The name is absent

63

Appendix A

Implementation of minimization of total variation
(min-TV) algorithm

This appendix describes the implementation of the Fast Total Variation deconvolution
(FTVd) algorithm [58] used to generate the imaging results of the Chinese character
“light” in Figure 4.2 for the single-pixel CS imaging system.

The CS reconstruction problem, in this case, based on the minimization of the
total variation of the image x is given by,

minZV(x) + 77∣∣Φs — y∣∣²,                      (A.l)

X             2

where TVix) is defined as ɪv ∣∣-D(prr∣∣, ^with ∣∣79p)a7∣∣ being the total variation of x at
pixel г, Φ is the measurement matrix, у is the acquired data, and μ is the regularization
parameter to be chosen based on the problem. The FTVd algorithm approximates
the minimization problem in (A.l) as

minɪ^ ι∣^wd∣ + f ∑2 ∣∣^w≈ ~ ⅞)^s∣ι² + ⅛∣∣^φ∙^τ - y∣ι²>          (ʌ-²)

i                             i

where β and w₁ are new variables introduced into the optimization. Equation (A.2)
can be solved by alternating minimization, where the w-subproblem contains the two
leftmost terms in (A.2) and the æ-subproblem contains the two rightmost terms in
(A.2). The W-Subproblem has a closed-form solution while the ʃ-subproblem can be
simplified into a least-square problem [58]. The original FTVd algorithm solves the

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