Analysis of A Nonsmooth Optimization Approach to Robust Estimation

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault detection, state estimation in lossy networks, hybrid system identification, robust estimation, etc. The problem is hard because it exhibits some intrinsic combinatorial features. Therefore, obtaining an effective solution necessitates relaxations that are both solvable at a reasonable cost and effective in the sense that they can return the true parameter vector. The current paper discusses a nonsmooth convex optimization approach and provides a new analysis of its behavior. In particular, it is shown that under appropriate conditions on the data, an exact estimate can be recovered from data corrupted by a large (even infinite) number of gross errors.Comment: 17 pages, 9 figure

Compressive system identification of LTI and LTV ARX models: The limited data set case

In this paper, we consider identifying Auto Regressive with eXternal input (ARX) models for both Linear Time-Invariant (LTI) and Linear Time-Variant (LTV) systems. We aim at doing the identification from the smallest possible number of observations. This is inspired by the field of Compressive Sensing (CS), and for this reason, we call this problem Compressive System Identification (CSI). In the case of LTI ARX systems, a system with a large number of inputs and unknown input delays on each channel can require a model structure with a large number of parameters, unless input delay estimation is performed. Since the complexity of input delay estimation increases exponentially in the number of inputs, this can be difficult for high dimensional systems. We show that in cases where the LTI system has possibly many inputs with different unknown delays, simultaneous ARX identification and input delay estimation is possible from few observations, even though this leaves an apparently ill-conditioned identification problem. We discuss identification guarantees and support our proposed method with simulations. We also consider identifying LTV ARX models. In particular, we consider systems with parameters that change only at a few time instants in a piecewise-constant manner where neither the change moments nor the number of changes is known a priori. The main technical novelty of our approach is in casting the identification problem as recovery of a block-sparse signal from an underdetermined set of linear equations. We suggest a random sampling approach for LTV identification, address the issue of identifiability and again support our approach with illustrative simulations

Synthesis of hybrid automata with affine dynamics from time-series data

Formal design of embedded and cyber-physical systems relies on mathematical modeling. In this paper, we consider the model class of hybrid automata whose dynamics are defined by affine differential equations. Given a set of time-series data, we present an algorithmic approach to synthesize a hybrid automaton exhibiting behavior that is close to the data, up to a specified precision, and changes in synchrony with the data. A fundamental problem in our synthesis algorithm is to check membership of a time series in a hybrid automaton. Our solution integrates reachability and optimization techniques for affine dynamical systems to obtain both a sufficient and a necessary condition for membership, combined in a refinement framework. The algorithm processes one time series at a time and hence can be interrupted, provide an intermediate result, and be resumed. We report experimental results demonstrating the applicability of our synthesis approach

FOE NET: Segmentation of Fetal in Ultrasound Images Using V-NET

Ultrasound is a non-invasive method to diagnose and treat medical conditions. It is becoming increasingly popular to use portable ultrasound scanning devices to reduce patient wait times and make healthcare more convenient for patients. By using ultrasound imaging, you will be able to obtain images with better quality and also gain information about soft tissues. The interference caused by tissues reflected in ultrasound waves resulted in intensified speckle sound, complicating imaging. In this paper, a novel Foe-Net has been proposed for segmenting the fetal in ultrasound images. Initially, the input US images are noise removal phase using two different filters Adaptive Gaussian Filter (AGF) and Adaptive Bilateral Filter (ABF) used to reduce the noise artifacts. Then, the US images are enhanced using CLAHE and MSR for smoothing to enhance the image quality. Finally, the denoised images are input to the V-net is used to segment the fetal in the US images. The experimental outcomes of the proposed Multi-Scale Retinex (MSR) is an image enhancement technique that improves image quality by adjusting its illumination and enhancing details. Foe-Net was measured by specific parameters such as specificity, precision, and accuracy. The proposed Foe-Net achieves an overall accuracy of 99.48%, specificity of 98.56 %, and precision of 96.82 % for segmented fetal in ultrasound images. The proposed Foe-Net attains better pre-processing outcomes at low error rates and, high SNR, high PSNR, and high SSIM values