Y = A X + V
to
Y = A W W^{-1} X + V = A' X' + V
such that A' has unit-norm columns. Once you obtain the result, you can obtain X by X = W X'.
The calling of T-MSBL is easy:
o When noise is large (e.g. SNR <=6 dB)
X_est = TMSBL(A, Y, 'noise', 'large')
o When noise is mild (e.g. 7 dB <= SNR <=22 dB)
X_est = TMSBL(A, Y, 'noise', 'mild')
o When noise is small (e.g. SNR >22 dB)
X_est = TMSBL(A, Y, 'noise', 'small')
o When no noise
X_est = TMSBL(A, Y, 'noise', 'no')But note that the above number 6dB or 22dB is not an exact value. The two values just give you a rough concept of what is the 'small noisy case', what is the 'mild noisy case', and what is the 'strongly noisy case'.
In this sense, this does not mean T-MSBL requires to know the noise level.
When you use T-MSBL in some practical problems when you really have no idea what is the range of noise strength (such as gene feature extraction), simply use the calling corresponding to the 'mild noise case', i.e.
X_est = TMSBL(A, Y, 'noise', 'mild')
I will update the code in the near future, such that in any case(noisy, noiseless, real variable, complex variable, large-scale data or small-scale data) you only need to input X_est = TMSBL(A,Y). But I currently am very busy on my on-going papers (four journal papers in three fields), so please forgive me that I cannot do this now.
