Abstract: The technique of Fourier deconvolution is a powerful tool for testing distributional predictions of stage models of reaction time. However, direct application of Fourier theory to reaction time data has sometimes produced disappointing results. This article reviews Fourier transform theory as it applies to the problem of deconvolving a component of the reaction time distribution. Problems encountered in deconvolution are shown to be due to the presence of noise in the Fourier transforms of the sampled distributions, which is amplified by the operation of deconvolution. A variety of filtering techniques for the removal of noise are discussed, including window functions, adaptive kernel smoothing, and optimal Wiener filtering. The best results were obtained using a window function whose pass band was determined empirically from the power spectrum of the deconvolved distribution. These findings are discussed in relation to other, nontrigonometric approaches to the problem of deconvolution.

Abstract: A curve extraction algorithm which is defined within a multiresolution framework is described An image model based on local features such as lines and edges is assumed, and the parameters of this model are estimated using the multiresolution Fourier transform The estimated features, which exist at different spatial resolutions, are then combined into curves using an appropriate curvature measure The scheme is generally applicable and can be implemented in an efficient manner within a hierarchical data structure Results presented demonstrate that it is capable of identifying curves in natural images >

Abstract: In many imaging situations the quality of the image is degraded by phase errors. In this paper we describe an algorithm for correcting phase errors. It is applicable to cases in which the phase- error-degraded complex Fourier transform of the aberrated image is available; these include imaging with heterodyne sensors or with interferometric sensors. The phase-error correction algorithm is a variation on the iterative Fourier transform (phase retrieval) algorithm. It uses a support constraint on the object, making it useful for imaging bright objects on dark backgrounds. It can be extended to include uncertainties in both the modulus and the phase of the Fourier transform.

Abstract: The phase retrieval method using an exponential filter based on Fourier series expansion is used in the reconstruction of phase objects from experimental far field intensities. The phase objects in this experiment are a converging lens and a circular aperture placed on the center of the lens. The object is illuminated by a laser beam, and the complex amplitude function on the circular aperture is reconstructed from three far field intensities, which are obtained with and without the exponential filter at the aperture. A cross section of the reconstructed phase is found to be almost the same as that of the theoretical phase at the aperture.

Abstract: Significant research and development have been made on various kinds of CT's such as the X-ray, the MRI and the positron, which are applied widely in practice. The CT device is divided into the measurement system and the image reconstruction system. Efforts are still being made at present to improve the resolution and speed of those systems. This paper discusses the 2-D Fourier transform method, which is one of the image reconstruction methods that have been investigated and applied in the image reconstruction in various types of CT's. Traditionally, the 2-D Fourier transform method has been considered as suffering from low image quality, although the image can be reconstructed with a high speed. The reason for image degradation is the lack of accuracy in the interpolation in the 2-D Fourier transform domain, which can be remedied by improving the accuracy. A problem then is that the coordinate transformation in the Fourier domain depends on the individual CT. From such a viewpoint, this paper analyzes the relation between the coordinate transformation and the reconstructed image to indicate the reason for the image degradation. A systematic analysis is made of the reconstructed image when the linear interpolation is applied to each coordinate transformation, to indicate the reason for the image degradation and to describe the artifact appearing in the reconstructed image. Based on the result of this analysis, an algorithm is constructed which can eliminate the artifact from the reconstructed image. The algorithm is composed of the normalization algorithm for the interpolation characteristics, the interpolation by the fast-Fourier transform and the inverse 2-D Fourier transform enlarging the reconstructed image region. The effectiveness of the method is demonstrated by applying the method to the transformation from the polar to the Cartesian coordinate.

Abstract: An image registration algorithm combining image analysis and signal processing techniques is applied to a sequence of complex images. The frequency-domain registration technique described here is faster than the conventional spatial domain correlation techniques and does not suffer from the non-uniqueness of solution. The specific technique used in this work involves power spectrum for rotation correction and power cepstrum for translation correction. Furthermore, a comparison of another frequency-domain translation correction technique namely phase correlation and power cepstrum technique reveals clear superiority of the latter method for noisy images and for specific application namely registration of sequential complex images. The general procedure of employing feature extraction techniques prior to registration for simplifying the image and subsequent registration of images based on power spectrum and 2-D cepstrum techniques provide an unambiguous, accurate and fast method of comparison for a broad range of sequential complex images.

Abstract: Considers the development and evaluation of real-time image processing algorithms capable of measuring, to sub-pixel accuracy, the displacement between images subjected to simultaneous translation and rotation. The techniques could have a number of applications, for example, in stabilising imagery recorded from vibrating platforms or in the data compression of moving imagery. The following classes of algorithm were investigated: phase correlation algorithms (both 2-dimensional and 1-dimensional); and intensity gradient based algorithms.

Abstract: A model-based approach for superresolution signal reconstruction from noisy bandlimited Fourier data is proposed. The approach combines the virtues of parametric and nonparametric techniques by maximum-likelihood fitting of the data by a mixture of exponentials and smooth basis functions. Performance bounds are derived and analyzed, and a model computationally efficient algorithm is described. The performance of the algorithm in simulations closely matches the bounds over a wide range of operating conditions. Overall, the reconstructions are far superior to those obtained by traditional Fourier transform processing. >

Abstract: A technique involving the use of a 2-D fast Fourier transform has been developed to evaluate the plane-polar near-field-to-far-field transformation. Because of the efficiency of the interpolation, which makes it possible to compute the field in any plane comprising the origin of the polar grid, a software package including probe correction has been written to perform both plane-polar and plane-rectangular near-field-to-far-field transformations. A highly directive antenna with rapidly varying near fields has been used to test the proposed method. >

Abstract: A new, technique is proposed to reconstruct an astronomical image by using a phase retrieval from exponential filtered and unfiltered images based on the Fourier series expansion method. The amplitude of the Fourier transform of the filtered image is a mixture of the information of the Fourier amplitude and phase corresponding to the unfiltered image. Therefore, the phase information can be derived from the Fourier modulus of the filtered image based on the Fourier decomposition method. We have tried to apply this method to stellar speckle interferometry and the successful reconstruction of a double star image has been obtained.

Abstract: It is difficult to reconstruct an image of a complex-valued object from the modulus of its Fourier transform (i.e., retrieve the Fourier phase) except in some special cases. By using additionally a low-resolution intensity image from a telescope with a small aperture, a fine-resolution image of a general object can be reconstructed in a two-step approach. First the Fourier phase over the small aperture is retrieved, using the Gerchberg–Saxton algorithm. Then that phase is used, in conjunction with the Fourier modulus data over a large aperture together with a support constraint on the object, to reconstruct a fine-resolution image (retrieve the phase over the large aperture) by the iterative Fourier-transform algorithm. The second step requires a modified algorithm that employs an expanding weighting function on the Fourier modulus.