Hybrid Input Output Research Articles

Iterative phase retrieval without support

An iterative phase retrieval method for nonperiodic objects has been developed from the charge-flipping algorithm proposed in crystallography. A combination of the hybrid input-output (HIO) algorithm and the flipping algorithm has greatly improved performance. In this combined algorithm the flipping algorithm serves to find the support (object boundary) dynamically, and the HIO part improves convergence and moves the algorithm out of local minima. It starts with a single intensity measurement in the Fourier domain and does not require a priori knowledge of the support in the image domain. This method is suitable for general image recovery from oversampled diffuse elastic x-ray and electron-diffraction intensities. The relationship between this algorithm and the output-output algorithm is elucidated.

Hybrid projection-reflection method for phase retrieval.

The phase-retrieval problem, fundamental in applied physics and engineering, addresses the question of how to determine the phase of a complex-valued function from modulus data and additional a priori information. Recently we identified two important methods for phase retrieval, namely, Fienup's basic input-output and hybrid input-output (HIO) algorithms, with classical convex projection methods and suggested that further connections between convex optimization and phase retrieval should be explored. Following up on this work, we introduce a new projection-based method, termed the hybrid projection-reflection (HPR) algorithm, for solving phase-retrieval problems featuring nonnegativity constraints in the object domain. Motivated by properties of the HPR algorithm for convex constraints, we recommend an error measure studied by Fienup more than 20 years ago. This error measure, which has received little attention in the literature, lends itself to an easily implementable stopping criterion. In numerical experiments we found the HPR algorithm to be a competitive alternative to the HIO algorithm and the stopping criterion to be reliable and robust.

Experimental lensless soft-X-ray imaging using iterative algorithms: phasing diffuse scattering.

Images of randomly placed two-dimensional arrays of gold balls have been reconstructed from their soft-X-ray transmission diffraction patterns. An iterative hybrid input-output (HiO) algorithm was used to solve the phase problem for the continuous distribution of diffuse X-ray scattering. Knowledge of the approximate size of the clusters was required. The images compare well with scanning electron microscope (SEM) images of the same sample. The use of micrometre-sized silicon nitride window supports is suggested, and absorption filters have been used to allow collection of low spatial frequencies often obscured by a beam stop. This method of phasing diffuse scattering may have application to scattering from individual inorganic nanostructures or single macromolecules.

Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation

The hybrid input–output iterative algorithm, which solves the phase problem for scattering from non-periodic objects, is reviewed for application to X-ray and electron diffraction data. Desirable convex constraints, including the sign of the scattering potential for electrons, and compact support, are discussed. The cases of complex and real exit-face wavefunctions, strong and weak phase objects, various supports, and the use of coherent focussed radiation are reviewed. Reconstruction of general complex objects requires accurate knowledge of the support, which should consist of two holes or a triangle in an opaque mask. The support boundaries should be as sharp as possible. Strong phase objects without absorption can be recovered if the support consists of one hole, is accurately known and has sufficiently sharp boundaries. Real and weak phase objects with absorption can be recovered without accurate knowledge of the support area if the support boundaries are sufficiently sharp and the support consists of one or more holes. A sign constraint on the scattering potential is used to recover weak phase objects. The experimental realization of theoretically desirable support conditions is discussed. A two-stage method of finding the support for complex objects is proposed. Experimental results from applying the Gerchberg–Saxton–Fienup HiO-algorithm to coherent electron diffraction patterns are presented, using specially made e-beam lithographed support structures. Images with a resolution of about 5 nm are thus recovered from the intensities alone in coherent electron diffraction patterns from non-periodic objects. Limitations of the present experiments are identified and suggestions made for development of both X-ray and electron work.

A Hybrid Input-Output Approach to Model Metabolic Systems: An Application to Intracellular Thiamine Kinetics

Models of the dynamics of complex metabolic systems offer potential benefits to the deep comprehension of the system under study as well as for the performance of certain tasks. Unfortunately, dynamic modeling of a great deal of metabolic systems may be problematic due to the incompleteness of the available knowledge about the underlying mechanisms and to the lack of an adequate observational data set. In theory, a valid alternative to classical structural modeling through ordinary differential equations could be represented by input-output approaches. But, in practice, such methods, which learn the nonlinear dynamics of the system from input-output data, fail when the experimental data set is poor either in size or in quality. Such a situation is not rare in the case of metabolic systems. This paper deals with a hybrid approach which aims at overcoming the problems addressed above. More specifically, it allows us to solve the identification problems of the intracellular thiamine kinetics in the intestine tissue. The method, which is half way between the structural and input-output approach, uses the outcomes of the simulation of a qualitative structural model to build a good initialization of a fuzzy system identifier. Such an initialization allows us to efficiently cope with both the incompleteness of knowledge and the inadequacy of the available data set, and to derive an input-output model of the intracellular thiamine kinetics in the intestine tissue. The comparison of the predictions of the intracellular thiamine kinetics obtained by the application of such a model with those obtained by traditional approaches, namely compartmental models, neural networks, and fuzzy systems, highlighted a better performance of our model. As the structural assumptions are relaxed, we obtained a model slightly less informative than a purely structural one but robust enough to be used as a simulator. The paper also discusses the interpretative potential offered by such a model, as tested on diabetic subjects.

Reconstruction of an object from its noisy Fourier modulus: ideal estimate of the object to be reconstructed and a method that attempts to find that estimate

In general, the problem of reconstructing an object from its Fourier modulus has no solution when the Fourier modulus is contaminated by noise. Therefore a quasi solution, which we call the ideal estimate of the object to be reconstructed, is defined here based on the concept of territories of the convergence objects of the error-reduction algorithm, and a method that attempts to find that solution is presented. Keeping in mind that the ideal estimate is one of the output-stagnation objects of the hybrid input-output algorithm, we modify the hybrid input-output algorithm so that the output-stagnation objects can be located even when the value of the feedback parameter is not infinitesimally small, and this modified algorithm is combined with the hybrid input-output algorithm itself. The results of computer simulations carried out to test the performance of the proposed method are shown.

Further study on the convergence property of the hybrid input–output algorithm used for phase retrieval

In our previous paper [J. Opt. Soc. Am. A15, 2849 (1998)], we investigated the behavior of the hybrid input–output algorithm (HIO) used for phase retrieval and showed that the HIO with an infinitesimally small feedback parameter has two abilities that are extremely important in finding a solution: the ability to locate an output-stagnation object and the ability to emerge from an output-stagnation object if it is not a solution. The behavior of the HIO is analyzed further, and an additional aspect is demonstrated that is also important in finding a solution. That is, outside the support of the input object of the HIO, the output-object values outside the support that have been produced so far accumulate so that the probability is conjectured to be extremely low that the HIO will fall into a periodic state. On the other hand, it is also demonstrated that this aspect of the HIO is not usually effective in the combination algorithm composed of the HIO and the error-reduction algorithm. To give credibility to our arguments, we show results that were obtained by reexamining the examples adopted in Seldin and Fienup’s numerical experiments [J. Opt. Soc. Am. A7, 412 (1990)].

Study on the convergence property of the hybrid input–output algorithm used for phase retrieval

Even though the hybrid input–output algorithm (HIO) has been recognized empirically to be one of the most successful versions of the iterative Fourier transform algorithm used for phase retrieval, its behavior is not yet well understood. Therefore a theoretical investigation on the convergence property of the HIO with an infinitesimally small feedback parameter is presented, although on a rather intuitive level, and it is shown that, until a solution is found, this algorithm continues to travel among the objects seeking those that satisfy the Fourier-domain constraint and for which the object-domain error has a locally minimum value. The concept of the territory is introduced with use of the algorithm constructed by modifying the HIO, and then the results are presented of the computer simulations for 2×2 objects with L-shaped support that were carried out to test the validity of our theory and to gain insight into the case in which the value of the feedback parameter is finite.

Numerical investigation of the inverse blackbody radiation problem

A numerical algorithm for the inverse blackbody radiation problem, which is the determination of the temperature distribution of a thermal radiator (TDTR) from its total radiated power spectrum (TRPS), is presented, based on the general theory of amplitude-phase retrieval. With application of this new algorithm, the ill-posed nature of the Fredholm equation of the first kind can be largely overcome and a convergent solution to high accuracy can be obtained. By incorporation of the hybrid input–output algorithm into our algorithm, the convergent process can be substantially expedited and the stagnation problem of the solution can be averted. From model calculations it is found that the new algorithm can also provide a robust reconstruction of the TDTR from the noise-corrupted data of the TRPS. Therefore the new algorithm may offer a useful approach to solving the ill-posed inverse problem.

A Review of the Literature Supporting the Hybrid Approach to Constructing Regional Input–Output Models

Fueled by the high costs of survey-based models and the inherent inaccuracies of non-survey models, a literature has emerged on hybrid regional input–output models. Although this literature has been instructive on the general approach that should be taken in the construction of such models, authors have provided little information about the precise methods they have used to idenfy. the portions of the models for which superior data are worth the effort to obtain. In addition, the role of non-survey techniques used to produce survey-based tables has not been well articulated in the literature. This paper reviews approaches that have been used in input—output analysis that might be adopted for use in constructing hybrid input–output models. It is argued that hybrid model constructors should pursue the most accurate non-survey model of their region as possible (use accurate regional purchase coefficients and minimize aggregation), always seek superior data for households and establishments in resource-based ...

Iterative blind deconvolution algorithm applied to phase retrieval

The iterative blind deconvolution algorithm proposed by Ayers and Dainty [ Opt. Lett.13, 547 ( 1988)] and improved on by Davey et al. [ Opt. Commun.69, 353 ( 1989)] is applied to the problem of phase retrieval, which is a special case of the blind deconvolution problem. A close relationship between this algorithm and the error-reduction version of the iterative Fourier-transform phase-retrieval algorithm is shown analytically. The performance of the blind deconvolution algorithm is compared with the error-reduction and hybrid input–output versions of the iterative Fourier-transform algorithm by reconstruction experiments on real-valued, nonnegative images with and without noise.