# Questions tagged [total-variation]

The tag has no usage guidance.

46 questions
0answers
6 views

0answers
19 views

### If $(\pi_λ)_{λ\in\mathbb R}$ is a family of orthogonal projections, do $λ↦\left\|\pi_λx\right\|_H^2$ and $λ↦\pi_λx$ have the same variation?

Let $H$ be a $\mathbb R$-Hilbert space and $H_\lambda$ be a closed subspace of $H$ for $\lambda\in\mathbb R$. Assume $H_\lambda\subseteq H_\mu$ for all $\lambda,\mu\in\mathbb R$ with $\lambda\le\mu$ ...
1answer
40 views

0answers
12 views

0answers
12 views

### Multi-Variable CoArea formula for Total Variation

The total variation of a scalar function over a 2-manifold can be defined using the coarea formula. If I now use a N-d function, and I want to integrate the frobenius norm of its gradient over the 2-...
0answers
184 views

1answer
90 views

1answer
68 views

1answer
58 views

### On searching conditions, other than the continuity of $f,$ under which $\lim_{\mu (P) \rightarrow 0} V(f,P) = V_a^b f$ is also valid.

Let $f [a,b] \rightarrow \mathbb{R}, [a,b] \subset \mathbb{R}$ and a partition $P = \{ a=t_0 < t_1 < \cdots<t_n = b \}$ of $[a,b]$. If: $$V(f,P)=\sum_{i=1}^n |f(t_i) - f(t_{i-1})|$$ ...
1answer
114 views

2answers
232 views

### Derivative of total variation

Problem: Let $\alpha \in BV[a,b]$ (bounded variation on the interval $[a,b]$) and let $\beta(x) = V_a^x \alpha$ be the total variation of $\alpha(x)$ from $a$ to $x \in [a,b]$. Prove or disprove: If ...
0answers
27 views

### A reference on Total Variation and its applications in Image Processing

The title is almost self-explanatory; I need a beginners' readable reference (book or article) on total variation and its applications in image processing, know any? Thanks bunches.
1answer
167 views

### If $\Omega$ is a bounded domain, is a $BV(\Omega)$ function also $L^\infty(\Omega)$?

Let $\Omega$ be a (non-empty) bounded domain. The space of functions of bounded variation is defined by $$BV(\Omega) = \{ u\in L^1(\Omega) \mid \|u\|_{TV} < \infty \}$$ where  |u|_{TV} = \...
3answers
376 views

### Least Squares with Total Variation Regularization - How to Set the Lambda ($\lambda$) Parameter?

I am trying to use total-variation minimization for an image reconstruction problem. Essentially, I am trying to penalize different in the intensity of the two pixels in the reconstructed image. For ...