Image and Video Compression

167Compressive Sensing

solution for a sparse signal. Figure8.8 indicates the best approximation of a

point in

2



using the

p

 norms with p < 1.

8.5 Heart of Compressed Sensing: Measurement Matrix

One of the most important design criteria for a measurement matrix is to have

a one-to-one linkage between measurements and a signal. The linear mea-

surements y = Ψx, where

MN

Ψ∈

×

is a random measurement matrix, are static

in a sense that columns

ii

N

{}

1

Ψ

=

are xed a priori. They do not depend on the

signal or on the prior measurements. The most fundamental questions in the

design of a measurement matrix are as follows: (1) How much of the infor-

mation ...