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. Author manuscript; available in PMC: 2018 Jan 30.
Published in final edited form as: J Neurosci Methods. 2016 Nov 17;276:46–55. doi: 10.1016/j.jneumeth.2016.11.005

Figure 2.

Figure 2

Two-dimensional example: (a) The rowspace of A is the direction of data diversity, while the nullspace is perpendicular directions, which lack diversity. (b) The solution set to Ax = b is the affine space SEC, which is parallel to the nullspace; the ambiguity due to lack of data diversity results in ambiguity of possible solutions forming SEC. (c) The distribution of x resulting from the likelihood P(b|x), the high probability region is nearest SEC. (d) The set SDR formed by the intersection of a bound on P(b|x) enforced by ∥Ax – b∥2 ≤ α2, and a bound on the prior distribution P(x) enforced by ∥x∥1 ≤ α1; the LASSO solution x1 is based on a trade-off where the combination of bounds must be as tight as possible.