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bm3d.cpp
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/*
* Copyright (c) 2011, Marc Lebrun <[email protected]>
* All rights reserved.
*
* This program is free software: you can use, modify and/or
* redistribute it under the terms of the GNU General Public
* License as published by the Free Software Foundation, either
* version 3 of the License, or (at your option) any later
* version. You should have received a copy of this license along
* this program. If not, see <http://www.gnu.org/licenses/>.
*/
/**
* @file bm3d.cpp
* @brief BM3D denoising functions
*
* @author Marc Lebrun <[email protected]>
**/
#include <iostream>
#include <algorithm>
#include <math.h>
#include "bm3d.h"
#include "utilities.h"
#include "lib_transforms.h"
#define SQRT2 1.414213562373095
#define SQRT2_INV 0.7071067811865475
#define YUV 0
#define YCBCR 1
#define OPP 2
#define RGB 3
#define DCT 4
#define BIOR 5
#define HADAMARD 6
/*
* In order to reproduce the original BM3D the DC coefficients are
* thresholded (DCTHRESH uncommented) and are filtered using Wiener
* (DCWIENER uncommented), MTRICK activates undocumented tricks from
* Marc Lebrun's implementation of BM3D available in IPOL
* http://www.ipol.im/pub/art/2012/l-bm3d/, not in the original paper.
*/
#define DCTHRESH
#define DCWIENER
//#define MTRICK
using namespace std;
bool ComparaisonFirst(pair<float,unsigned> pair1, pair<float,unsigned> pair2)
{
return pair1.first < pair2.first;
}
/** ----------------- **/
/** - Main function - **/
/** ----------------- **/
/**
* @brief run BM3D process. Depending on if OpenMP is used or not,
* and on the number of available threads, it divides the noisy
* image in sub_images, to process them in parallel.
*
* @param sigma: value of assumed noise of the noisy image;
* @param img_noisy: noisy image;
* @param img_basic: will be the basic estimation after the 1st step
* @param img_denoised: will be the denoised final image;
* @param width, height, chnls: size of the image;
* @param useSD_h (resp. useSD_w): if true, use weight based
* on the standard variation of the 3D group for the
* first (resp. second) step, otherwise use the number
* of non-zero coefficients after Hard Thresholding
* (resp. the norm of Wiener coefficients);
* @param tau_2D_hard (resp. tau_2D_wien): 2D transform to apply
* on every 3D group for the first (resp. second) part.
* Allowed values are DCT and BIOR;
* @param color_space: Transformation from RGB to YUV. Allowed
* values are RGB (do nothing), YUV, YCBCR and OPP.
* @param patch_size: overrides the default patch size selection.
* patch_size=0: use default behavior
* patch_size>0: size to be used
* @param verbose: if true, print additional information;
*
* @return EXIT_FAILURE if color_space has not expected
* type, otherwise return EXIT_SUCCESS.
**/
int run_bm3d(
const float sigma
, vector<float> &img_noisy
, vector<float> &img_basic
, vector<float> &img_denoised
, const unsigned width
, const unsigned height
, const unsigned chnls
, const bool useSD_h
, const bool useSD_w
, const unsigned tau_2D_hard
, const unsigned tau_2D_wien
, const unsigned color_space
, const unsigned patch_size
, const unsigned nb_threads
, const bool verbose
){
//! Parameters
const unsigned nHard = 16; //! Half size of the search window
const unsigned nWien = 16; //! Half size of the search window
const unsigned NHard = 16; //! Must be a power of 2
const unsigned NWien = 32; //! Must be a power of 2
const unsigned pHard = 3;
const unsigned pWien = 3;
// patch_size must be larger than 0
if (patch_size == 0)
{
if (verbose) cout << "Parameter patch_size is selected automatically (8 or 12)." << endl;
} else {
// patch_size must be a power of 2 if tau_2D_* == BIOR
if ((tau_2D_hard == BIOR ||
tau_2D_wien == BIOR) &&
(patch_size & (patch_size - 1)) != 0)
{
cout << "Parameter patch_size must be a power of 2 if tau_2D_* == BIOR" << endl;
return EXIT_FAILURE;
}
}
//! Overrides size if patch_size>0, else default behavior (8 or 12 depending on test)
const unsigned kHard = patch_size > 0 ? patch_size :
((tau_2D_hard == BIOR || sigma < 40.f) ? 8 : 12);
const unsigned kWien = patch_size > 0 ? patch_size :
((tau_2D_wien == BIOR || sigma < 40.f) ? 8 : 12);
//! Check memory allocation
if (img_basic.size() != img_noisy.size())
img_basic.resize(img_noisy.size());
if (img_denoised.size() != img_noisy.size())
img_denoised.resize(img_noisy.size());
//! Transformation to YUV color space
if (color_space_transform(img_noisy, color_space, width, height, chnls, true)
!= EXIT_SUCCESS) return EXIT_FAILURE;
//! Check if OpenMP is used or if number of cores of the computer is > 1
unsigned _nb_threads = nb_threads;
if (verbose)
{
cout << "OpenMP multithreading is";
#ifndef _OPENMP
cout << " not";
#endif
cout << " available." << endl;
}
// set _nb_threads
#ifdef _OPENMP
unsigned avail_nb_threads = omp_get_max_threads();
unsigned avail_nb_cores = omp_get_num_procs();
// if specified number exceeds available threads of if not specified at all
// at least use all available threads
if (_nb_threads > avail_nb_threads || _nb_threads == 0)
{
// log if specified number of threads exeeds number of real cores
if (_nb_threads > avail_nb_cores)
cout << "Parameter nb_threads should not exceed the number of real cores." << endl;
_nb_threads = avail_nb_threads;
}
// In case the number of threads is not a power of 2
if (!power_of_2(_nb_threads))
_nb_threads = closest_power_of_2(_nb_threads);
#else
if (_nb_threads > 1)
{
cout << "Parameter nb_threads has no effect if OpenMP multithreading is not available." << endl;
}
_nb_threads = 1;
#endif
if (verbose)
{
cout << "Working threads: " << _nb_threads;
#ifdef _OPENMP
cout << " (Must be 2^n) (Total available threads/real cores: " << avail_nb_threads << "/" << avail_nb_cores << ")";
#endif
cout << endl;
}
//! Allocate plan for FFTW library
fftwf_plan plan_2d_for_1[_nb_threads];
fftwf_plan plan_2d_for_2[_nb_threads];
fftwf_plan plan_2d_inv[_nb_threads];
//! In the simple case
if (_nb_threads == 1)
{
//! Add boundaries and symetrize them
const unsigned h_b = height + 2 * nHard;
const unsigned w_b = width + 2 * nHard;
vector<float> img_sym_noisy, img_sym_basic, img_sym_denoised;
symetrize(img_noisy, img_sym_noisy, width, height, chnls, nHard);
//! Allocating Plan for FFTW process
if (tau_2D_hard == DCT)
{
const unsigned nb_cols = ind_size(w_b - kHard + 1, nHard, pHard);
allocate_plan_2d(&plan_2d_for_1[0], kHard, FFTW_REDFT10,
w_b * (2 * nHard + 1) * chnls);
allocate_plan_2d(&plan_2d_for_2[0], kHard, FFTW_REDFT10,
w_b * pHard * chnls);
allocate_plan_2d(&plan_2d_inv [0], kHard, FFTW_REDFT01,
NHard * nb_cols * chnls);
}
//! Denoising, 1st Step
if (verbose) cout << "BM3D 1st step...";
bm3d_1st_step(sigma, img_sym_noisy, img_sym_basic, w_b, h_b, chnls, nHard,
kHard, NHard, pHard, useSD_h, color_space, tau_2D_hard,
&plan_2d_for_1[0], &plan_2d_for_2[0], &plan_2d_inv[0]);
if (verbose) cout << "is done." << endl;
//! To avoid boundaries problem
for (unsigned c = 0; c < chnls; c++)
{
const unsigned dc_b = c * w_b * h_b + nHard * w_b + nHard;
unsigned dc = c * width * height;
for (unsigned i = 0; i < height; i++)
for (unsigned j = 0; j < width; j++, dc++)
img_basic[dc] = img_sym_basic[dc_b + i * w_b + j];
}
symetrize(img_basic, img_sym_basic, width, height, chnls, nHard);
//! Allocating Plan for FFTW process
if (tau_2D_wien == DCT)
{
const unsigned nb_cols = ind_size(w_b - kWien + 1, nWien, pWien);
allocate_plan_2d(&plan_2d_for_1[0], kWien, FFTW_REDFT10,
w_b * (2 * nWien + 1) * chnls);
allocate_plan_2d(&plan_2d_for_2[0], kWien, FFTW_REDFT10,
w_b * pWien * chnls);
allocate_plan_2d(&plan_2d_inv [0], kWien, FFTW_REDFT01,
NWien * nb_cols * chnls);
}
//! Denoising, 2nd Step
if (verbose) cout << "BM3D 2nd step...";
bm3d_2nd_step(sigma, img_sym_noisy, img_sym_basic, img_sym_denoised,
w_b, h_b, chnls, nWien, kWien, NWien, pWien, useSD_w, color_space,
tau_2D_wien, &plan_2d_for_1[0], &plan_2d_for_2[0], &plan_2d_inv[0]);
if (verbose) cout << "is done." << endl;
//! Obtention of img_denoised
for (unsigned c = 0; c < chnls; c++)
{
const unsigned dc_b = c * w_b * h_b + nWien * w_b + nWien;
unsigned dc = c * width * height;
for (unsigned i = 0; i < height; i++)
for (unsigned j = 0; j < width; j++, dc++)
img_denoised[dc] = img_sym_denoised[dc_b + i * w_b + j];
}
}
//! If more than 1 threads are used
else
{
//! Cut the image in _nb_threads parts
vector<vector<float> > sub_noisy(_nb_threads);
vector<vector<float> > sub_basic(_nb_threads);
vector<vector<float> > sub_denoised(_nb_threads);
vector<unsigned> h_table(_nb_threads);
vector<unsigned> w_table(_nb_threads);
sub_divide(img_noisy, sub_noisy, w_table, h_table, width, height, chnls,
2 * nWien, true);
//! Allocating Plan for FFTW process
if (tau_2D_hard == DCT)
for (unsigned n = 0; n < _nb_threads; n++)
{
const unsigned nb_cols = ind_size(w_table[n] - kHard + 1, nHard, pHard);
allocate_plan_2d(&plan_2d_for_1[n], kHard, FFTW_REDFT10,
w_table[n] * (2 * nHard + 1) * chnls);
allocate_plan_2d(&plan_2d_for_2[n], kHard, FFTW_REDFT10,
w_table[n] * pHard * chnls);
allocate_plan_2d(&plan_2d_inv [n], kHard, FFTW_REDFT01,
NHard * nb_cols * chnls);
}
//! denoising : 1st Step
if (verbose) cout << "BM3D 1st step...";
#pragma omp parallel shared(sub_noisy, sub_basic, w_table, h_table, \
plan_2d_for_1, plan_2d_for_2, plan_2d_inv)
{
#pragma omp for schedule(dynamic) nowait
for (unsigned n = 0; n < _nb_threads; n++)
{
bm3d_1st_step(sigma, sub_noisy[n], sub_basic[n], w_table[n],
h_table[n], chnls, nHard, kHard, NHard, pHard, useSD_h,
color_space, tau_2D_hard, &plan_2d_for_1[n],
&plan_2d_for_2[n], &plan_2d_inv[n]);
}
}
if (verbose) cout << "is done." << endl;
sub_divide(img_basic, sub_basic, w_table, h_table,
width, height, chnls, 2 * nHard, false);
sub_divide(img_basic, sub_basic, w_table, h_table, width, height, chnls,
2 * nHard, true);
//! Allocating Plan for FFTW process
if (tau_2D_wien == DCT)
for (unsigned n = 0; n < _nb_threads; n++)
{
const unsigned nb_cols = ind_size(w_table[n] - kWien + 1, nWien, pWien);
allocate_plan_2d(&plan_2d_for_1[n], kWien, FFTW_REDFT10,
w_table[n] * (2 * nWien + 1) * chnls);
allocate_plan_2d(&plan_2d_for_2[n], kWien, FFTW_REDFT10,
w_table[n] * pWien * chnls);
allocate_plan_2d(&plan_2d_inv [n], kWien, FFTW_REDFT01,
NWien * nb_cols * chnls);
}
//! Denoising: 2nd Step
if (verbose) cout << "BM3D 2nd step...";
#pragma omp parallel shared(sub_noisy, sub_basic, sub_denoised, w_table, \
h_table, plan_2d_for_1, plan_2d_for_2, \
plan_2d_inv)
{
#pragma omp for schedule(dynamic) nowait
for (unsigned n = 0; n < _nb_threads; n++)
{
bm3d_2nd_step(sigma, sub_noisy[n], sub_basic[n], sub_denoised[n],
w_table[n], h_table[n], chnls, nWien, kWien, NWien, pWien,
useSD_w, color_space, tau_2D_wien, &plan_2d_for_1[n],
&plan_2d_for_2[n], &plan_2d_inv[n]);
}
}
if (verbose) cout << "is done." << endl;
//! Reconstruction of the image
sub_divide(img_denoised, sub_denoised, w_table, h_table,
width, height, chnls, 2 * nWien, false);
}
//! Inverse color space transform to RGB
if (color_space_transform(img_denoised, color_space, width, height, chnls, false)
!= EXIT_SUCCESS) return EXIT_FAILURE;
if (color_space_transform(img_noisy, color_space, width, height, chnls, false)
!= EXIT_SUCCESS) return EXIT_FAILURE;
if (color_space_transform(img_basic, color_space, width, height, chnls, false)
!= EXIT_SUCCESS) return EXIT_FAILURE;
//! Free Memory
if (tau_2D_hard == DCT || tau_2D_wien == DCT)
for (unsigned n = 0; n < _nb_threads; n++)
{
fftwf_destroy_plan(plan_2d_for_1[n]);
fftwf_destroy_plan(plan_2d_for_2[n]);
fftwf_destroy_plan(plan_2d_inv[n]);
}
fftwf_cleanup();
return EXIT_SUCCESS;
}
/**
* @brief Run the basic process of BM3D (1st step). The result
* is contained in img_basic. The image has boundary, which
* are here only for block-matching and doesn't need to be
* denoised.
*
* @param sigma: value of assumed noise of the image to denoise;
* @param img_noisy: noisy image;
* @param img_basic: will contain the denoised image after the 1st step;
* @param width, height, chnls : size of img_noisy;
* @param nHard: size of the boundary around img_noisy;
* @param useSD: if true, use weight based on the standard variation
* of the 3D group for the first step, otherwise use the number
* of non-zero coefficients after Hard-thresholding;
* @param tau_2D: DCT or BIOR;
* @param plan_2d_for_1, plan_2d_for_2, plan_2d_inv : for convenience. Used
* by fftw.
*
* @return none.
**/
void bm3d_1st_step(
const float sigma
, vector<float> const& img_noisy
, vector<float> &img_basic
, const unsigned width
, const unsigned height
, const unsigned chnls
, const unsigned nHard
, const unsigned kHard
, const unsigned NHard
, const unsigned pHard
, const bool useSD
, const unsigned color_space
, const unsigned tau_2D
, fftwf_plan * plan_2d_for_1
, fftwf_plan * plan_2d_for_2
, fftwf_plan * plan_2d_inv
){
//! Estimatation of sigma on each channel
vector<float> sigma_table(chnls);
if (estimate_sigma(sigma, sigma_table, chnls, color_space) != EXIT_SUCCESS)
return;
//! Parameters initialization
const float lambdaHard3D = 2.7f; //! Threshold for Hard Thresholding
const float tauMatch = (chnls == 1 ? 3.f : 1.f) * (sigma_table[0] < 35.0f ? 2500 : 5000); //! threshold used to determinate similarity between patches
//! Initialization for convenience
vector<unsigned> row_ind;
ind_initialize(row_ind, height - kHard + 1, nHard, pHard);
vector<unsigned> column_ind;
ind_initialize(column_ind, width - kHard + 1, nHard, pHard);
const unsigned kHard_2 = kHard * kHard;
vector<float> group_3D_table(chnls * kHard_2 * NHard * column_ind.size());
vector<float> wx_r_table;
wx_r_table.reserve(chnls * column_ind.size());
vector<float> hadamard_tmp(NHard);
//! Check allocation memory
if (img_basic.size() != img_noisy.size())
img_basic.resize(img_noisy.size());
//! Preprocessing (KaiserWindow, Threshold, DCT normalization, ...)
vector<float> kaiser_window(kHard_2);
vector<float> coef_norm(kHard_2);
vector<float> coef_norm_inv(kHard_2);
preProcess(kaiser_window, coef_norm, coef_norm_inv, kHard);
//! Preprocessing of Bior table
vector<float> lpd, hpd, lpr, hpr;
bior15_coef(lpd, hpd, lpr, hpr);
//! For aggregation part
vector<float> denominator(width * height * chnls, 0.0f);
vector<float> numerator (width * height * chnls, 0.0f);
//! Precompute Bloc-Matching
vector<vector<unsigned> > patch_table;
precompute_BM(patch_table, img_noisy, width, height, kHard, NHard, nHard, pHard, tauMatch);
//! table_2D[p * N + q + (i * width + j) * kHard_2 + c * (2 * nHard + 1) * width * kHard_2]
vector<float> table_2D((2 * nHard + 1) * width * chnls * kHard_2, 0.0f);
//! Loop on i_r
for (unsigned ind_i = 0; ind_i < row_ind.size(); ind_i++)
{
const unsigned i_r = row_ind[ind_i];
//! Update of table_2D
if (tau_2D == DCT)
dct_2d_process(table_2D, img_noisy, plan_2d_for_1, plan_2d_for_2, nHard,
width, height, chnls, kHard, i_r, pHard, coef_norm,
row_ind[0], row_ind.back());
else if (tau_2D == BIOR)
bior_2d_process(table_2D, img_noisy, nHard, width, height, chnls,
kHard, i_r, pHard, row_ind[0], row_ind.back(), lpd, hpd);
wx_r_table.clear();
group_3D_table.clear();
//! Loop on j_r
for (unsigned ind_j = 0; ind_j < column_ind.size(); ind_j++)
{
//! Initialization
const unsigned j_r = column_ind[ind_j];
const unsigned k_r = i_r * width + j_r;
//! Number of similar patches
const unsigned nSx_r = patch_table[k_r].size();
//! Build of the 3D group
vector<float> group_3D(chnls * nSx_r * kHard_2, 0.0f);
for (unsigned c = 0; c < chnls; c++)
for (unsigned n = 0; n < nSx_r; n++)
{
const unsigned ind = patch_table[k_r][n] + (nHard - i_r) * width;
for (unsigned k = 0; k < kHard_2; k++)
group_3D[n + k * nSx_r + c * kHard_2 * nSx_r] =
table_2D[k + ind * kHard_2 + c * kHard_2 * (2 * nHard + 1) * width];
}
//! HT filtering of the 3D group
vector<float> weight_table(chnls);
ht_filtering_hadamard(group_3D, hadamard_tmp, nSx_r, kHard, chnls, sigma_table,
lambdaHard3D, weight_table, !useSD);
//! 3D weighting using Standard Deviation
if (useSD)
sd_weighting(group_3D, nSx_r, kHard, chnls, weight_table);
//! Save the 3D group. The DCT 2D inverse will be done after.
for (unsigned c = 0; c < chnls; c++)
for (unsigned n = 0; n < nSx_r; n++)
for (unsigned k = 0; k < kHard_2; k++)
group_3D_table.push_back(group_3D[n + k * nSx_r +
c * kHard_2 * nSx_r]);
//! Save weighting
for (unsigned c = 0; c < chnls; c++)
wx_r_table.push_back(weight_table[c]);
} //! End of loop on j_r
//! Apply 2D inverse transform
if (tau_2D == DCT)
dct_2d_inverse(group_3D_table, kHard, NHard * chnls * column_ind.size(),
coef_norm_inv, plan_2d_inv);
else if (tau_2D == BIOR)
bior_2d_inverse(group_3D_table, kHard, lpr, hpr);
//! Registration of the weighted estimation
unsigned dec = 0;
for (unsigned ind_j = 0; ind_j < column_ind.size(); ind_j++)
{
const unsigned j_r = column_ind[ind_j];
const unsigned k_r = i_r * width + j_r;
const unsigned nSx_r = patch_table[k_r].size();
for (unsigned c = 0; c < chnls; c++)
{
for (unsigned n = 0; n < nSx_r; n++)
{
const unsigned k = patch_table[k_r][n] + c * width * height;
for (unsigned p = 0; p < kHard; p++)
for (unsigned q = 0; q < kHard; q++)
{
const unsigned ind = k + p * width + q;
numerator[ind] += kaiser_window[p * kHard + q]
* wx_r_table[c + ind_j * chnls]
* group_3D_table[p * kHard + q + n * kHard_2
+ c * kHard_2 * nSx_r + dec];
denominator[ind] += kaiser_window[p * kHard + q]
* wx_r_table[c + ind_j * chnls];
}
}
}
dec += nSx_r * chnls * kHard_2;
}
} //! End of loop on i_r
//! Final reconstruction
for (unsigned k = 0; k < width * height * chnls; k++)
img_basic[k] = numerator[k] / denominator[k];
}
/**
* @brief Run the final process of BM3D (2nd step). The result
* is contained in img_denoised. The image has boundary, which
* are here only for block-matching and doesn't need to be
* denoised.
*
* @param sigma: value of assumed noise of the image to denoise;
* @param img_noisy: noisy image;
* @param img_basic: contains the denoised image after the 1st step;
* @param img_denoised: will contain the final estimate of the denoised
* image after the second step;
* @param width, height, chnls : size of img_noisy;
* @param nWien: size of the boundary around img_noisy;
* @param useSD: if true, use weight based on the standard variation
* of the 3D group for the second step, otherwise use the norm
* of Wiener coefficients of the 3D group;
* @param tau_2D: DCT or BIOR.
*
* @return none.
**/
void bm3d_2nd_step(
const float sigma
, vector<float> const& img_noisy
, vector<float> const& img_basic
, vector<float> &img_denoised
, const unsigned width
, const unsigned height
, const unsigned chnls
, const unsigned nWien
, const unsigned kWien
, const unsigned NWien
, const unsigned pWien
, const bool useSD
, const unsigned color_space
, const unsigned tau_2D
, fftwf_plan * plan_2d_for_1
, fftwf_plan * plan_2d_for_2
, fftwf_plan * plan_2d_inv
){
//! Estimatation of sigma on each channel
vector<float> sigma_table(chnls);
if (estimate_sigma(sigma, sigma_table, chnls, color_space) != EXIT_SUCCESS)
return;
//! Parameters initialization
const float tauMatch = (sigma_table[0] < 35.0f ? 400 : 3500); //! threshold used to determinate similarity between patches
//! Initialization for convenience
vector<unsigned> row_ind;
ind_initialize(row_ind, height - kWien + 1, nWien, pWien);
vector<unsigned> column_ind;
ind_initialize(column_ind, width - kWien + 1, nWien, pWien);
const unsigned kWien_2 = kWien * kWien;
vector<float> group_3D_table(chnls * kWien_2 * NWien * column_ind.size());
vector<float> wx_r_table;
wx_r_table.reserve(chnls * column_ind.size());
vector<float> tmp(NWien);
//! Check allocation memory
if (img_denoised.size() != img_noisy.size())
img_denoised.resize(img_noisy.size());
//! Preprocessing (KaiserWindow, Threshold, DCT normalization, ...)
vector<float> kaiser_window(kWien_2);
vector<float> coef_norm(kWien_2);
vector<float> coef_norm_inv(kWien_2);
preProcess(kaiser_window, coef_norm, coef_norm_inv, kWien);
//! For aggregation part
vector<float> denominator(width * height * chnls, 0.0f);
vector<float> numerator (width * height * chnls, 0.0f);
//! Precompute Bloc-Matching
vector<vector<unsigned> > patch_table;
precompute_BM(patch_table, img_basic, width, height, kWien, NWien, nWien, pWien, tauMatch);
//! Preprocessing of Bior table
vector<float> lpd, hpd, lpr, hpr;
bior15_coef(lpd, hpd, lpr, hpr);
//! DCT_table_2D[p * N + q + (i * width + j) * kWien_2 + c * (2 * ns + 1) * width * kWien_2]
vector<float> table_2D_img((2 * nWien + 1) * width * chnls * kWien_2, 0.0f);
vector<float> table_2D_est((2 * nWien + 1) * width * chnls * kWien_2, 0.0f);
//! Loop on i_r
for (unsigned ind_i = 0; ind_i < row_ind.size(); ind_i++)
{
const unsigned i_r = row_ind[ind_i];
//! Update of DCT_table_2D
if (tau_2D == DCT)
{
dct_2d_process(table_2D_img, img_noisy, plan_2d_for_1, plan_2d_for_2,
nWien, width, height, chnls, kWien, i_r, pWien, coef_norm,
row_ind[0], row_ind.back());
dct_2d_process(table_2D_est, img_basic, plan_2d_for_1, plan_2d_for_2,
nWien, width, height, chnls, kWien, i_r, pWien, coef_norm,
row_ind[0], row_ind.back());
}
else if (tau_2D == BIOR)
{
bior_2d_process(table_2D_img, img_noisy, nWien, width, height,
chnls, kWien, i_r, pWien, row_ind[0], row_ind.back(), lpd, hpd);
bior_2d_process(table_2D_est, img_basic, nWien, width, height,
chnls, kWien, i_r, pWien, row_ind[0], row_ind.back(), lpd, hpd);
}
wx_r_table.clear();
group_3D_table.clear();
//! Loop on j_r
for (unsigned ind_j = 0; ind_j < column_ind.size(); ind_j++)
{
//! Initialization
const unsigned j_r = column_ind[ind_j];
const unsigned k_r = i_r * width + j_r;
//! Number of similar patches
const unsigned nSx_r = patch_table[k_r].size();
//! Build of the 3D group
vector<float> group_3D_est(chnls * nSx_r * kWien_2, 0.0f);
vector<float> group_3D_img(chnls * nSx_r * kWien_2, 0.0f);
for (unsigned c = 0; c < chnls; c++)
for (unsigned n = 0; n < nSx_r; n++)
{
const unsigned ind = patch_table[k_r][n] + (nWien - i_r) * width;
for (unsigned k = 0; k < kWien_2; k++)
{
group_3D_est[n + k * nSx_r + c * kWien_2 * nSx_r] =
table_2D_est[k + ind * kWien_2 + c * kWien_2 * (2 * nWien + 1) * width];
group_3D_img[n + k * nSx_r + c * kWien_2 * nSx_r] =
table_2D_img[k + ind * kWien_2 + c * kWien_2 * (2 * nWien + 1) * width];
}
}
//! Wiener filtering of the 3D group
vector<float> weight_table(chnls);
wiener_filtering_hadamard(group_3D_img, group_3D_est, tmp, nSx_r, kWien,
chnls, sigma_table, weight_table, !useSD);
//! 3D weighting using Standard Deviation
if (useSD)
sd_weighting(group_3D_est, nSx_r, kWien, chnls, weight_table);
//! Save the 3D group. The DCT 2D inverse will be done after.
for (unsigned c = 0; c < chnls; c++)
for (unsigned n = 0; n < nSx_r; n++)
for (unsigned k = 0; k < kWien_2; k++)
group_3D_table.push_back(group_3D_est[n + k * nSx_r + c * kWien_2 * nSx_r]);
//! Save weighting
for (unsigned c = 0; c < chnls; c++)
wx_r_table.push_back(weight_table[c]);
} //! End of loop on j_r
//! Apply 2D dct inverse
if (tau_2D == DCT)
dct_2d_inverse(group_3D_table, kWien, NWien * chnls * column_ind.size(),
coef_norm_inv, plan_2d_inv);
else if (tau_2D == BIOR)
bior_2d_inverse(group_3D_table, kWien, lpr, hpr);
//! Registration of the weighted estimation
unsigned dec = 0;
for (unsigned ind_j = 0; ind_j < column_ind.size(); ind_j++)
{
const unsigned j_r = column_ind[ind_j];
const unsigned k_r = i_r * width + j_r;
const unsigned nSx_r = patch_table[k_r].size();
for (unsigned c = 0; c < chnls; c++)
{
for (unsigned n = 0; n < nSx_r; n++)
{
const unsigned k = patch_table[k_r][n] + c * width * height;
for (unsigned p = 0; p < kWien; p++)
for (unsigned q = 0; q < kWien; q++)
{
const unsigned ind = k + p * width + q;
numerator[ind] += kaiser_window[p * kWien + q]
* wx_r_table[c + ind_j * chnls]
* group_3D_table[p * kWien + q + n * kWien_2
+ c * kWien_2 * nSx_r + dec];
denominator[ind] += kaiser_window[p * kWien + q]
* wx_r_table[c + ind_j * chnls];
}
}
}
dec += nSx_r * chnls * kWien_2;
}
} //! End of loop on i_r
//! Final reconstruction
for (unsigned k = 0; k < width * height * chnls; k++)
img_denoised[k] = numerator[k] / denominator[k];
}
/**
* @brief Precompute a 2D DCT transform on all patches contained in
* a part of the image.
*
* @param DCT_table_2D : will contain the 2d DCT transform for all
* chosen patches;
* @param img : image on which the 2d DCT will be processed;
* @param plan_1, plan_2 : for convenience. Used by fftw;
* @param nHW : size of the boundary around img;
* @param width, height, chnls: size of img;
* @param kHW : size of patches (kHW x kHW);
* @param i_r: current index of the reference patches;
* @param step: space in pixels between two references patches;
* @param coef_norm : normalization coefficients of the 2D DCT;
* @param i_min (resp. i_max) : minimum (resp. maximum) value
* for i_r. In this case the whole 2d transform is applied
* on every patches. Otherwise the precomputed 2d DCT is re-used
* without processing it.
**/
void dct_2d_process(
vector<float> &DCT_table_2D
, vector<float> const& img
, fftwf_plan * plan_1
, fftwf_plan * plan_2
, const unsigned nHW
, const unsigned width
, const unsigned height
, const unsigned chnls
, const unsigned kHW
, const unsigned i_r
, const unsigned step
, vector<float> const& coef_norm
, const unsigned i_min
, const unsigned i_max
){
//! Declarations
const unsigned kHW_2 = kHW * kHW;
const unsigned size = chnls * kHW_2 * width * (2 * nHW + 1);
//! If i_r == ns, then we have to process all DCT
if (i_r == i_min || i_r == i_max)
{
//! Allocating Memory
float* vec = (float*) fftwf_malloc(size * sizeof(float));
float* dct = (float*) fftwf_malloc(size * sizeof(float));
for (unsigned c = 0; c < chnls; c++)
{
const unsigned dc = c * width * height;
const unsigned dc_p = c * kHW_2 * width * (2 * nHW + 1);
for (unsigned i = 0; i < 2 * nHW + 1; i++)
for (unsigned j = 0; j < width - kHW; j++)
for (unsigned p = 0; p < kHW; p++)
for (unsigned q = 0; q < kHW; q++)
vec[p * kHW + q + dc_p + (i * width + j) * kHW_2] =
img[dc + (i_r + i - nHW + p) * width + j + q];
}
//! Process of all DCTs
fftwf_execute_r2r(*plan_1, vec, dct);
fftwf_free(vec);
//! Getting the result
for (unsigned c = 0; c < chnls; c++)
{
const unsigned dc = c * kHW_2 * width * (2 * nHW + 1);
const unsigned dc_p = c * kHW_2 * width * (2 * nHW + 1);
for (unsigned i = 0; i < 2 * nHW + 1; i++)
for (unsigned j = 0; j < width - kHW; j++)
for (unsigned k = 0; k < kHW_2; k++)
DCT_table_2D[dc + (i * width + j) * kHW_2 + k] =
dct[dc_p + (i * width + j) * kHW_2 + k] * coef_norm[k];
}
fftwf_free(dct);
}
else
{
const unsigned ds = step * width * kHW_2;
//! Re-use of DCT already processed
for (unsigned c = 0; c < chnls; c++)
{
unsigned dc = c * width * (2 * nHW + 1) * kHW_2;
for (unsigned i = 0; i < 2 * nHW + 1 - step; i++)
for (unsigned j = 0; j < width - kHW; j++)
for (unsigned k = 0; k < kHW_2; k++)
DCT_table_2D[k + (i * width + j) * kHW_2 + dc] =
DCT_table_2D[k + (i * width + j) * kHW_2 + dc + ds];
}
//! Compute the new DCT
float* vec = (float*) fftwf_malloc(chnls * kHW_2 * step * width * sizeof(float));
float* dct = (float*) fftwf_malloc(chnls * kHW_2 * step * width * sizeof(float));
for (unsigned c = 0; c < chnls; c++)
{
const unsigned dc = c * width * height;
const unsigned dc_p = c * kHW_2 * width * step;
for (unsigned i = 0; i < step; i++)
for (unsigned j = 0; j < width - kHW; j++)
for (unsigned p = 0; p < kHW; p++)
for (unsigned q = 0; q < kHW; q++)
vec[p * kHW + q + dc_p + (i * width + j) * kHW_2] =
img[(p + i + 2 * nHW + 1 - step + i_r - nHW)
* width + j + q + dc];
}
//! Process of all DCTs
fftwf_execute_r2r(*plan_2, vec, dct);
fftwf_free(vec);
//! Getting the result
for (unsigned c = 0; c < chnls; c++)
{
const unsigned dc = c * kHW_2 * width * (2 * nHW + 1);
const unsigned dc_p = c * kHW_2 * width * step;
for (unsigned i = 0; i < step; i++)
for (unsigned j = 0; j < width - kHW; j++)
for (unsigned k = 0; k < kHW_2; k++)
DCT_table_2D[dc + ((i + 2 * nHW + 1 - step) * width + j) * kHW_2 + k] =
dct[dc_p + (i * width + j) * kHW_2 + k] * coef_norm[k];
}
fftwf_free(dct);
}
}
/**
* @brief Precompute a 2D bior1.5 transform on all patches contained in
* a part of the image.
*
* @param bior_table_2D : will contain the 2d bior1.5 transform for all
* chosen patches;
* @param img : image on which the 2d transform will be processed;
* @param nHW : size of the boundary around img;
* @param width, height, chnls: size of img;
* @param kHW : size of patches (kHW x kHW). MUST BE A POWER OF 2 !!!
* @param i_r: current index of the reference patches;
* @param step: space in pixels between two references patches;
* @param i_min (resp. i_max) : minimum (resp. maximum) value
* for i_r. In this case the whole 2d transform is applied
* on every patches. Otherwise the precomputed 2d DCT is re-used
* without processing it;
* @param lpd : low pass filter of the forward bior1.5 2d transform;
* @param hpd : high pass filter of the forward bior1.5 2d transform.
**/
void bior_2d_process(
vector<float> &bior_table_2D
, vector<float> const& img
, const unsigned nHW
, const unsigned width
, const unsigned height
, const unsigned chnls
, const unsigned kHW
, const unsigned i_r
, const unsigned step
, const unsigned i_min
, const unsigned i_max
, vector<float> &lpd
, vector<float> &hpd
){
//! Declarations
const unsigned kHW_2 = kHW * kHW;
//! If i_r == ns, then we have to process all Bior1.5 transforms
if (i_r == i_min || i_r == i_max)
{
for (unsigned c = 0; c < chnls; c++)
{
const unsigned dc = c * width * height;
const unsigned dc_p = c * kHW_2 * width * (2 * nHW + 1);
for (unsigned i = 0; i < 2 * nHW + 1; i++)
for (unsigned j = 0; j < width - kHW; j++)
{
bior_2d_forward(img, bior_table_2D, kHW, dc +
(i_r + i - nHW) * width + j, width,
dc_p + (i * width + j) * kHW_2, lpd, hpd);
}
}
}
else
{
const unsigned ds = step * width * kHW_2;
//! Re-use of Bior1.5 already processed
for (unsigned c = 0; c < chnls; c++)
{
unsigned dc = c * width * (2 * nHW + 1) * kHW_2;
for (unsigned i = 0; i < 2 * nHW + 1 - step; i++)
for (unsigned j = 0; j < width - kHW; j++)
for (unsigned k = 0; k < kHW_2; k++)
bior_table_2D[k + (i * width + j) * kHW_2 + dc] =
bior_table_2D[k + (i * width + j) * kHW_2 + dc + ds];
}
//! Compute the new Bior
for (unsigned c = 0; c < chnls; c++)
{
const unsigned dc = c * width * height;
const unsigned dc_p = c * kHW_2 * width * (2 * nHW + 1);
for (unsigned i = 0; i < step; i++)
for (unsigned j = 0; j < width - kHW; j++)
{
bior_2d_forward(img, bior_table_2D, kHW, dc +
(i + 2 * nHW + 1 - step + i_r - nHW) * width + j,
width, dc_p + ((i + 2 * nHW + 1 - step)
* width + j) * kHW_2, lpd, hpd);
}
}
}
}
/**
* @brief HT filtering using Welsh-Hadamard transform (do only third
* dimension transform, Hard Thresholding and inverse transform).
*
* @param group_3D : contains the 3D block for a reference patch;
* @param tmp: allocated vector used in Hadamard transform for convenience;
* @param nSx_r : number of similar patches to a reference one;
* @param kHW : size of patches (kHW x kHW);
* @param chnls : number of channels of the image;
* @param sigma_table : contains value of noise for each channel;
* @param lambdaHard3D : value of thresholding;
* @param weight_table: the weighting of this 3D group for each channel;
* @param doWeight: if true process the weighting, do nothing
* otherwise.
*
* @return none.
**/
void ht_filtering_hadamard(
vector<float> &group_3D
, vector<float> &tmp
, const unsigned nSx_r
, const unsigned kHard
, const unsigned chnls
, vector<float> const& sigma_table
, const float lambdaHard3D
, vector<float> &weight_table
, const bool doWeight
){
//! Declarations
const unsigned kHard_2 = kHard * kHard;
for (unsigned c = 0; c < chnls; c++)
weight_table[c] = 0.0f;
const float coef_norm = sqrtf((float) nSx_r);
const float coef = 1.0f / (float) nSx_r;
//! Process the Welsh-Hadamard transform on the 3rd dimension
for (unsigned n = 0; n < kHard_2 * chnls; n++)
hadamard_transform(group_3D, tmp, nSx_r, n * nSx_r);
//! Hard Thresholding