Campus Event Calendar
Event Entry
What and Who
Approximate Bayesian Inference and Measurement Design Optimization for Low-Level Computer Vision and Imaging
Matthias Seeger
Cluster of Excellence - Multimodal Computing and Interaction - MMCI
Talk
TBA
AG 4
AG Audience
English
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Date, Time and Location
Tuesday, 24 March 2009
13:00
45 Minutes
E1 4
019
Saarbrücken
Abstract
Modern nonlinear image reconstruction algorithms (wavelet shrinkage, total variation penalization, MAP estimation, nonlinear diffusion) tend to improve dramatically upon least squares estimation, and novel algorithms can be scaled up to very large problems. In a growing number of imaging applications (for example, magnetic resonance imaging), speed and cost limits are due to measurements today, not due to reconstruction, and automatic design optimization techniques become very valuable. The traditional Nyquist limit restricts designs when linear reconstruction is used, but can be improved upon in the general case, if only the measurement design is chosen so as to support the reconstruction method well.
As a higher-order optimal decision problem, design optimization needs more than point estimation or reconstruction for fixed setups. I show that the Bayesian posterior, beyond its mode, can be used to compute meaningful figures of merit for designs. Roughly, a design can be improved along directions in which the posterior spreads widely, since along those, a point estimate is imprecise and cannot be relied upon. I will introduce a novel class of variational algorithms for approximating this non-Gaussian posterior on large scales required for real-world imaging applications. Large parts of these convex algorithms are closely related to convex MAP estimation, and they reduce entirely to standard primitives of numerical mathematics and optimization, so can be scaled up in the same way.
My current interest is in sampling trajectory optimization (in Fourier space) for magnetic resonance imaging, and I will use this problem to motivate my talk. However, the algorithms should apply more widely, to low-level computer vision problems such as computational photography (optimization of coded apertures, etc.), other medical imaging applications, or sensing applications out of the visible wavelenghts. While I focus on the (sequential) design optimization problem, there are other problems which benefit from a posterior approximation beyond its mode. The methods are (at present) specific to continuous variable non-Gaussian models.
In this talk, I will discuss the algorithm in some detail and point out links to common estimation methods. Being new in Saarbruecken, I am keen to obtain feedback as to how these techniques might apply to scenarios currently investigated here.
As a higher-order optimal decision problem, design optimization needs more than point estimation or reconstruction for fixed setups. I show that the Bayesian posterior, beyond its mode, can be used to compute meaningful figures of merit for designs. Roughly, a design can be improved along directions in which the posterior spreads widely, since along those, a point estimate is imprecise and cannot be relied upon. I will introduce a novel class of variational algorithms for approximating this non-Gaussian posterior on large scales required for real-world imaging applications. Large parts of these convex algorithms are closely related to convex MAP estimation, and they reduce entirely to standard primitives of numerical mathematics and optimization, so can be scaled up in the same way.
My current interest is in sampling trajectory optimization (in Fourier space) for magnetic resonance imaging, and I will use this problem to motivate my talk. However, the algorithms should apply more widely, to low-level computer vision problems such as computational photography (optimization of coded apertures, etc.), other medical imaging applications, or sensing applications out of the visible wavelenghts. While I focus on the (sequential) design optimization problem, there are other problems which benefit from a posterior approximation beyond its mode. The methods are (at present) specific to continuous variable non-Gaussian models.
In this talk, I will discuss the algorithm in some detail and point out links to common estimation methods. Being new in Saarbruecken, I am keen to obtain feedback as to how these techniques might apply to scenarios currently investigated here.
Contact
Thorsten Thormählen
+49 681 9325-417
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Thorsten Thormählen, 03/05/2009 17:41
Thorsten Thormählen, 03/05/2009 17:41 -- Created document.
Thorsten Thormählen, 03/05/2009 17:41 -- Created document.