binary phase system made by bleaching ordinary halftoned input is analyzed.

Nonlinear optical processing: effects of input medium and precompensation.

The halftone screen process for obtaining nonlinear functions with coherent optical systems utilizes a preiprocessing step with an ideally hard-clipping binaryinput recording medium. This paper analyzes in detail the effects of using film or other media with finite gamma and saturation density. A mathematical model to predict the system performance for both one-step and two-step copying procedures is developed, and numerous computer results of parameter variation are given. It is found that nonlinear functions with threshold or jump characteristics are the most sensitive to the nonideal effects. A precompensation technique allowingnonideal copy film to be used with minimum degradation of the transfer characteristic is presented, and an algorithm for calculating compensated halftone cell shapes is given, with examples.

Restoration of noisy blurred images by a smoothing spline filter.

For the restoration of noisy blurred images, a controllable smoothing criterion based on the locally variable statistics and minimization of the second derivative is defined, and the corresponding filter, applicable to both space-variant and space-invariant degradations, is obtained. The output of this filter is a cubic spline function. The parameters of the filter determine the local smoothing window and over-all extent of smoothing, and thus the tradeoff between resolution and smoothing is controllable in a spatially nonstationary manner. The interesting properties of this filter have made it capable of restoring signal-dependent noisy images, and it has been successfully applied for filtering images degraded by film-grain noise. Since the matrices of this filter are banded circulant or Toeplitz, efficient algorithms are used for matrix manipulations.

Image restoration by spline functions.

Spline functions, because of their highly desirable interpolating and approximating characteristics, are used as a potential alternative to the conventional pulse approximation method in digital image processing. In space-invariant imaging systems, the object and point-spread function are represented by a class of spline functions called B-splines. Exploiting the convolutional property of B-splines, the deterministic part of the degraded image is another B-spline of higher degree. A minimum norm principle leading to pseudoinversion is used for the restoration of space-invariant degradations with underdetermined and overdetermined models. The singular-value-decomposition technique is used to determine the pseudoinverse.

Estimation of images degraded by film-grain noise.

Film-grain noise describes the intrinsic noise produced by a photographic emulsion during the process of image recording and reproduction. In this paper we consider the restoration of images degraded by film-grain noise. First a detailed model for the over-all photographic imaging system is presented. The model includes linear blurring effects and the signal-dependent effect of film-grain noise. The accuracy of this model is tested by simulating images according to it and comparing the results to images of similar targets that were actually recorded on film. The restoration of images degraded by film-grain noise is then considered in the context of estimation theory. A discrete Wiener filer is developed which explicitly allows for the signal dependence of the noise. The filter adaptively alters its characteristics based on the nonstationary first order statistics of an image and is shown to have advantages over the conventional Wiener filter. Experimental results for modeling and the adaptive estimation filter are presented.

Detection of low-contrast images in film-grain noise.

When low contrast photographic images are digitized by a very small aperture, extreme film-grain noise almost completely obliterates the image information. Using a large aperture to average out the noise destroys the fine details of the image. In these situations conventional statistical restoration techniques have little effect, and well chosen heuristic algorithms have yielded better results. In this paper we analyze the noisecheating algorithm of Zweig et al. [J. Opt. Soc. Am. 65, 1347 (1975)] and show that it can be justified by classical maximum-likelihood detection theory. A more general algorithm applicable to a broader class of images is then developed by considering the signal-dependent nature of film-grain noise. Finally, a Bayesian detection algorithm with improved performance is presented.

Computer-generated double-phase holograms.

A method of computer generating binary holograms based on the decomposition of a complex value into two phase quantities is described. Each Fourier transform cell is divided into subcells, and phase quantities are encoded by the detour phase technique. Noise due to the displacement of the subcells and the phase coding is discussed. Methods of suppressing this noise are also included.

Cellular interconnects optimization algorithm for optoelectronic single-instruction multiple data.

We present a novel algorithm for designing optimal cellular interconnects (OCI's), which can significantly accelerate the communications among processors in single-instruction multiple-data machines with optoelectronic interconnections. We present the foundations of the OCI architecture and show that the optoelectronic OCI is the optimal topology for a space-invariant interconnect pattern. The OCI is optimal in achieving a minimum number of clock cycles per data shift for a given number of optoelectronic links. In addition, our algorithm for designing the OCI is deterministic, whereas previous designs required a trial-and-error procedure.

Detection of moving point objects against a moving background.

The temporal spectral characteristics of a dim moving point object and a moving background, as observed by a sensor array, are analyzed. This type of problem occurs in remote sensing, machine vision, and many other applications. The diffraction limitation of the sensor optics ensures that the temporal spectrum of the background moving with a finite velocity has a finite maximum bandwidth, regardless of background structure. Because the outputs of the sensor array are time sampled, its spectrum is infinitely replicated over an interval of temporal frequency equal to the reciprocal of the sampling time. If this interval is at least twice as large as the maximum background temporal frequency, there is a region with no background components in the middle of each interval. However, because the point object temporal spectrum in the sampled sensor array output is continuously distributed, this region will contain part of the point object signal. Thus, a criterion for the existence of an effective background suppression filter is that the point object fundamental frequency must be greater than the maximum background temporal frequency. When this criterion is satisfied, the amount of background leakage in the filter depends on the sharpness of its passband response and its stopband characteristics. In general, higher-order filters have sharper response and hence better performance. If the criterion is not met, all types of filter lose their effectiveness since the background signal will leak through the passband of the filter. The fundamental concepts developed here were examined for some typical parameter values. It is shown that for this system the point object can be effectively discriminated. In some cases the point object and background temporal spectral responses vary significantly with spatial position within the field of view. Because the filter's center frequency must match the point object temporal fundamental frequency, it is necessary to use an adaptive filter in these situations.

Nonlinear optical processing with halftones: accurate predictions for degradation and compensation.

A general analysis of the halftone process for nonlinear transformations in optical signal processing is presented. The analysis considers the effects of the nonideal characteristics of the recording medium. The results predict output errors due to different parts of the recording medium characteristic curve for any nonlinear transformation. A synthesis method for a discrete halftone screen density profile is also described. This produces an optimum halftone screen density profile for any form of recording medium characteristic curve and any type of nonlinearity in the sense that it minimizes the mean-square difference between desired and degraded outputs. The results of a computer simulation for logarithmic and level slice functions are given.

Image algebra representation of parallel optical binary arithmetic.

A binary image algebra (BIA) that gives a mathematical description of parallel processing operations is described. Rigorous and concise BIA representations of parallel arithmetic and symbolic substitution operations are given. A sequence of programming steps for implementation of these operations on a parallel architecture is specified by the BIA representation. Examples of arithmetic operations implemented on a digital optical cellular image processor architecture are given.