Uncertainty principle for axial power content of highly focused fields.

In the analysis of the on-axis intensity for a highly focused optical field, it is highly desirable to deal with effective relations aimed at characterizing the field behavior in a rather simple fashion. Here, a novel and adequate measure for the size of the region where the axial power content mainly concentrates is proposed on the basis of an uncertainty principle. Accordingly, a meaningful relationship is provided for both the spread of the incident beam at the entrance of the highly focused optical system and the size of the region where the on-axis power mainly concentrates.

Characterisation of fan-beam collimators.

Fan-beam collimators offer a good balance between resolution and noise. The collimator response may be included in iterative reconstruction algorithms in order to improve single-photon emission tomography (SPET) resolution. To this end, accurate determination of the focal region and characterisation of the collimator response as a function of the source co-ordinates must be performed. In this paper, a method to characterise fanbeam collimators is evaluated. First, we calculated the real focal region and the accuracy of the collimator convergence. Then, we confirmed the hypothesis that Gaussian distributions adequately fit the collimator responses, although no individualised treatment was performed for the tails of detector response which are associated with scattering and septal penetration. Finally, analytical functions were used to model the resolution and sensitivity. The parameter values in these functions were obtained from experimental measures by non-linear regression fitting. Our findings show differences of 1.43% between nominal and real focal length and standard deviations of 2.5 mm in the x-direction and 7.1 mm in the y-direction for the focal convergence. The correlation coefficients between experimental and predicted values were 0.994 for resolution and 0.991 for sensitivity. As a consequence, the proposed method can be used to characterise the collimator response.

Optical correlation by use of partial phase-only modulation with VGA liquid-crystal displays.

The development of liquid-crystal panels for use in commercial equipment has been aimed at improving the pixel resolution and the display efficiency. These improvements have led to a reduction in the thickness of such devices, among other outcomes, that involves a loss in phase modulation. We propose a modification of the classical phase-only filter to permit displays in VGA liquid-crystal panels with a constant amplitude modulation and less than a 2pi phase modulation. The method was tested experimentally in an optical setup.

On-axis joint transform correlation based on a four-level power spectrum.

We propose a method to obtain a single centered correlation with use of a joint transform correlator. We analyze the required setup to carry out the whole process optically, and we also present experimental results.

Evaluation of a cross-validation stopping rule in MLE SPECT reconstruction.

One of the problems in the routine use of the maximum-likelihood estimator method-expectation maximization (MLE-EM) algorithm is to decide when the iterative process should be stopped. We studied a cross-validation stopping rule to assess its usefulness in SPECT. We tested this stopping rule criterion in the MLE-EM algorithm without acceleration as well as in two accelerating algorithms, the successive substitutions algorithm (SSA) and the additive algorithm (AA). Different values of an acceleration factor were tested in SSA and AA. Our results from numerical and physical phantoms show that the stopping rule based on the cross-validation ratio (CVR) takes into account the similarity of the reconstructed image to the ideal image, noise and the contrast of the image. CVR yields reconstructed images with balanced values of the figures of merit (FOM) employed to assess the image quality. The CVR criterion can be used in the original MLE-EM algorithm as well as in SSA and AA. The reconstructed images obtained with SSA and AA showed FOM values that were very similar. These results were justified by considering AA to be an approximate form of SSA. The range of validity for the acceleration factor in SSA and AA was found to be [1, 2]. In this range, an inverse function connects the acceleration factor to the number of iterations needed to attain prefixed values of FOMs.

Correlation postprocessing-based method for the detection of defocused images.

We present a method to detect patterns in defocused scenes by means of a joint transform correlator. We describe analytically the correlation plane, and we also introduce an original procedure to recognize the target by postprocessing the correlation plane. The performance of the methodology when the defocused images are corrupted by additive noise is also considered.

The influence of a relaxation parameter on SPECT iterative reconstruction algorithms.

Algebraic reconstruction techniques (ARTs) have been intensively studied in image reconstruction. However, reconstructed images often exhibit a characteristic noise when applied to emission tomography. In this work, we study the influence of the ART relaxation parameter and identify values of that parameter which yield smooth images and good convergence. The study includes both simulated and real single photon emission computed tomographic (SPECT) data. In the simulated studies, scattering, attenuation, noise and detector response were included. Relaxation factors ranging between 0.01 and 0.35 were considered. Total counts in projections were between 2.5 x 10(5) and 10(6) in one slice. The goodness of the reconstructions was assessed by using the correlation coefficient between the pattern and the actual reconstruction (CC), the background coefficient of variation (CV), the contrast (CON) and the signal-to-noise ratio (SNR). The results show that values for the relaxation factor and number of interations close to 0.1 and 8, respectively, yield reconstructed images in which CC, CV, CON and SNR have well balanced values and CC, CV and SNR are very close to the extremal. An increase in either the number of iterations or in the relaxation factor results in a rise of CON but the other three FOMs deteriorate. The results from the real phantom, which are in agreement with those of the simulated studies, validate the simulation method and demonstrate the influence of the relaxation parameter.

Computation of arbitrarily constrained synthetic discriminant functions.

An algorithm for computing correlation filters based on synthetic discriminant functions that can be displayed on current spatial light modulators is presented. The procedure is nondivergent, computationally feasible, and capable of producing multiple solutions, thus overcoming some of the pitfalls of previous methods.

Nonlinear filtering in object and Fourier space in a joint transform optical correlator: comparison and experimental realization.

The use of different kinds of nonlinear filtering in a joint transform correlator are studied and compared. The study is divided into two parts, one corresponding to object space and the second to the Fourier domain of the joint power spectrum. In the first part, phase and inverse filters are computed; their inverse Fourier transforms are also computed, thereby becoming the reference in the object space. In the Fourier space, the binarization of the power spectrum is realized and compared with a new procedure for removing the spatial envelope. All cases are simulated and experimentally implemented by a compact joint transform correlator.

Diffraction theory of optimized low-resolution Fresnel encoded lenses.

A mathematical model describing the behavior of low-resolution Fresnel encoded lenses (LRFEL's) encoded in any low-resolution device (e.g., a spatial light modulator) has recently been developed. From this model, an LRFEL with a short focal length was optimized by our imposing the maximum intensity of light onto the optical axis. With this model, analytical expressions for the light-amplitude distribution, the diffraction efficiency, and the frequency response of the optimized LRFEL's are derived.

Sidelobe elimination for generalized synthetic discriminant functions by a two-filter correlation and subsequent postprocessing of the intensity distributions.

One of the most important problems in optical pattern recognition by correlation is the appearance of sidelobes in the correlation plane, which causes false alarms. We present a method that eliminate sidelobes of up to a given height if certain conditions are satisfied. The method can be applied to any generalized synthetic discriminant function filter and is capable of rejecting lateral peaks that are even higher than the central correlation. Satisfactory results were obtained in both computer simulations and optical implementation.

Controlled-intensity detection peaks in a binary joint transform correlator.

In multiobject pattern recognition the height of the correlation peaks should be controlled when the power spectrum of ajoint transform correlator is binarized. In this paper a method to predetermine the value of detection peaks is demonstrated. The technique is based on a frequency-variant threshold in order to remove the intraclass terms and on a suitable factor to normalize the binary joint power spectrum. Digital simulations and experimental hybrid implementation of this method were carried out.

Diffraction efficiency of low-resolution Fresnel encoded lenses.

A mathematical model to describe the behavior of low-resolution Fresnel lenses encoded in any low-resolution device (e.g., a spatial light modulator) is developed. From this model the diffraction efficiency is calculated in terms of all the parameters that characterize these lenses.

Effects of thresholding level variation in fringe binarization of multiobject joint transform correlation.

It is possible to improve the fringe binarization method of joint transform correlation by choosing a suitable threshold level.

Evaluation of thallium myocardial-perfusion imaging by means of washout parametric images: a simulation study.

A method for the evaluation of myocardial perfusion with 201Tl scintigraphic images is presented. The method is based on making a pixel-by-pixel comparison of the stress and the redistribution images aligned by using bidimensional correlation techniques between the nonpathologic regions of the myocardium. The comparison is made by means of parametric images of the washout, which are evaluated by calculating separately the mean values in the normal and the abnormal regions. The study is carried out on controlled models that contain myocardium, an artifact, and noise. The results show the suitability of the method and confirm the validity of its application to individualized studies of clinical interest.

Thallium-201 myocardial planar scintigrams. Alignment of stress and rest images by correlation.

The utility of the correlation for alignment of myocardial perfusion imaging with 201TI was studied. The tests were made by numerical simulation of a heart model with an artefact and a theoretical background superimposed in normal and pathological situations. The methods used were bidimensional and unidimensional correlation techniques and were applied either with or without previous background subtraction. Our results show the suitability of this alignment technique, useful in finding the displacement between images with an average error inferior to one pixel in different situations of myocardial damage.

Methods of background subtraction in myocardial perfusion imaging with thallium-201: a comparative study in the presence of an artefact.

For thallium imaging quantitation, a simulation study has been made using different methods of interpolation for background subtraction and studying their behaviour in the presence of an artefact. Two artefacts were used, one simulating hepatic or splenic uptake and the other diaphragmatic activity. The interpolative methods used were three classic techniques using standard masks. Their algorithms were modified so that they could also be used with arbitrarily shaped masks enclosing myocardium, and a comparison between the original and modified methods was made. Our results show an improvement when using the modified algorithms adapted to the arbitrarily outlined mask.

Atypical cristae (paracrystalline inclusions) in mitochondria of epithelial cell of the rat ureter. II. Image analysis.

Long mitochondria containing paracrystalline inclusions have been detected in the epithelial cells of the basal layer of the rat ureter close to the bladder (Barastegui and Ruano-Gil, 1978). In the first part of this investigation the origin of these inclusions from alterations of the cristae has been suggested. The current report deals with an analysis by microdensitometry, optical diffraction and goniometry of the inclusions as well as with their possible architecture. A tridimensional model of the paracrystalline inclusions is proposed.