Inverse Problems in Vision and 3D Tomography [Hardcover]

The concept of an inverse problem is a familiar one to most scientists and engineers, particularly in the field of signal and image processing, imaging systems (medical, geophysical, industrial non-destructive testing, etc.), and computer vision. In imaging systems, the aim is not just to estimate unobserved images but also their geometric characteristics from observed quantities that are linked to these unobserved quantities by a known physical or mathematical relationship. In this manner techniques such as image enhancement or addition of hidden detail can be delivered. This book focuses on imaging and vision problems that can be clearly described in terms of an inverse problem where an estimate for the image and its geometrical attributes (contours and regions) is sought.

The book uses a consistent methodology to examine inverse problems such as: noise removal; restoration by deconvolution; 2D or 3D reconstruction in X-ray, tomography or microwave imaging; reconstruction of the surface of a 3D object using X-ray tomography or making use of its shading; reconstruction of the surface of a 3D landscape based on several satellite photos; super-resolution; motion estimation in a sequence of images; separation of several images mixed using instruments with different sensitivities or transfer functions; and much more.

Preface 13

Chapter 1. Introduction to Inverse Problems in Imaging and Vision 15
Ali MOHAMMAD-DJAFARI

1.1. Inverse problems 16

1.2. Specific vision problems 21

1.3. Models for time-dependent quantities 26

1.4. Inverse problems with multiple inputs and multiple outputs (MIMO) 27

1.5. Non-linear inverse problems 30

1.6. 3D reconstructions 33

1.7. Inverse problems with multimodal observations 33

1.8. Classification of inversion methods:l#0