Underdetermined system of linear equations

1 Underdetermined system of linear equations Assume that the inverse problem 

Thus we have the following problem find the m that minimizes /(m) subject to the constraint that 

We can solve this problem of the conditioned minimum by using the method of Lagrange multipliers  

Thus we have the following expression for the solution of our problem  

On the othei hand, this scjlution must satisfy equation (3.18)  

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The key point is that the underdetermined system of linear equations is rendered soluble by an assumption of the prior probabilities of the unknown coefficients. It is important to realize that truncating the number of modes creates... 

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