70 research outputs found
Filtering of image sequences: on line edge detection and motion reconstruction
L'argomento della Tesi riguarda lĂelaborazione di sequenze di immagini, relative ad una
scena in cui uno o piË oggetti (possibilmente deformabili) si muovono e acquisite da un
opportuno strumento di misura. A causa del processo di misura, le immagini sono corrotte da
un livello di degradazione. Si riporta la formalizzazione matematica dellĂinsieme delle
immagini considerate, dellĂinsieme dei moti ammissibili e della degradazione introdotta dallo
strumento di misura. Ogni immagine della sequenza acquisita ha una relazione con tutte le
altre, stabilita dalla legge del moto della scena. LĂidea proposta in questa Tesi Ă quella di
sfruttare questa relazione tra le diverse immagini della sequenza per ricostruire grandezze di
interesse che caratterizzano la scena.
Nel caso in cui si conosce il moto, lĂinteresse Ă quello di ricostruire i contorni dellĂimmagine
iniziale (che poi possono essere propagati attraverso la stessa legge del moto, in modo da
ricostruire i contorni della generica immagine appartenente alla sequenza in esame), stimando
lĂampiezza e del salto del livello di grigio e la relativa localizzazione.
Nel caso duale si suppone invece di conoscere la disposizione dei contorni nellĂimmagine
iniziale e di avere un modello stocastico che descriva il moto; lĂobiettivo Ă quindi stimare i
parametri che caratterizzano tale modello.
Infine, si presentano i risultati dellĂapplicazione delle due metodologie succitate a dati reali
ottenuti in ambito biomedicale da uno strumento denominato pupillometro. Tali risultati sono
di elevato interesse nellĂottica di utilizzare il suddetto strumento a fini diagnostici
Foundations of Stochastic Thermodynamics
Small systems in a thermodynamic medium --- like colloids in a suspension or
the molecular machinery in living cells --- are strongly affected by the
thermal fluctuations of their environment. Physicists model such systems by
means of stochastic processes. Stochastic Thermodynamics (ST) defines entropy
changes and other thermodynamic notions for individual realizations of such
processes. It applies to situations far from equilibrium and provides a unified
approach to stochastic fluctuation relations. Its predictions have been studied
and verified experimentally.
This thesis addresses the theoretical foundations of ST. Its focus is on the
following two aspects: (i) The stochastic nature of mesoscopic observations has
its origin in the molecular chaos on the microscopic level. Can one derive ST
from an underlying reversible deterministic dynamics? Can we interpret ST's
notions of entropy and entropy changes in a well-defined
information-theoretical framework? (ii) Markovian jump processes on finite
state spaces are common models for bio-chemical pathways. How does one quantify
and calculate fluctuations of physical observables in such models? What role
does the topology of the network of states play? How can we apply our abstract
results to the design of models for molecular motors?
The thesis concludes with an outlook on dissipation as information written to
unobserved degrees of freedom --- a perspective that yields a consistency
criterion between dynamical models formulated on various levels of description.Comment: Ph.D. Thesis, G\"ottingen 2014, Keywords: Stochastic Thermodynamics,
Entropy, Dissipation, Markov processes, Large Deviation Theory, Molecular
Motors, Kinesi
Deconvolution of Quantized-Input Linear Systems: An Information-Theoretic Approach
The deconvolution problem has been drawing the attention of mathematicians, physicists and engineers since the early sixties.
Ubiquitous in the applications, it consists in recovering the unknown input of a convolution system from noisy measurements of the output. It is a typical instance of inverse, ill-posed problem: the existence and uniqueness of the solution are not assured and even small perturbations in the data may cause large deviations in the solution.
In the last fifty years, a large amount of estimation techniques have been proposed by different research communities to tackle deconvolution, each technique being related to a peculiar engineering application or mathematical set. In many occurrences, the unknown input presents some known features, which can be exploited to develop ad hoc algorithms. For example, prior information about regularity and smoothness of the input function are often considered, as well as the knowledge of a probabilistic distribution on the input source: the estimation techniques arising in different scenarios
are strongly diverse.
Less effort has been dedicated to the case where the input is known to be affected by discontinuities and switches, which is becoming an important issue in modern technologies. In fact, quantized signals, that is, piecewise constant functions that can assume only a finite number of values, are nowadays widespread in the applications, given the
ongoing process of digitization concerning most of information and communication systems. Moreover, hybrid systems are often encountered, which are characterized by the introduction of quantized signals into physical, analog communication channels.
Motivated by such consideration, this dissertation is devoted to the study of the deconvolution of continuous systems with quantized input; in particular, our attention will be focused on linear systems. Given the discrete nature of the input, we will
show that the whole problem can be interpreted as a paradigmatic digital transmission problem and we will undertake an Information-theoretic approach to tackle it.
The aim of this dissertation is to develop suitable deconvolution algorithms for quantized-input linear systems, which will be derived from known decoding procedures, and to test them in different scenarios. Much consideration will be given to the
theoretical analysis of these algorithms, whose performance will be rigorously described in mathematical terms
On lâ performance optimization: linear switched systems and systems with cone constraints
The lâ performance of Linear Time-Invariant (LTI) systems has been one of the corner stones of the robust control theory for over the past 30 years. The lâ performance has been studied mostly for LTI systems and the scarcity of the results for other types of systems is prominent in this area. This dissertation aims to depart from LTI systems and investigate the lâ performance for other classes of systems. In particular, the lâ performance of Linear Switched Systems (LSS) and of linear systems with cone constraints is studied in the first and second part of this dissertation, respectively.
Part I: In Part I, we first consider the worst-case lâ induced norm computation of LSS. That is, sup_ÏâG_Ïâ, where G_Ï is a LSS, Ï is the switching sequence, and the norm, â.â, is the lâ induced norm. This problem can be linked to robustness of systems when the switching is arbitrary. We provide lower and upper bounds of this quantity. These bounds are hard to compute and in general conservative. Hence, we narrow our attention to special classes of LSS by defining the classes of input, output, and input-output LSS and show that for these classes, exact expressions for the worst-case lâ induced norm can be found. Moreover, we introduce the class of generalized input-output LSS and show how their lâ gains can be computed exactly via Linear Programming (LP). The class of generalized input-output LSS proves to be a sufficiently rich class as it is dense in the set of all stable LSS. We further derive new stability and stabilizability conditions and control synthesis in terms of LP utilizing generalized input-output LSS.
The other extreme from the worst-case norm is the minimal norm, i.e., inf_Ï âG_Ïâ. The interest in this type of problem is motivated by situations where there may be limited sensor and/or actuator resources for filtering and control. We show that for Finite Impulse Response (FIR)switching systems the minimizing switching sequence can be chosen to be periodic. For input-only or output-only switching systems an exact characterization of the minimal lâ gain is provided, and it is shown that the minimizing switching sequence is constant, which, as also shown, is not true for input-output switching.
Moreover, we study Markov Linear Switched Systems (MLSS). These are LSS whose switching sequence is a Markov process. We introduce the notion of the stochastic lâ gain and provide exact expression to compute it. However, this computation is challenging, as we show, and hence we resort to a more relaxed but tractable notion of lâ mean performance. We provide tractable computation and control synthesis method with respect to the lâ mean performance.
Part II: Part II of this dissertation deals with the lâ gain of linear systems with positivity type of constraints. The study of such systems is well justified as there are many physical problems in which some variables are restricted be non-negative (or non-positive); examples can be found in biology, economics, and many other areas. We consider the case when the output is forced to be in the positive lâ cone when the input is in this cone. This reflects as, so-called, an external positivity constraint on the system. As we point out, if such a constraint is imposed on the closed loop map, finding an optimal controller is LP and hence a tractable problem. If, on the other hand, the constraint known as internal positivity is sought, we show that a dynamic controller offers no advantage over a static one. These results can be used to obtain an optimal (static) state feedback controller. However, designing an optimal output feedback controller (which is static) is a harder problem and in general leads to a bilinear program. We show that this bilinear program can be reduced to LP, if the null space of the measurement matrix is invariant under multiplication by diagonal matrices.
Besides the positive systems mentioned above, we consider the case where only the input is restricted to be in the positive cone of lâ, denoted by lâ+, and seek to characterize the induced norm from lâ+ to lâ. We stress here that no positivity constraint is imposed on the system itself. As an example, consider a positive nonlinear system with positive input that is linearized about a point other than origin. The linearized model is no longer a positive system as it is not linearized about the origin. Its inputs, however, remain positive and hence fit into this class of problems. We obtain an exact characterization of this norm (the induced norm from lâ+ to lâ which can be used to synthesis a controller minimizing the induced norm from lâ+ to lâ via LP
Hidden Markov Models
Hidden Markov Models (HMMs), although known for decades, have made a big career nowadays and are still in state of development. This book presents theoretical issues and a variety of HMMs applications in speech recognition and synthesis, medicine, neurosciences, computational biology, bioinformatics, seismology, environment protection and engineering. I hope that the reader will find this book useful and helpful for their own research
Survey on time-delay approach to networked control
This paper provides a survey on time-delay approach to networked control systems (NCSs). The survey begins from a brief summary on fundamental network-induced issues in NCSs and the main approaches to the modelling of NCSs. In particular, a comprehensive introduction to time-delay approach to sampled-data and networked control is provided. Then, recent results on time-delay approach to event-triggered control are recalled. The survey highlights time-delay approach developed to modelling, analysis and synthesis of NCSs, under communication constraints, with a particular focus on Round-Robin, Try-once-discard and stochastic protocols. The time-delay approach allows communication delays to be larger than the sampling intervals in the presence of scheduling protocols. Moreover, some results on networked control of distributed parameter systems are surveyed. Finally, conclusions and some future research directions are briefly addressed
Deconvolution of Quantized-Input Linear Systems : an Information-Theoretic Approach
The deconvolution problem has been drawing the attention of mathematicians, physicists
and engineers since the early sixties.
Ubiquitous in the applications, it consists in recovering the unknown input of a
convolution system from noisy measurements of the output. It is a typical instance of
inverse, ill-posed problem: the existence and uniqueness of the solution are not assured
and even small perturbations in the data may cause large deviations in the solution.
In the last fifty years, a large amount of estimation techniques have been proposed by
di fferent research communities to tackle deconvolution, each technique being related
to a peculiar engineering application or mathematical set. In many occurrences, the
unknown input presents some known features, which can be exploited to develop ad
hoc algorithms. For example, prior information about regularity and smoothness of
the input function are often considered, as well as the knowledge of a probabilistic
distribution on the input source: the estimation techniques arising in diff erent scenarios
are strongly diverse.
Less eff ort has been dedicated to the case where the input is known to be aff ected by
discontinuities and switches, which is becoming an important issue in modern technologies.
In fact, quantized signals, that is, piecewise constant functions that can assume
only a fi nite number of values, are nowadays widespread in the applications, given the
ongoing process of digitization concerning most of information and communication systems.
Moreover, hybrid systems are often encountered, which are characterized by the
introduction of quantized signals into physical, analog communication channels.
Motivated by such consideration, this dissertation is devoted to the study of the
deconvolution of continuous systems with quantized input; in particular, our attention
will be focused on linear systems. Given the discrete nature of the input, we will
show that the whole problem can be interpreted as a paradigmatic digital transmission
problem and we will undertake an Information-theoretic approach to tackle it.
The aim of this dissertation is to develop suitable deconvolution algorithms for
quantized-input linear systems, which will be derived from known decoding procedures,
and to test them in diff erent scenarios. Much consideration will be given to the
theoretical analysis of these algorithms, whose performance will be rigorously described
in mathematical terms
- âŠ