On generalized adaptive neural filter

Linear filters have historically been used in the past as the most useful tools for suppressing noise in signal processing. It has been shown that the optimal filter which minimizes the mean square error (MSE) between the filter output and the desired output is a linear filter provided that the noise is additive white Gaussian noise (AWGN). However, in most signal processing applications, the noise in the channel through which a signal is transmitted is not AWGN; it is not stationary, and it may have unknown characteristics. To overcome the shortcomings of linear filters, nonlinear filters ranging from the median filters to stack filters have been developed. They have been successfully used in a number of applications, such as enhancing the signal-to-noise ratio of the telecommunication receivers, modeling the human vocal tract to synthesize speech in speech processing, and separating out the maternal and fetal electrocardiogram signals to diagnose prenatal ailments. In particular, stack filters have been shown to provide robust noise suppression, and are easily implementable in hardware, but configuring an optimal stack filter remains a challenge. This dissertation takes on this challenge by extending stack filters to a new class of nonlinear adaptive filters called generalized adaptive neural filters (GANFs). The objective of this work is to investigate their performance in terms of the mean absolute error criterion, to evaluate and predict the generalization of various discriminant functions employed for GANFs, and to address issues regarding their applications and implementation. It is shown that GANFs not only extend the class of stack filters, but also have better performance in terms of suppressing non-additive white Gaussian noise. Several results are drawn from the theoretical and experimental work: stack filters can be adaptively configured by neural networks; GANFs encompass a large class of nonlinear sliding-window filters which include stack filters; the mean absolute error (MAE) of the optimal GANF is upper-bounded by that of the optimal stack filter; a suitable class of discriminant functions can be determined before a training scheme is executed; VC dimension (VCdim) theory can be applied to determine the number of training samples; the algorithm presented in configuring GANFs is effective and robust

Geometry Processing of Conventionally Produced Mouse Brain Slice Images

Brain mapping research in most neuroanatomical laboratories relies on conventional processing techniques, which often introduce histological artifacts such as tissue tears and tissue loss. In this paper we present techniques and algorithms for automatic registration and 3D reconstruction of conventionally produced mouse brain slices in a standardized atlas space. This is achieved first by constructing a virtual 3D mouse brain model from annotated slices of Allen Reference Atlas (ARA). Virtual re-slicing of the reconstructed model generates ARA-based slice images corresponding to the microscopic images of histological brain sections. These image pairs are aligned using a geometric approach through contour images. Histological artifacts in the microscopic images are detected and removed using Constrained Delaunay Triangulation before performing global alignment. Finally, non-linear registration is performed by solving Laplace's equation with Dirichlet boundary conditions. Our methods provide significant improvements over previously reported registration techniques for the tested slices in 3D space, especially on slices with significant histological artifacts. Further, as an application we count the number of neurons in various anatomical regions using a dataset of 51 microscopic slices from a single mouse brain. This work represents a significant contribution to this subfield of neuroscience as it provides tools to neuroanatomist for analyzing and processing histological data.Comment: 14 pages, 11 figure

Simplification of the generalized adaptive neural filter and comparative studies with other nonlinear filters

Recently, a new class of adaptive filters called Generalized Adaptive Neural Filters (GANFs) has emerged. They share many characteristics in common with stack filters, include all stack filters as a subset. The GANFs allow a very efficient hardware implementation once they are trained. However, there are some problems associated with GANFs. Three of these arc slow training speeds and the difficulty in choosing a filter structure and neural operator. This thesis begins with a tutorial on filtering and traces the GANF development up through its origin -- the stack filter. After the GANF is covered in reasonable depth, its use as an image processing filter is examined. Its usefulness is determined based on simulation comparisons with other common filters. Also, some problems of GANFs are looked into. A brief study which investigates different types of neural networks and their applicability to GANFs is presented. Finally, some ideas on increasing the speed of the GANF are discussed. While these improvements do not completely solve the GANF\u27s problems, they make a measurable difference and bring the filter closer to reality

Image convolution: a linear programming approach for filters design

AbstractImage analysis is a branch of signal analysis that focuses on the extraction of meaningful information from images through digital image processing techniques. Convolution is a technique used to enhance specific characteristics of an image, while deconvolution is its inverse process. In this work, we focus on the deconvolution process, defining a new approach to retrieve filters applied in the convolution phase. Given an image I and a filtered image $$I' = f(I)$$ I ′ = f ( I ) , we propose three mathematical formulations that, starting from I and $$I'$$ I ′ , are able to identify the filter $$f'$$ f ′ that minimizes the mean absolute error between $$I'$$ I ′ and $$f'(I)$$ f ′ ( I ) . Several tests were performed to investigate the applicability of our approaches in different scenarios. The results highlight that the proposed algorithms are able to identify the filter used in the convolution phase in several cases. Alternatively, the developed approaches can be used to verify whether a specific input image I can be transformed into a sample image $$I'$$ I ′ through a convolution filter while returning the desired filter as output

Morphological filter mean-absolute-error representation theorems and their application to optimal morphological filter design

The present thesis derives error representations and develops design methodologies for optimal mean-absolute-error (MAE) morphological-based filters. Four related morphological-based filter-types are treated. Three are translation-invariant, monotonically increasing operators, and our analysis is based on the Matheron (1975) representation. In this class we analyze conventional binary, conventional gray-scale, and computational morphological filters. The fourth filter class examined is that of binary translation invariant operators. Our analysis is based on the Banon and Barrera (1991) representation and hit-or-miss operator of Serra (1982). A starting point will be the optimal morphological filter paradigm of Dougherty (1992a,b) whose analysis de scribes the optimal filter by a system of nonlinear inequalities with no known method of solution, and thus reduces filter design to minimal search strategies. Although the search analysis is definitive, practical filter design remained elu sive because the search space can be prohibitively large if it not mitigated in some way. The present thesis extends from Dougherty\u27s starting point in several ways. Central to the thesis is the MAE analysis for the various filter settings, where in each case, a theorem is derived that expresses overall filter MAE as a sum of MAE values of individual structuring-element filters and MAE of combinations of unions (maxima) of those elements. Recursive forms of the theorems can be employed in a computer algorithm to rapidly evaluate combinations of structuring elements and search for an optimal filter basis. Although the MAE theorems provide a rapid means for examining the filter design space, the combinatoric nature of this space is, in general, too large for a exhaustive search. Another key contribution of this thesis concerns mitigation of the computational burden via design constraints. The resulting constrained filter will be suboptimal, but, if the constraints are imposed in a suitable man ner, there is little loss of filter performance in return for design tractability. Three constraint approaches developed here are (1) limiting the number of terms in the filter expansion, (2) constraining the observation window, and (3) employing structuring element libraries from which to search for an optimal basis. Another contribution of this thesis concerns the application of optimal morphological filters to image restoration. Statistical and deterministic image and degradation models for binary and low-level gray images were developed here that relate to actual problems in the optical character recognition and electronic printing fields. In the filter design process, these models are employed to generate realizations, from which we extract single-erosion and single-hit-or-miss MAE statistics. These realization-based statistics are utilized in the search for the optimal combination of structuring elements

Model and Appearance Based Analysis of Neuronal Morphology from Different Microscopy Imaging Modalities

The neuronal morphology analysis is key for understanding how a brain works. This process requires the neuron imaging system with single-cell resolution; however, there is no feasible system for the human brain. Fortunately, the knowledge can be inferred from the model organism, Drosophila melanogaster, to the human system. This dissertation explores the morphology analysis of Drosophila larvae at single-cell resolution in static images and image sequences, as well as multiple microscopy imaging modalities. Our contributions are on both computational methods for morphology quantification and analysis of the influence of the anatomical aspect. We develop novel model-and-appearance-based methods for morphology quantification and illustrate their significance in three neuroscience studies. Modeling of the structure and dynamics of neuronal circuits creates understanding about how connectivity patterns are formed within a motor circuit and determining whether the connectivity map of neurons can be deduced by estimations of neuronal morphology. To address this problem, we study both boundary-based and centerline-based approaches for neuron reconstruction in static volumes. Neuronal mechanisms are related to the morphology dynamics; so the patterns of neuronal morphology changes are analyzed along with other aspects. In this case, the relationship between neuronal activity and morphology dynamics is explored to analyze locomotion procedures. Our tracking method models the morphology dynamics in the calcium image sequence designed for detecting neuronal activity. It follows the local-to-global design to handle calcium imaging issues and neuronal movement characteristics. Lastly, modeling the link between structural and functional development depicts the correlation between neuron growth and protein interactions. This requires the morphology analysis of different imaging modalities. It can be solved using the part-wise volume segmentation with artificial templates, the standardized representation of neurons. Our method follows the global-to-local approach to solve both part-wise segmentation and registration across modalities. Our methods address common issues in automated morphology analysis from extracting morphological features to tracking neurons, as well as mapping neurons across imaging modalities. The quantitative analysis delivered by our techniques enables a number of new applications and visualizations for advancing the investigation of phenomena in the nervous system