Computational algorithms that utilize nondifferentiable functions have proven highly effective in machine learning applications. This study introduces a novel framework for incorporating nondifferentiable functions into the objective functions of random-weight neural networks, specifically focusing on functional link random vector functional-link (RVFL) networks and extreme learning machines (ELMs). Our framework explores six nondifferentiable functions: the norms $ L_{1,1}$ , $ L_{1,2}$ , and $ L_{2,2}$ and the functions AbsMin, AbsMax, and a seminorm MaxMin. To enhance robustness, Fourier random assignments are applied as activation functions within these networks. The integration of these nondifferentiable functions into the objective functions of RVFL and ELM aims to reduce computational time in both training and testing stages, without compromising accuracy. We conducted extensive experiments on 12 benchmark datasets, encompassing small, medium, and large datasets, to evaluate the proposed algorithms against the $L_{2,1}$ -regularized random Fourier feature ELM ( $L_{2,1}$ -RF-ELM), which uses joint-norm regularization ( $L_{r,p}$ ) as documented in previous studies. Our findings indicate that the algorithms based on nondifferentiable functions not only achieve high accuracy but also significantly reduce computation time compared to the $L_{2,1}$ -based algorithm and other standard machine learning approaches.

An important task when processing dynamic PET images is to identify the time-activity curves (TACs) of the pure tissues, along with their corresponding spatial proportions. This step, often referred to as unmixing or factor analysis, is based on a loss function which measures the discrepancy between the observed data and the model. This loss function should be chosen according to the statistical properties of the noise, which is in this case hard to characterize. Indeed, while dynamic PET images results from a decay process that can be statistically described by a Poisson distribution, acquisition and post-filtering reconstruction drastically change the nature of the noise. In the literature dedicated to factor analysis of dynamic PET images, a common and underlying assumption consists in assuming that the dynamic PET images are corrupted by an additive Gaussian or by a Poisson noise. These assumptions lead to the choice of the squared Euclidian distance and the Kullback-Leibler divergence. We propose here to consider the β-divergence, which is able to encompass a wide family of divergence measures corresponding to various noise distributions. This loss function is incorporated into three different factor models and evaluated using four sets of synthetic data.

Factor analysis has proven to be a relevant tool for extracting tissue time-activity curves (TACs) in dynamic PET images, since it allows for an unsupervised analysis of the data. Reliable and interpretable results are possible only if it is considered with respect to suitable noise statistics. However, the noise in reconstructed dynamic PET images is very difficult to characterize, despite the Poissonian nature of the count rates. Rather than explicitly modeling the noise distribution, this paper proposes to study the relevance of several divergence measures to be used within a factor analysis framework. To this end, the β-divergence, widely used in other applicative domains, is considered to design the data-fitting term involved in three different factor models. The performances of the resulting algorithms are evaluated for different values of β, in a range covering Gaussian, Poissonian, and Gamma-distributed noises. The results obtained on two different types of synthetic images and one real image show the interest of applying non-standard values of β to improve the factor analysis.

We propose a spatio-spectral deconvolution approach for partial volume correction in 3D vector-valued imaging. We adopt a variational point of view where we obtain the latent 4D image as a global minimizer of a convex energy function. The prior that we use leverages recent vectorial extensions of the total variation penalty. Specifically, it encourages different channels to share common gradient directions. We discuss why such an approach is appropriate for dynamic PET image deconvolution and derive an efficient algorithm by working in a product-space setting and using the Douglas-Rachford algorithm as a primitive. We use simulations based on a numerical phantom and realistic kinetics of two radioactive tracers to assess the performance of the proposed method.

In this paper, we extend the gradient vector flow field to the vector-valued case for robust variational segmentation of 4D images with active surfaces. Instead of only exploiting scalar edge strength in order to identify vector edges, we propagate both directions and amplitudes of vector gradients computed from the analysis of a structure tensor of the vector-valued image. To reduce contributions from noise in the calculation of the structure tensor, image channels are weighted according to a blind estimator of contrast that take profit of the deformable models framework. The proposed 4DGVF vector field is validated on synthetic image datasets and applied to biological volume delineation in dynamic PET imaging.

In this paper, we propose a new method for vector-valued image restoration in order to reduce noise while simultaneously sharpening vector edges. Our approach is a coupled anisotropic diffusion and shock filtering scheme that exploits a new robust 4DGVF vector field tailored for vector-valued images. The proposed scheme sharpens edges in directions diffused from the entire spatio-spectral information available with a more precise and a more stable sharpening effect along the iterative processing. We validate our method on color images as well as on realistic simulations of dynamic PET images.

In this paper, we extend the gradient vector flow field for robust variational segmentation of vector-valued images. Rather than using scalar edge information, we define a vectorial edge map derived from a weighted local structure tensor of the image that enables the diffusion of the gradient vectors in accurate directions through the 4D gradient vector flow equation. To reduce the contribution of noise in the structure tensor, image channels are weighted according to a blind estimator of contrast. The method is applied to biological volume delineation in dynamic PET imaging, and validated on realistic Monte Carlo simulations of numerical phantoms as well as on real images.

In this paper, we propose a new method to reconstruct high resolution images from structured illumination microscopy. It consists of estimating the illumination pattern parameters with a multiscale analysis in the Fourier domain and filtering the significative features with a statistical test. Our method is fast and automatic, aiming at being computationally effective for in vivo biomedical applications.

Segmentation with active contours is heavily dependent on the initialization. In this paper we propose a novel method for a quasi-automatic initialization of deformable models. Our method relies on the use of an additional energy based on the gradient vector flow. We define the centers of strong and weak divergence and use them to set up the initial curve. As our goal is the segmentation of the heart cavities, we also propose a new gradient vector field for ultrasound images based on the coefficient of variation. Results on real ultra-sound images are presented and compared to the boundaries manually outlined by an expert. They confirm the potential of the method.

This paper deals with anisotropic diffusion in images affected by speckle. Two existing methods are reviewed. The first is a robust diffusion technique, non adapted to speckle, based on the Tukey function. The second applies an isotropic diffusion to speckle but lacks robustness. The contribution of this paper is to create a robust anisotropic diffusion filter adapted to speckle. The proposed approach is based on the two reviewed methods and introduces an original diffusion tensor Experimentation results are presented and the performance of the three methods compared. The proposed algorithm shows significant enhancement.