Exploiting sparsity and low-rank structure for the recovery of multi-slice breast MRIs with reduced sampling error

It has been shown that, magnetic resonance images (MRIs) with sparsity representation in a transformed domain, e.g. spatial finite-differences (FD), or discrete cosine transform (DCT), can be restored from undersampled k-space via applying current compressive sampling theory. The paper presents a model-based method for the restoration of MRIs. The reduced-order model, in which a full-system-response is projected onto a subspace of lower dimensionality, has been used to accelerate image reconstruction by reducing the size of the involved linear system. In this paper, the singular value threshold (SVT) technique is applied as a denoising scheme to reduce and select the model order of the inverse Fourier transform image, and to restore multi-slice breast MRIs that have been compressively sampled in k-space. The restored MRIs with SVT for denoising show reduced sampling errors compared to the direct MRI restoration methods via spatial FD, or DCT. Compressive sampling is a technique for finding sparse solutions to underdetermined linear systems. The sparsity that is implicit in MRIs is to explore the solution to MRI reconstruction after transformation from significantly undersampled k-space. The challenge, however, is that, since some incoherent artifacts result from the random undersampling, noise-like interference is added to the image with sparse representation. These recovery algorithms in the literature are not capable of fully removing the artifacts. It is necessary to introduce a denoising procedure to improve the quality of image recovery. This paper applies a singular value threshold algorithm to reduce the model order of image basis functions, which allows further improvement of the quality of image reconstruction with removal of noise artifacts. The principle of the denoising scheme is to reconstruct the sparse MRI matrices optimally with a lower rank via selecting smaller number of dominant singular values. The singular value threshold algorithm is performed by minimizing the nuclear norm of difference between the sampled image and the recovered image. It has been illustrated that this algorithm improves the ability of previous image reconstruction algorithms to remove noise artifacts while significantly improving the quality of MRI recovery.

GFAM: Evolving Fuzzy ARTMAP neural networks

This paper focuses on the evolution of Fuzzy ARTMAP neural network classifiers, using genetic algorithms, with the objective of improving generalization performance (classification accuracy of the ART network on unseen test data) and alleviating the ART category proliferation problem (the problem of creating more than necessary ART network categories to solve a classification problem). We refer to the resulting architecture as GFAM. We demonstrate through extensive experimentation that GFAM exhibits good generalization and is of small size (creates few ART categories), while consuming reasonable computational effort. In a number of classification problems, GFAM produces the optimal classifier. Furthermore, we compare the performance of GFAM with other competitive ARTMAP classifiers that have appeared in the literature and addressed the category proliferation problem in ART. We illustrate that GFAM produces improved results over these architectures, as well as other competitive classifiers.

Experiments with Safe muARTMAP : effect of the network parameters on the network performance

Fuzzy ARTMAP (FAM) is currently considered to be one of the premier neural network architectures in solving classification problems. One of the limitations of Fuzzy ARTMAP that has been extensively reported in the literature is the category proliferation problem. That is, Fuzzy ARTMAP has the tendency of increasing its network size, as it is confronted with more and more data, especially if the data are of the noisy and/or overlapping nature. To remedy this problem a number of researchers have designed modifications to the training phase of Fuzzy ARTMAP that had the beneficial effect of reducing this category proliferation. One of these modified Fuzzy ARTMAP architectures was the one proposed by Gomez-Sanchez, and his colleagues, referred to as Safe muARTMAP. In this paper we present reasonable analytical arguments that demonstrate of how we should choose the range of some of the Safe muARTMAP network parameters. Through a combination of these analytical arguments and experimentation we were able to identify good default parameter values for some of the Safe muARTMAP network parameters. This feat would allow one to save computations when a good performing Safe muARTMAP network is needed to be identified for a new classification problem. Furthermore, we performed an exhaustive experimentation to find the best Safe muARTMAP network for a variety of problems (simulated and real problems), and we compared it with other best performing ART networks, including other ART networks that claim to resolve the category proliferation problem in Fuzzy ARTMAP. These experimental results allow one to make appropriate statements regarding the pair-wise comparison of a number of ART networks (including Safe muARTMAP).

Accurate and Fast Off and Online Fuzzy ARTMAP-Based Image Classification With Application to Genetic Abnormality Diagnosis

We propose and investigate the fuzzy ARTMAP neural network in off and online classification of fluorescence in situ hybridization image signals enabling clinical diagnosis of numerical genetic abnormalities. We evaluate the classification task (detecting a several abnormalities separately or simultaneously), classifier paradigm (monolithic or hierarchical), ordering strategy for the training patterns (averaging or voting), training mode (for one epoch, with validation or until completion) and model sensitivity to parameters. We find the fuzzy ARTMAP accurate in accomplishing both tasks requiring only very few training epochs. Also, selecting a training ordering by voting is more precise than if averaging over orderings. If trained for only one epoch, the fuzzy ARTMAP provides fast, yet stable and accurate learning as well as insensitivity to model complexity. Early stop of training using a validation set reduces the fuzzy ARTMAP complexity as for other machine learning models but cannot improve accuracy beyond that achieved when training is completed. Compared to other machine learning models, the fuzzy ARTMAP does not loose but gain accuracy when overtrained, although increasing its number of categories. Learned incrementally, the fuzzy ARTMAP reaches its ultimate accuracy very fast obtaining most of its data representation capability and accuracy by using only a few examples. Finally, the fuzzy ARTMAP accuracy for this domain is comparable with those of the multilayer perceptron and support vector machine and superior to those of the naive Bayesian and linear classifiers.

A modified K-means algorithm for circular invariant clustering

Several important pattern recognition applications are based on feature vector extraction and vector clustering. Directional patterns are commonly represented by rotation-variant vectors Fd formed from features uniformly extracted in M directions. It is often desirable that pattern recognition algorithms are invariant under pattern rotation. This paper introduces a distance measure and a K-means-based algorithm, namely, Circular K-means (CK-means) to cluster vectors containing directional information, such as Fd, in a circular-shift invariant manner. A circular shift of Fd corresponds to pattern rotation, thus, the algorithm is rotation invariant. An efficient Fourier domain representation of the proposed measure is presented to reduce computational complexity. A split and merge approach (SMCK-means), suited to the proposed CK-means technique, is proposed to reduce the possibility of converging at local minima and to estimate the correct number of clusters. Experiments performed for textural images illustrate the superior performance of the proposed algorithm for clustering directional vectors Fd, compared to the alternative approach that uses the original K-means and rotation-invariant feature vectors transformed from Fd.

Data-partitioning using the Hilbert space filling curves: effect on the speed of convergence of Fuzzy ARTMAP for large database problems

The Fuzzy ARTMAP algorithm has been proven to be one of the premier neural network architectures for classification problems. One of the properties of Fuzzy ARTMAP, which can be both an asset and a liability, is its capacity to produce new nodes (templates) on demand to represent classification categories. This property allows Fuzzy ARTMAP to automatically adapt to the database without having to a priori specify its network size. On the other hand, it has the undesirable side effect that large databases might produce a large network size (node proliferation) that can dramatically slow down the training speed of the algorithm. To address the slow convergence speed of Fuzzy ARTMAP for large database problems, we propose the use of space-filling curves, specifically the Hilbert space-filling curves (HSFC). Hilbert space-filling curves allow us to divide the problem into smaller sub-problems, each focusing on a smaller than the original dataset. For learning each partition of data, a different Fuzzy ARTMAP network is used. Through this divide-and-conquer approach we are avoiding the node proliferation problem, and consequently we speedup Fuzzy ARTMAP's training. Results have been produced for a two-class, 16-dimensional Gaussian data, and on the Forest database, available at the UCI repository. Our results indicate that the Hilbert space-filling curve approach reduces the time that it takes to train Fuzzy ARTMAP without affecting the generalization performance attained by Fuzzy ARTMAP trained on the original large dataset. Given that the resulting smaller datasets that the HSFC approach produces can independently be learned by different Fuzzy ARTMAP networks, we have also implemented and tested a parallel implementation of this approach on a Beowulf cluster of workstations that further speeds up Fuzzy ARTMAP's convergence to a solution for large database problems.