u-subproblem DFT solver for TV-regularized deconvolution More...

#include <string.h>
#include "util_deconv.h"

Functions
static void	SymmetricPadding (num Dest, const num Src, int Width, int Height, int NumChannels)
	Symmetrically pad an image to twice its size. More...

static void	AdjBlurFourier (numcomplex ATrans, num A, FFT(plan) TransformA, const numcomplex KernelTrans, const num ztilde, int Width, int Height, int NumChannels, num Alpha)
	Compute ATrans = Alpha . conj(KernelTrans) . DFT[ztilde].

static int	InitDeconvFourier (tvregsolver *S)
	Intializations to prepare TvRestore for Fourier deconvolution. More...

static void	UTransSolveFourier (numcomplex BTrans, num B, FFT(plan) TransformB, numcomplex ATrans, const numvec2 dtilde, const num *DenomTrans, int Width, int Height, int NumChannels)
	Compute BTrans = ( ATrans - DFT[div(dtilde)] ) / DenomTrans. More...

static num	UDeconvFourier (tvregsolver *S)
	Solve the u-subproblem using DFT transforms (UseZ = 0) More...

static num	UDeconvFourierZ (tvregsolver *S)
	Solve the u-subproblem using DFT transforms (UseZ = 1) More...

Detailed Description

u-subproblem DFT solver for TV-regularized 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 usolve_dft_inc.c.

Function Documentation

static int InitDeconvFourier ( tvregsolver * S )

static

Intializations to prepare TvRestore for Fourier deconvolution.

Parameters

S	tvreg solver state

Returns: 1 on success, 0 on failure

Definition at line 94 of file usolve_dft_inc.c.

static void SymmetricPadding	(	num *	Dest,
		const num *	Src,
		int	Width,
		int	Height,
		int	NumChannels
	)

static

Symmetrically pad an image to twice its size.

Parameters

Dest	the destination
Src	the source image
Width,Height,NumChannels	the dimensions of Src

The Src image of size Width by Height is reflected over each axis to create an image that is 2*Width by 2*Height.

Definition at line 27 of file usolve_dft_inc.c.

static num UDeconvFourier ( tvregsolver * S )

static

Solve the u-subproblem using DFT transforms (UseZ = 0)

This routine solves the u-subproblem

$\tfrac{\lambda}{\gamma}K^* Ku -\Delta u = \tfrac{\lambda}{ \gamma}K^* f -\operatorname{div}\tilde{d},$

where K denotes the blur operator $Ku := \varphi * u$ . The solution is obtained using the discrete Fourier transform (DFT) as

$u=\mathcal{F}^{-1}\left[\frac{\frac{\lambda}{\gamma}\overline{ \mathcal{F}(\varphi)}\cdot\mathcal{F}(Ef)- \mathcal{F}\bigl(E \operatorname{div}(d-b)\bigr)}{\frac{\lambda}{\gamma}\lvert\mathcal{F}( \varphi)\rvert^2 - \mathcal{F}(\Delta)}\right],$

where E denotes symmetric extension and $\mathcal{F}$ denotes the DFT.

Definition at line 227 of file usolve_dft_inc.c.

static num UDeconvFourierZ ( tvregsolver * S )

static

Solve the u-subproblem using DFT transforms (UseZ = 1)

This extended version of UDeconvFourier is used when performing Fourier- based deconvolution with the three-auxiliary variable algorithm (UseZ = 1), that is, in a deconvolution problem with a non-symmetric kernel and non- Gaussian noise model.

Definition at line 249 of file usolve_dft_inc.c.

static void UTransSolveFourier	(	numcomplex *	BTrans,
		num *	B,
		FFT(plan)	TransformB,
		numcomplex *	ATrans,
		const numvec2 *	dtilde,
		const num *	DenomTrans,
		int	Width,
		int	Height,
		int	NumChannels
	)

static

Compute BTrans = ( ATrans - DFT[div(dtilde)] ) / DenomTrans.

This subroutine is a part of the DFT u-subproblem solution that is common to both the d,u splitting (UseZ=0) and d,u,z splitting (UseZ=1).

Definition at line 183 of file usolve_dft_inc.c.

Functions

Detailed Description

Function Documentation