To deal well with the problem of the image with intensity inhomogeneity, we use c 1 L and c 2 L to replace c 1 and c 2. Therefore, the level set formulation (3) can be rewritten as ∂ϕ ∂t = δ μ div ∇ ϕ | ∇ ϕ | − λ 1 ( I ( x, y ) − c 1 L ) 2 + λ 2 ( I ( x, y ) − c 2 L ) 2, (13).
end{aligned} (19) It then follows from (10) that formulation (17) can be rewritten as begin{aligned} t^{T}[M_{0}+M_{s}]t+ bigl(t^{T},y^{T} bigr begin{pmatrix} M_{0}l+q_{0} u-l end{pmatrix} +t^{T}M_{s}l+sum _{s = 1}^{S} biglvert t^{T}q_{s} bigrvert leq z. end{aligned}.
The formulation in (16) can be rewritten as an unconstrained regularized problem min_{mathbf{x}in mathbb{R}^{n}}|mathbf{y}-mathsf{Phi} mathbf{x}|_{1}+tau| mathbf{x}|_{0}.
Letting,,,,, and, the expression (1.4) can be rewritten as (1.5).
Based on (8), the formulation of the problem can be rewritten as max F d min x ̆ ∈ X ̆ d x ̆ 2 = x ̆ ∗ F d ∗ H v ∗ H v F d x ̆. (13).
The previous expression, for example, can be rewritten as (x+3)(x+3).
This equation can be rewritten in a matrix formulation: (5) Err Z − C D X = Z − C D C D T C D − 1 C D T Z.
Thus, the model can be rewritten in a matrix formulation: (3) Z C D X, X = C D T C D − 1 C D T Z, where Z = (g k ); X = (x i ) and C is the marking matrix recording whether the DHS sites are within the transcriptional regulatory regions of differentially expressed genes or not.
If we define w(k) = x, Equation (5) can be rewritten as: If we define w(k) = x, Equation (5) is transferred to the formulation as follows: F ( x ) = x - η ( x 5 - x 3 ).
