In many restoration problems, the a-priori knowledge of a finite number of pixel amplitudes of the original image is available (e.g. blurred blackand-white images). It is shown how to incorporate this information into optimal image reconstruction. The degradation of a discrete image is modeled as a two-dimensional, finite-state Markov process. Dynamic programming is then applied to get an optim...

This paper addresses optimal estimation for time varying autoregressive (TVAR) models. First, we propose a statistical model on the time evolution of the frequencies, moduli and real poles instead of a standard model on the AR coefficients as it makes more sense from a physical viewpoint. Second, optimal estimation involves solving a complex optimal filtering problem which does not admit any cl...

This paper investigates the optimal estimation problem for networked control systems, where the control packets are randomly dropped without acknowledgement to the estimator. Most existing results for this setup are concerned with the design of controller, while the optimal estimation and its performance evaluation have not been fully studied. This paper shows, unlike many other cases such as i...

In this paper, we study the noise-reduction problem in the KarhunenLoève expansion domain. We develop two classes of optimal filters. The first class estimates a frame of speech by filtering the corresponding frame of the noisy speech. We will show that several well-known existing methods belong or are closely related to this category. The second class, which has not been studied before, obtain...

In this paper we attempt to give a historical account of the main ideas leading to the development of non-linear filtering and stochastic control as we know it today. The paper contains six sections. In Section 2 we present a development of linear filtering theory, beginning with Wiener-Kolmogoroff filtering and ending with Kalman filtering. The method of development is the innovations method a...

The recording of heart signal is called Electrocardiogram (ECG). ECG is used to measure, analyze, observe the heart function and heart abnormalities like cardiac murmur, myocardial infarction etc. The ECG electrodes are sensitive in nature, even the small noise mixed with original signal changes the ECG wave pattern. The ECG signal voltage ranges from 0.5 to 6mV and artifacts can be easily mixe...