Digital Signal Processing Seminar

In this talk the problem of signal recovery from partially-known (random) linear degradation operators is presented in the framework of image restoration. This situation arises in many real-life applications, such as tomographic reconstructions from projections, inverse scattering problems, and in displacement-vector-field (DVF) estimation applications. For the image restoration problem the actual degradation is modeled by a linear space-invariant (LSI) impulse response, which is the sum of a deterministic (known) and a random (unknown) component. Two approaches are proposed based on this model. The first approach is based on the Expectation-Maximization (EM) algorithm, and the second algorithm utilizes the Empirical Bayesian (EB) analysis. Both algorithms, unlike all previous work on this problem, have the capability to simultaneously restore the image and identify the unknown parameters of the observation and image models. In the expectation step of the proposed EM-based algorithm the linear minimum mean square error (LMMSE) restoration is obtained, based on the current estimates of unknown parameters. At the restoration step of the proposed EB-based algorithm the maximum a posteriori (MAP) restoration is obtained. The relationships of both algorithms with our previous work on this problem which was based on regularization and the constrained total least squares (TLS) approach is established. The proposed algorithms are demonstrated experimentally in the image restoration simulations and for the problem of tomographic reconstructions from projections.

A list of digital signal processing seminars is available at from the ECE department Web pages under "Seminars". The Web address for the digital signal processing seminars is http://www.ece.utexas.edu/~bevans/dsp_seminars.html