1. Home
  2. Compressive sensing
  3. Compressive sensing
  4. Introduction

Introduction

<< Chapter < Page
  Compressive sensing   Page 1 / 1
Chapter >> Page >

Throughout this course, we shall be interested in the analog to digital conversion of signals f ( t ) , t ∈ R . We shall always assume f ∈ L 2 and usually assume additional properties of f in order to get meaningful results. In particular, we want to study two mappings: theencoding of f into bit streams and the decoding of the bit streams into approximations or estimates of f ,

E : f → bits streams (Encoder) D : bits streams → f ¯ (Decoder)
where f ¯ is the approximation of f defined by f ¯ : = D ( E ( f ) ) . In general, f ¯ ≠ f , so we shall need some way of quantifying how well f ¯ approximates f . Normally, the distortion between is measured by some norm ∥ f - f ¯ ∥ . Typical choices include:

the L 2 norm ∥ f ∥ L 2 : = ∫ | f ( t ) | 2 d t 1 / 2 the L ∞ norm ∥ f ∥ L ∞ : = sup t | f ( t ) | the L p norm ∥ f ∥ L p : = ∫ | f ( t ) | p d t 1 / p
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Compressive sensing. OpenStax CNX. Sep 21, 2007 Download for free at http://cnx.org/content/col10458/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Compressive sensing' conversation and receive update notifications?

Ask