Utility routines used in both DCT and DFT based deconvolution. More...

#include "tvregopt.h"

Functions
static void	Divergence (num DivV, int DivWidth, int DivHeight, const numvec2 V, int Width, int Height, int NumChannels)
	Compute discrete 2D divergence. More...

static num	UUpdate (tvregsolver *S)
	Trims padding, computes \|\|B - u\|\|, and assigns u = B. More...

static ATTRIBUTE_ALWAYSINLINE int	WSymExtension (int N, int i)
	Boundary handling function for whole-sample symmetric extension. More...

static ATTRIBUTE_ALWAYSINLINE int	PeriodicExtension (int N, int i)
	Boundary handling function for periodic extension. More...

Detailed Description

Utility routines used in both DCT and DFT based deconvolution.

Author: Pascal Getreuer getre.nosp@m.uer@.nosp@m.gmail.nosp@m..com

This program is free software: you can use, modify and/or redistribute it under the terms of the simplified BSD License. You should have received a copy of this license along this program. If not, see http://www.opensource.org/licenses/bsd-license.html.

Definition in file util_deconv.h.

Function Documentation

static void Divergence	(	num *	DivV,
		int	DivWidth,
		int	DivHeight,
		const numvec2 *	V,
		int	Width,
		int	Height,
		int	NumChannels
	)

static

Compute discrete 2D divergence.

Parameters

DivV	the divergence of V
DivWidth,DivHeight	the dimensions of DivV
V	input vector field
Width,Height,NumChannels	the dimensions of V

The discrete divergence is defined as the negative adjoint of the discrete gradient operator, $\operatorname{div}:=-\nabla^* =-\partial^*_x-\partial^*_y,$ where $-\partial^*$ is

$\begin{pmatrix}-\partial^* g_0 \\-\partial^* g_1 \\ \vdots \\ -\partial^* g_{N-2} \\ -\partial^* g_{N-1}\end{pmatrix} = \begin{pmatrix} \hphantom{-}1 & & & & \\ -1 & 1 & & & \\ & \ddots & \ddots & & \\ & & -1 & \hphantom{-}1 & \\ & & & -1 & 0 \end{pmatrix}\begin{pmatrix} g_0 \\ g_1 \\ \vdots \\ g_{N-2} \\ g_{N-1}\end{pmatrix}.$

In the interior of the domain, the discrete divergence reduces to backward differences,

$\operatorname{div}V_{i,j}=V^x_{i,j}-V^x_{i-1,j} +V^y_{i,j}-V^y_{i,j-1},$

for i = 1, ..., Width-2, j = 1, ..., Height-2.

The input vector field V is represented as an array of numvec2 elements,

V[i + Width*(j + Height*k)].x = x-component at pixel (i,j) channel k,

V[i + Width*(j + Height*k)].y = y-component at pixel (i,j) channel k,

where i = 0, ..., Width-1, j = 0, ..., Height-1, and k = 0, ..., NumChannels-1.

Definition at line 49 of file util_deconv.h.

static ATTRIBUTE_ALWAYSINLINE int PeriodicExtension	(	int	N,
		int	i
	)

static

Boundary handling function for periodic extension.

Parameters

N	is the data length
i	is an index into the data

Returns: an index that is always between 0 and N - 1

Extends data "abcde" to "...deabcdeabcdeabc..."

Definition at line 158 of file util_deconv.h.

static num UUpdate ( tvregsolver * S )

static

Trims padding, computes ||B - u||, and assigns u = B.

Parameters

S	tvreg solver state

Returns: the norm ||B - u||

Definition at line 102 of file util_deconv.h.

static ATTRIBUTE_ALWAYSINLINE int WSymExtension	(	int	N,
		int	i
	)

static

Boundary handling function for whole-sample symmetric extension.

Parameters

N	is the data length
i	is an index into the data

Returns: an index that is always between 0 and N - 1

Extends data "abcde" to "...cbabcdedcbabcde..."

Definition at line 136 of file util_deconv.h.

Functions

Detailed Description

Function Documentation