Total Variation Based Image Restoration

Abstract

For the purpose of image restoration the process of image formation can be modeled in a first approximation by the formula [207]

$$ {u_d} = Q\{ II(k*u) + n\} , $$

(1.1)

where u represents the photonic flux k is the point spread function of the optical-captor joint apparatus П is a sampling operator, i.e., a Dirac comb supported by the centers of the matrix of digital sensors, n represents a random perturbation due to photonic or electronic noise, and Qis a uniform quantization operator mapping ℝ to a discrete interval of values, typically [0, 255].