Compressive Acquisition - Sparse Representations and Compressive Sensing for Imaging and Vision - page 33

Fig. 3.12 Measured point spread functions for conventional imaging and imaging with a cubic
phase. PSFs for conventional system at (a) 113” (2870 mm), (b) 146.5” (3721 mm), and (c) 180”
(4572 mm). (d)-(f) PSFs for a system with cubic phase at the same distances for (a)-(c)

ˆ ˆ

of the signal-to-noise ratio, and the functions Φ N are the expected power

spectra of the object and noise, respectively. The optical transfer function is usually
estimated from the experimentally measured point responses. One can view the
estimated i p (

Φ L and

x , y ) as a diffraction limited response. Eq. ( 3.18 ) can be written in

matrix notation as

i p = Wi

= WHo g , (3.20)

where i p is the N 2 × 1 column vector corresponding to array i p ( x , y ) and W is the

N 2 N 2 . The issue

we address in the remainder of this chapter is with what fidelity can one estimate i p
using less than N 2

× convolution matrix corresponding to the Wiener filter w ( x , y )

measurements of i .

3.4.2 Accelerated Imaging with Extended Depth-of-Field

Since the objective is to form mmW images with reduced number of samples,
the following sampling strategy was proposed in [104]. Because the sensor is a