Digital Signal & Image Processing

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.

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.