Donald Fraser

Interpolation by the FFT revisited-an experimental investigation

A numerical investigation into the accuracy of interpolation by, fast Fourier transform (FFT), using a sinusoidal test signal, is described. The method is precisely defined, including a previously unnoticed detail which makes a significant difference to the accuracy of the result. The experiments show that, with no input windowing, the accuracy of interpolation is almost independent of sinusoidal wavelength very close to the Nyquist limit. The resulting RMS error is inversely proportional to input sequence length and is very low for sequence lengths likely to be encountered in practice. As wavelength passes through the Nyquist limit, there is a sudden increase in error, as is expected from sampling theory. If the sequence ends are windowed by short, cosine half-bells, accuracy is further improved at longer wavelengths. In comparison, small-kernal convolution methods, such as linear interpolation and cubic convolution, perform badly at wavelengths anywhere near the Nyquist limit. >

Atmospheric turbulence visualization with wide-area motion-blur restoration

A new technique for visualizing the effects of turbulence in clear air and concurrent wide-area motion-blur image restoration is described. Time sequences of images of a scene are captured with an optical telescope covering a comparatively wide field of view. With short-exposure times, atmospheric distortion is frozen to provide a sequence of randomly warped images. Point-by-point registration results in x and y shift maps describing the warp for each image. These maps provide not only a striking visualization of the turbulence but also a means for dewarping each image prior to averaging to form a wide-area motion-blur-corrected result. It is believed that the technique will be of benefit in astronomy, atmospheric physics, and surveillance.

Multisource data fusion with multiple self-organizing maps

This paper presents a self-organizing neural network approach, known as multiple self-organizing maps (MSOMs), to multisource data fusion and compound classification. The authors use the Kohonen SOM as a building block to set up a design framework for a range of classifiers. They demonstrate that the MSOM is suitable for multisource fusion, where the issues of high dimensionality, complex characteristics and disparity, and joint exploration of spatiality and temporality of mixed data can be adequately addressed. Experiments with a bitemporal data set show the effectiveness of their approach.

Super Resolution for Remote Sensing Images Based on a Universal Hidden Markov Tree Model

In this paper, we propose a new super resolution (SR) method called the maximum a posteriori based on a universal Hidden Markov Tree (HMT) model for remote sensing images. The HMT theory is first used to set up a prior model for reconstructing super resolved images from a sequence of warped, blurred, subsampled, and noise-contaminated low-resolution (LR) images. Because the wavelet coefficients of images can be well characterized as a mixed Gaussian distribution, an HMT model is better able to capture the dependences between multiscale wavelet coefficients. The new method is tested first against simulated LR views from a single Landsat7 panchromatic scene and, then, with actual data from four Landsat7 panchromatic images captured on different dates. Both tests show that our method achieves better SR results both visually and quantitatively than other methods.

Universal HMT based super resolution for remote sensing images

In this paper, we propose a new super resolution method Maximum a Posteriori based on a universal hidden Markov tree model (MAP-uHMT) for remote sensing images. The hidden Markov tree theory in the wavelet domain is used to set up a prior model for reconstructing super resolution images from a sequence of warped, blurred, sub-sampled and contaminated low resolution images. Both the simulation results with a Landsat7 panchromatic image and actual results with four Landsat7 panchromatic images which were captured on different dates show that our method achieves better super resolution images both visually and quantitatively than other methods, based on PSNR in the simulation and derived PSF with actual data.

Avoidance of additional aliasing in multipass image rotations

The two-pass (or multipass) image geometric transformation algorithm is ideally suited to real-time, parallel implementation, but is known to introduce frequency aliasing during rotation, over and above any aliasing which may result from the usual one-pass algorithm. We develop a unified framework and theory that precisely explains this added-aliasing for many of the well-known multipass algorithms, and show that it is usually less than might be expected at first sight. In some cases, the aliasing occurs in nondestructive, and therefore, theoretically recoverable, forms. We also show that the aliasing is very easily reduced, or avoided altogether, while commenting that this problem should be considered as a special case of a general alias-avoidance strategy in geometric transformation. Finally, we include some examples of multipass image rotations which seem to confirm our predictions.

Comparison at high spatial frequencies of two-pass and one-pass geometric transformation algorithms

Abstract Two-pass image geometric transformation algorithms, in which an image is resampled first in one dimension, forming an intermediate image, then in the resulting orthogonal dimension, have many computational advantages over traditional, one-pass algorithms. For example, interpolation and anti-aliasing are easier to implement, being 1-dimensional operations; computer memory requirements are greatly reduced, with access to image data in external memory regularized; while pipelined parallel computation is greatly simplified. An apparent drawback of the two-pass algorithm which has tended to limit its universal adoption is a reported corruption at high spatial frequencies due to apparent undersampling, in certain cases, in the necessary intermediate image. This experimental study set out to resolve the question of possible corruption by computing the mean-square error when a sinusoidal grating test image is rotated, either by an efficient two-pass algorithm or by a traditional one-pass algorithm. It was found that the method used for interpolation has a major effect on the accuracy of the result, poorer methods accentuating differences between the two algorithms. A totally unexpected and fortuitous result is that, by using near-perfect interpolation (e.g., by the FFT), the two-pass algorithm is almost as accurate as one pleases, for rotations up to 45°, to very close to the Nyquist limit (as also is the one-pass algorithm, with near-perfect interpolation). For rotations of φ > 45°, the two-pass algorithm breaks down before the Nyquist limit, but these can be replaced by rotations of 90° - φ and transposition. Thus, the supposed drawback of the two-pass algorithm can be nullified by near-perfect interpolation, at least in the case of rotation, while a major bonus is the greater ease with which interpolation by the FFT may be implemented, in the two-pass case, leading to the possibility of highly faithful geometric transformation in practice, aided by the increasing availability of fast DSP and FFT microcircuits.

M2dSOMAP: clustering and classification of remotely sensed imagery by combining multiple Kohonen self-organizing maps and associative memory

This paper investigates a hybrid neural network framework by combining unsupervised and supervised neural learning paradigms on a unified representation platform of multiple Kohonen 2D self-organizing maps (M2dSOM) with the assistance of associative memory for clustering and classification of remotely sensed (RS) imagery. The M2dSOM is a regional form of such for both cluster region and decision region. A new supervised learning algorithm is proposed that exploits the input portion of supervising samples to discover mismatches between cluster and decision regions by a k-winner selection process and then correct the cluster boundaries based on a majority vote for a new cluster membership from the k winners. Finally, an associative memory is employed to form a mapping between clusters and classification labels by samples. Two association configurations are suggested. Analysis of this mapping SONN model (called M2dSOMAP) in relation to RS imagery analysis with comparison to other methods is briefly discussed.

Linear systems approach to simulation of optical diffraction

The diffractive processes within an optical system can be simulated by computer to compute the diffraction-altered electric-field distribution at the output of the system from the electric-field distribution at the input. In the paraxial approximation the system can be described by an ABCD ray matrix whose elements in turn can be used to simplify the computation such that only a single computational step is required. We describe two rearrangements of such computations that allow the simulation to be expressed in a linear systems formulation, in particular using the fast-Fourier-transform algorithm. We investigate the sampling requirements for the kernel-modifying function or chirp that arises. We also use the special properties of the chirp to determine the spreading imposed by the diffraction. This knowledge can be used to reduce the computation if only a limited region of either the input or the output is of interest.

Bispectral analysis and recovery of images distorted by a moving water surface

We propose a new algorithm to recover a geometrically correct image of an object or scene from a set of images distorted by the wave motion of a water surface. Under mild conditions where the wavy surface normals weakly satisfy a Gaussian distribution, we demonstrate that the geometric distortion can be removed and a corrected image can be recovered. Our method is based on higher-order spectra analysis-in particular, the bispectrum, similar to its use in astronomical speckle imaging. In adapting this technique to imaging through or over a moving water surface, special care must be taken, and specifically tailored techniques are discussed in this paper. Our algorithm has been tested under two different scenarios: the refraction of light through a water surface (the underwater case) and the reflection of light from a water surface (the reflection case). Results in both cases have been encouraging.