A Dynamical Systems Approach to Classification of Surgical Gestures in Kinematic and Video Data

In Computer Assisted Intervention (CAI) systems, a surgeon performs the surgery using an interface connected to a computer that remotely controls a set of surgical tools attached to a robot. Such systems are particularly appealing for minimally invasive surgeries since they allow for a larger and more precise set of movements than in traditional laparoscopic interventions, and provide enhanced vision capabilities such as 3D vision and augmented reality. These features directly translate into benefits for the patients such as smaller incisions, less pain and quicker healing. However, the benefits of the technology might be reduced due to the steep learning curve associated with CAI systems. This makes it necessary to account for a fair and objective criterion for the evaluation and assessment of the skills of a novice surgeon. Furthermore, it is desirable to automate the process in order to avoid constant supervision of an expert surgeon, a time consuming, subjective and rather inefficient method. It is therefore necessary to develop algorithmic methods that extract information from kinematic cues provided by the robot and video recordings of the interventions. A common approach is to divide the surgical procedure into smaller actions, forming a vocabulary able to to describe different surgical tasks. Following such an approach requires a method capable of providing temporal segmentation, recognition of the action and final skill assessment. Prior work has usually modeled the interactions between these atomic actions using generative models such as Hidden Markov Models, Factor-Analysis and Switching Linear Dynamical Systems. In this thesis, we focus on the classification problem and assume segmented data. We propose to follow a discriminative approach using Linear Dynamical Systems (LDS) to model and characterize a particular action. We develop new methods for the extraction of meaningful representations by means of averaging in the space of LDSs. These representative points are then used into a discriminative framework for surgical gesture classification. We propose a novel SVM classification method for time series of data that reduces computation at the expense of some degradation in performance. Our contributions are fairly general and can be applied to any temporal signal coming from an LDS

Topology Optimization For Energy-Efficient Communications In Consensus Wireless Networks

Over the past years there has been an increasing interest in developing distributed computation methods over wireless networks. A new communication paradigm has emerged where distributed algorithms such as consensus have played a key role in the development of such networks. A special case are wireless sensor networks (WSN) which have found application in a large variety of problems such as environmental monitoring, surveillance, or localization, to cite a few. One major design issue in WSNs is energy efficiency. Nodes are typically battery-powered devices and thus, it is critical to make a proper use of the scarce energy resources. This fact motivates the search for optimal conditions that favor the communication environment. It is well known that the rate at which the information is spread across the network depends on the topology of the network and that finding the optimal topology is a hard combinatorial problem. However, using convex optimization tools, we propose a method that tries to find the optimal topology in a consensus wireless network that uses broadcast messages. Our results show that exploiting the broadcast nature of the wireless channel leads to more energy efficient configurations than using dedicated unicast messages and that our algorithm performs very close to the optimal solution

Enhancing local-Transmitting less-Improving global

Super-resolving a natural image is an ill-posed problem. The classical approach is based on the registration and subsequent interpolation of a given set of low-resolution images. However, achieving satisfactory results typically requires the combination of a large number of them. Such an approach would be impractical over heterogeneous rate-constrained wireless networks due to the associated communication cost and limited data available. In this paper, we present an approach for local image enhancement following the finite rate of innovation sampling framework, and motivate its application to the super-resolution problem over heterogeneous networks. Local estimates can be exchanged among the nodes of the network in order to regularize the super-resolution problem while, at the same time, reduce data exchange

Shape from bandwidth: the 2-D orthogonal projection case

Could bandwidth—one of the most classic concepts in signal processing—have a new purpose? In this paper, we investigate the feasibility of using bandwidth to infer shape from a single image. As a first analysis, we limit our attention to orthographic projection and assume a 2-D world. We show that, under certain conditions, a single image of a surface, painted with a bandlimited texture, is enough to deduce the surface up to an equivalence class. This equivalence class is unavoidable, since it stems from surface transformations that are invisible to orthographic projections. A proof of concept algorithm is presented and tested with both a simulation and a simple practical experiment

Unlabeled Sensing: Reconstruction Algorithm and Theoretical Guarantees

It often happens that we are interested in reconstructing an unknown signal from partial measurements. Also, it is typically assumed that the location (temporal or spatial) of the samples is known and that the only distortion present in the observations is due to additive measurement noise. However, there are some applications where such location information is lost. In this paper, we consider the situation in which the order of noisy samples out of a linear measurement system is missing. Previous work on this topic has only considered the noiseless case and exhaustive search combinatorial algorithms. We propose a much more efficient algorithm based on a geometrical viewpoint of the problem. We also study the uniqueness of the solution under different choices of the sampling matrix and its robustness to noise for the case of two-dimensional signals. Finally we provide simulation results to confirm the theoretical findings of the paper

Sampling at unknown locations: Uniqueness and reconstruction under constraints

Traditional sampling results assume that the sample locations are known. Motivated by simultaneous localization and mapping (SLAM) and structure from motion (SfM), we investigate sampling at unknown locations. Without further constraints, the problem is often hopeless. For example, we recently showed that, for polynomial and bandlimited signals, it is possible to find two signals, arbitrarily far from each other, that fit the measurements. However, we also showed that this can be overcome by adding constraints to the sample positions. In this paper, we show that these constraints lead to a uniform sampling of a composite of functions. Furthermore, the formulation retains the key aspects of the SLAM and SfM problems, whilst providing uniqueness, in many cases. We demonstrate this by studying two simple examples of constrained sampling at unknown locations. In the first, we consider sampling a periodic bandlimited signal composite with an unknown linear function. We derive the sampling requirements for uniqueness and present an algorithm that recovers both the bandlimited signal and the linear warping. Furthermore, we prove that, when the requirements for uniqueness are not met, the cases of multiple solutions have measure zero. For our second example, we consider polynomials sampled such that the sampling positions are constrained by a rational function. We previously proved that, if a specific sampling requirement is met, uniqueness is achieved. In addition, we present an alternate minimization scheme for solving the resulting non-convex optimization problem. Finally, fully reproducible simulation results are provided to support our theoretical analysis

Sampling Continuous-time Sparse Signals: A Frequency-domain Perspective

We address the problem of sampling and reconstruction of sparse signals with finite rate of innovation. We derive general conditions under which perfect reconstruction is possible for sampling kernels satisfying Strang-Fix conditions. Previous results on the subject consider two particular cases; when the kernel is able to reproduce (complex) exponentials, or when it has the polynomial reproduction property. In this work we extend such analysis to the case where both properties could be found in the sampling kernel and show that the former two sitations can be regarded as special cases. As a result of our analysis, we provide general conditions under which perfect recovery in the noiseless case is possible. In practice, a given sampling kernel might not satisfy Strang-Fix conditions. When dealing with arbitrary sampling kernels we propose a unified view for sampling and reconstruction in the frequency domain. Our formulation generalizes previous approaches and provides new insights for devising optimal reconstruction schemes. We also propose a novel algorithm for denoising treating the problem as a particular instance of structured low-rank approximation. Finally, we provide some numerical experiments and a comparison between different state-of-the-art methods showing the improved estimation performance of the proposed approach.

Energy Efficient Collaborative Beamforming in Wireless Sensor Networks

Energy efficiency is a major design issue in the context of Wireless Sensor Networks (WSN). If the acquired data is to be sent to a far-away base station, collaborative beamforming performed by the sensors may help to distribute the communication load among the nodes and to reduce fast battery depletion. However, collaborative beamforming techniques are far from optimality and in many cases we might be wastingmore power than required. We consider the issue of energy efficiency in beamforming applications. Using a convex optimization framework, we propose the design of a virtual beamformer that maximizes the network lifetime while satisfying a pre-specified Quality of Service (QoS) requirement. We derive both centralized and distributed algorithms for the solution of the problem using convex optimization and consensus algorithms. In order to account for other sources of battery depletion different from that of communications beamforming, we consider an additional random energy term in the consumption model. The formulation then switches to a probabilistic design that generalizes the deterministic case. Conditions under which the general problem is convex are also provided