ADMM优化求解

TV正则化(Total variation)

isotropic TV

anisotropic

ADMM的一般形式

deconvolution with TV prior

对应ADMM的一般形式

罚函数方法

bring constraints into objective

y: lagrange multiplier

增广拉格朗日函数法

augmented lagrangian is differentiable under mild conditions(usually better convergence)

ADMM

ADMM consist of 3 steps per iteration k:

一般形式

split f(x) and g(x) into independent problems!
u connects them
scaled dual variable:

TV deconvolution

子问题求解

x-update

solve normal equations


利用块循环矩阵的假设，使用FFT进行求解

一些参数可以迭代前预计算

z-update

element-wise threshold

u-update