Total Variation
The total variation of a vector, matrix, or list of matrices. Uses L1 norm of discrete gradients for vectors and L2 norm of discrete gradients for matrices.
tv(value, ...)
value |
An Expression, vector, or matrix. |
... |
(Optional) Expression objects or numeric constants that extend the third dimension of value. |
An Expression representing the total variation of the input.
rows <- 10
cols <- 10
Uorig <- matrix(sample(0:255, size = rows * cols, replace = TRUE), nrow = rows, ncol = cols)
# Known is 1 if the pixel is known, 0 if the pixel was corrupted
Known <- matrix(0, nrow = rows, ncol = cols)
for(i in 1:rows) {
for(j in 1:cols) {
if(stats::runif(1) > 0.7)
Known[i,j] <- 1
}
}
Ucorr <- Known %*% Uorig
# Recover the original image using total variation in-painting
U <- Variable(rows, cols)
obj <- Minimize(tv(U))
constraints <- list(Known * U == Known * Ucorr)
prob <- Problem(obj, constraints)
result <- solve(prob, solver = "SCS")
result$getValue(U)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.