**Image Enhancement & Super-Resolution**

Signal and image acquisition of the data is performed with a loss of original information. This is apparent in the loss of high-frequency resolution of the recorded signal or image and is usually due to either (or both) of the following:

- Instrument resolution loss introduced by the original signal convolution with the instrument response function (IRF), or optical transfer function (OTF) in the case of images.
- Sampling resolution loss introduced by the finite sampling performed by the digital recording instrument.

Super resolution techniques are designed to make use of additional information available to the user in order to restore some of the high-frequency missing information. For example, when the value of the convolving IRF (or OTF) function is available, various methods of regularized inverse problem methods can be applied for signal deconvolution. For the situation when multiple records slightly translated in time (or space) of the original signal exist, they can be combined to generate a single higher resolution new set of data.

**Signal Modeling & Parameter Estimation**

Signals and systems can be broadly classified in deterministic or random. The former are usually investigated with the aid of Fourier, Laplace, Hilbert or wavelet transforms to determine their spectral content, trend and transitory behavior, and the undesired components are filtered out using linear or dynamical filters. Random signals are processed by statistical techniques using non-parametric (windows, filter banks, periodograms) or parametric methods. In the later case, when additional information is available, it is customary to select a time-series ARMA model and determine its parameters based on some optimization criterion. Alternatively, a subspace-based spectral estimation can be performed (MUSIC, ESPRIT), in which the correct estimation of the covariance signal matrix plays a fundamental role.

**Spectral Analysis**

Spectral analysis methods attempt, starting from a finite sample of the digitally recorded signal or image, to establish how the total power is distributed over the frequency spectrum. They are used in order to reveal hidden periodicities in the data (economics, metrology), infer the location of the sources (radar), provide additional help for patient diagnostics (medicine), or characterize the dynamic behavior of a system, among others. In nonparametric methods, the signal is passed through a set of narrow band-pass filters and the output power is determined. In contrast, the parametric methods postulate a model for the data, and the data is used to estimate its parameters. They can estimate the signal spectrum more accurately than the nonparametric methods when the model is properly selected, but they will fail if the considered model is not accurate.

**Pattern Recognition & Image Segmentation**

The primary objective of pattern recognition is the classification of image and signal objects (patterns) into a set of well-defined categories or classes. Speech recognition, computer-aided diagnostics, face recognition, or optical character recognition are among the most popular applications of these statistical techniques.