How to get an optimal alpha iteratively in Image Reconstruction based on Least Square in Philips Method

In 

Ib = Io @ h + n

@ is used to denote 2D convolution.

where Io is the original image (unknown), h is the blurring filter, Ib
is the blurred image and n is the noise, respectively. What we have
known is Ib, h and the mean mu and variance sigma of n. Io is to be
reconstructed. The so-called Philips method based on smoothing
reconstructs Io by minimising the following constraint least square
function
                    2                             2        2
J(Ioe) = ||Q * Ioe||  + alpha * (|| Ib - h @ Ioe||  - ||n||  )

where alpha is a constant, Ioe is the reconstructed Io, and
     2                       2       2
||n||  = (M - 1)(N - 1) * [mu + sigma ]

The frequency response of Ioe is (for each Hioe(w1, w2))
                      T
                     H (w1, w2) * Hb(w1, w2)
Hioe(w1, w2) = ---------------------------------------
                          2                          2
               |H(w1, w2)|  + (1/alpha) * |Hp(w1, w2)| 

where T denotes complex conjugate, and Hp is just the frequency
response of 2D Laplacian operator hp, that is,
     0  1  0
hp = 1 -4  1
     0  1  0

Then Ioe can be gained by doing inverse Fourier transform of Hioe.

Now, alpha needs to be adjusted to satisfy
                 2        2
|| Ib - h @ Ioe||  = ||n|| 

So how to determine alpha? Is there any algorithm to solve it? Is it
sole or multiple?

Thanks a lot!!!


With Kindly Regards,
Theron