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CS_recovery_algorithms.zip （8个子文件）

CS_recovery_algorithms

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Demo_CS_SP.m 3KB

Demo_CS_CoSaMP.m 3KB

Demo_CS_IHT.m 3KB

lena.bmp 65KB

Demo_CS_IRLS.m 3KB

Demo_CS_OMP.m 3KB

Demo_CS_GBP.m 8KB

CS Recovery Algorithms.pdf 418KB

Compressed Sensing Recovery Algorithms

Chengfu Huo

roy@mail.ustc.edu.cn

There are many compressed sensing (CS) recovery algorithms that have been proposed.

Here I list some of them, and provide the corresponding experimental results. Essentially, the

recovery algorithms are similar to the sparse coding based on the over-complete dictionary. The

corresponding Matlab Codes of the following algorithms can be downloaded from my

homepage, http://home.ustc.edu.cn/~roy.

1. Orthogonal Matching Pursuit (OMP) [1]

Algorithm 1: CS recovery using OMP

Input: The CS observation

, and a measurement matrix

{ , 1,2, , }

im  Ω ΦΨ 



where



Φ

and



Ψ

Initialization: Index

I=

, residual

ry

, sparse representation

R



Iteration:

while (stopping criterion false)

argmax | , |

i   



;

{}iI = I

;

†

(:, )[ (:, )] Ω Ωr = y I I y

;

end while

†

( ) [ (:, )] Ω



I I y

;

Output: Sparse representation



, and the original signal

 Ψ



Fig. 1. Recovery result by using OMP

original image

50 100 150 200 250

100

150

200

250

measurement mat

50 100 150 200 250

1d dct mat

50 100 150 200 250

100

150

200

250

1d rec img22.0812dB

50 100 150 200 250

100

150

200

250

I employ the OMP to recovery an image in the column-by-column fashion, i.e. process each

column separately. The recovery result is shown in Fig. 1. The advantages of OMP are easy

implementation and fast speed.

2. Compressive Sampling Matching Pursuit (CoSaMP) [2]

The foundation of this algorithm is that “For an s-sparse signal x, the vector

Φ Φy = x

can

serve as a proxy for the signal because the energy in each set of s components of y approximates

the energy in the corresponding s components of x. In particular, the largest s entries of the proxy

y point toward the largest s entries of the signal x.”

Algorithm 2: CS recovery using CoSaMP

Input: The CS observation y, a measurement matrix

{ , 1,2, , }

im  Ω ΦΨ 



where



Φ

and



Ψ

, and the sparsity of signal x based on

is s.

Initialization: Residual

ry

, sparse representation

R



Iteration:

while (stopping criterion false)

 Ω r



;

sup( | )



;

sup( )



p = p

;

†

( ) (:, ) Ω



p p y

;

  

;

 Ω



r = y

;

end while

Output: Sparse representation



, and the original signal

 Ψ



original image

50 100 150 200 250

100

150

200

250

measurement mat

50 100 150 200 250

1d dct mat

50 100 150 200 250

100

150

200

250

1d rec img20.2462dB

50 100 150 200 250

100

150

200

250

Fig. 2. Recovery result by using CoSaMP

Fig. 2 illustrates the recovered result of CoSaMP. Specifically, the image is recovered in

column-by-column fashion, so as to reduce the complexity. My experimental results depict that

the OMP has a better performance than the CoSaMP, while the CoSaMP is much more complex

than the OMP in the sense of computation.

3. Greedy Basis Pursuit (GBP) [3]

The authors declared that the GBP could discard some inappropriate atoms from the selected set

of atoms. Note that, this property is not reflected in the following description.

Algorithm 3: CS recovery using GBP

Input: The CS observation

, and a measurement matrix

{ , 1,2, , }

im  Ω ΦΨ 



where



Φ

and



Ψ

Initialization: Index

I=

, sparse representation

R



Procedure:

/ || ||n y y

;

argmax | , |

i   n



;

{}iI=

;

( ) ,

i  y



;

()





;

while (stopping criterion false)

(1)

d  



;

( / )

d,  

  

y y n y

;





r y y

;

|| ||

  

r r n n

;

argmin (arctan( , / , ))

j j H j H

k       



y n y v



;

{}kI = I

;

k H k H

= < , > < , >   n y n v y v n



;

( ) ,where

i , i I



  





; // refer the reference [3] for details

= Ω





;

end while

Output: Sparse representation



, and the original signal

 Ψ



According to my experimental results, the performance of GBP, shown in Fig. 3, is better than

that of OMP and CoSaMP. However, the GBP is much more complex than OMP and CoSaMP as

well.

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zl0508

2012-12-04

对于学习cs算法很有帮助，谢谢分享。

Compressive Sensing Recovery Algorithms(Matlab代码及相关文档)

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