pickrst.c

/*
 *  Copyright (c) 2010 The WebM project authors. All Rights Reserved.
 *
 *  Use of this source code is governed by a BSD-style license
 *  that can be found in the LICENSE file in the root of the source
 *  tree. An additional intellectual property rights grant can be found
 *  in the file PATENTS.  All contributing project authors may
 *  be found in the AUTHORS file in the root of the source tree.
 */

#include <assert.h>
#include <float.h>
#include <limits.h>
#include <math.h>

#include "./aom_scale_rtcd.h"

#include "aom_dsp/psnr.h"
#include "aom_dsp/aom_dsp_common.h"
#include "aom_mem/aom_mem.h"
#include "aom_ports/mem.h"

#include "av1/common/onyxc_int.h"
#include "av1/common/quant_common.h"

#include "av1/encoder/encoder.h"
#include "av1/encoder/picklpf.h"
#include "av1/encoder/pickrst.h"
#include "av1/encoder/quantize.h"

const int frame_level_restore_bits[RESTORE_TYPES] = { 2, 2, 2, 2 };

static int64_t sse_restoration_tile(const YV12_BUFFER_CONFIG *src,
                                    AV1_COMMON *const cm, int h_start,
                                    int width, int v_start, int height) {
  int64_t filt_err;
#if CONFIG_AOM_HIGHBITDEPTH
  if (cm->use_highbitdepth) {
    filt_err = aom_highbd_get_y_sse_part(src, cm->frame_to_show, h_start, width,
                                         v_start, height);
  } else {
    filt_err = aom_get_y_sse_part(src, cm->frame_to_show, h_start, width,
                                  v_start, height);
  }
#else
  filt_err = aom_get_y_sse_part(src, cm->frame_to_show, h_start, width, v_start,
                                height);
#endif  // CONFIG_AOM_HIGHBITDEPTH
  return filt_err;
}

static int64_t try_restoration_tile(const YV12_BUFFER_CONFIG *src,
                                    AV1_COMP *const cpi, RestorationInfo *rsi,
                                    int partial_frame, int tile_idx,
                                    int subtile_idx, int subtile_bits) {
  AV1_COMMON *const cm = &cpi->common;
  int64_t filt_err;
  int tile_width, tile_height, nhtiles, nvtiles;
  int h_start, h_end, v_start, v_end;
  const int ntiles = av1_get_rest_ntiles(cm->width, cm->height, &tile_width,
                                         &tile_height, &nhtiles, &nvtiles);
  (void)ntiles;

  av1_loop_restoration_frame(cm->frame_to_show, cm, rsi, 1, partial_frame);
  av1_get_rest_tile_limits(tile_idx, subtile_idx, subtile_bits, nhtiles,
                           nvtiles, tile_width, tile_height, cm->width,
                           cm->height, 0, 0, &h_start, &h_end, &v_start,
                           &v_end);
  filt_err = sse_restoration_tile(src, cm, h_start, h_end - h_start, v_start,
                                  v_end - v_start);

  // Re-instate the unfiltered frame
  aom_yv12_copy_y(&cpi->last_frame_db, cm->frame_to_show);
  return filt_err;
}

static int64_t try_restoration_frame(const YV12_BUFFER_CONFIG *src,
                                     AV1_COMP *const cpi, RestorationInfo *rsi,
                                     int partial_frame) {
  AV1_COMMON *const cm = &cpi->common;
  int64_t filt_err;
  av1_loop_restoration_frame(cm->frame_to_show, cm, rsi, 1, partial_frame);
#if CONFIG_AOM_HIGHBITDEPTH
  if (cm->use_highbitdepth) {
    filt_err = aom_highbd_get_y_sse(src, cm->frame_to_show);
  } else {
    filt_err = aom_get_y_sse(src, cm->frame_to_show);
  }
#else
  filt_err = aom_get_y_sse(src, cm->frame_to_show);
#endif  // CONFIG_AOM_HIGHBITDEPTH

  // Re-instate the unfiltered frame
  aom_yv12_copy_y(&cpi->last_frame_db, cm->frame_to_show);
  return filt_err;
}

static int search_bilateral_level(const YV12_BUFFER_CONFIG *src, AV1_COMP *cpi,
                                  int filter_level, int partial_frame,
                                  int *bilateral_level, double *best_cost_ret,
                                  double *best_tile_cost) {
  AV1_COMMON *const cm = &cpi->common;
  int i, j, tile_idx;
  int64_t err;
  int bits;
  double cost, best_cost, cost_norestore, cost_bilateral,
      cost_norestore_subtile;
  const int bilateral_level_bits = av1_bilateral_level_bits(&cpi->common);
  const int bilateral_levels = 1 << bilateral_level_bits;
  MACROBLOCK *x = &cpi->td.mb;
  RestorationInfo rsi;
  int tile_width, tile_height, nhtiles, nvtiles;
  int h_start, h_end, v_start, v_end;
  const int ntiles = av1_get_rest_ntiles(cm->width, cm->height, &tile_width,
                                         &tile_height, &nhtiles, &nvtiles);

  //  Make a copy of the unfiltered / processed recon buffer
  aom_yv12_copy_y(cm->frame_to_show, &cpi->last_frame_uf);
  av1_loop_filter_frame(cm->frame_to_show, cm, &cpi->td.mb.e_mbd, filter_level,
                        1, partial_frame);
  aom_yv12_copy_y(cm->frame_to_show, &cpi->last_frame_db);

  // RD cost associated with no restoration
  rsi.frame_restoration_type = RESTORE_NONE;
  err = try_restoration_frame(src, cpi, &rsi, partial_frame);
  // err = sse_restoration_tile(src, cm, 0, cm->width, 0, cm->height);
  bits = frame_level_restore_bits[rsi.frame_restoration_type]
         << AV1_PROB_COST_SHIFT;
  cost_norestore = RDCOST_DBL(x->rdmult, x->rddiv, (bits >> 4), err);

  // RD cost associated with bilateral filtering
  rsi.frame_restoration_type = RESTORE_BILATERAL;
  rsi.bilateral_level = (int *)aom_malloc(sizeof(*rsi.bilateral_level) *
                                          ntiles * BILATERAL_SUBTILES);
  assert(rsi.bilateral_level != NULL);

  for (j = 0; j < ntiles * BILATERAL_SUBTILES; ++j) bilateral_level[j] = -1;

  // TODO(debargha): This is a pretty inefficient way to find the best
  // parameters per tile. Needs fixing.
  // Find best filter for each tile
  for (tile_idx = 0; tile_idx < ntiles; ++tile_idx) {
    int subtile_idx;
    for (subtile_idx = 0; subtile_idx < BILATERAL_SUBTILES; ++subtile_idx) {
      const int fulltile_idx = tile_idx * BILATERAL_SUBTILES + subtile_idx;
      av1_get_rest_tile_limits(tile_idx, subtile_idx, BILATERAL_SUBTILE_BITS,
                               nhtiles, nvtiles, tile_width, tile_height,
                               cm->width, cm->height, 0, 0, &h_start, &h_end,
                               &v_start, &v_end);
      err = sse_restoration_tile(src, cm, h_start, h_end - h_start, v_start,
                                 v_end - v_start);
#if BILATERAL_SUBTILES
      // #bits when a subtile is not restored
      bits = av1_cost_bit(RESTORE_NONE_BILATERAL_PROB, 0);
#else
      bits = 0;
#endif
      cost_norestore_subtile =
          RDCOST_DBL(x->rdmult, x->rddiv, (bits >> 4), err);
      best_cost = cost_norestore_subtile;
      for (j = 0; j < ntiles * BILATERAL_SUBTILES; ++j)
        rsi.bilateral_level[j] = -1;

      for (i = 0; i < bilateral_levels; ++i) {
        rsi.bilateral_level[fulltile_idx] = i;
        err = try_restoration_tile(src, cpi, &rsi, partial_frame, tile_idx,
                                   subtile_idx, BILATERAL_SUBTILE_BITS);
        bits = bilateral_level_bits << AV1_PROB_COST_SHIFT;
        bits += av1_cost_bit(RESTORE_NONE_BILATERAL_PROB, 1);
        cost = RDCOST_DBL(x->rdmult, x->rddiv, (bits >> 4), err);
        if (cost < best_cost) {
          bilateral_level[fulltile_idx] = i;
          best_cost = cost;
        }
      }
    }
    if (best_tile_cost) {
      bits = 0;
      for (j = 0; j < ntiles * BILATERAL_SUBTILES; ++j)
        rsi.bilateral_level[j] = -1;
      for (subtile_idx = 0; subtile_idx < BILATERAL_SUBTILES; ++subtile_idx) {
        const int fulltile_idx = tile_idx * BILATERAL_SUBTILES + subtile_idx;
        rsi.bilateral_level[fulltile_idx] = bilateral_level[fulltile_idx];
        if (rsi.bilateral_level[fulltile_idx] >= 0)
          bits += bilateral_level_bits << AV1_PROB_COST_SHIFT;
#if BILATERAL_SUBTILES
        bits += av1_cost_bit(RESTORE_NONE_BILATERAL_PROB,
                             rsi.bilateral_level[fulltile_idx] >= 0);
#endif
      }
      err = try_restoration_tile(src, cpi, &rsi, partial_frame, tile_idx, 0, 0);
      best_tile_cost[tile_idx] = RDCOST_DBL(
          x->rdmult, x->rddiv,
          (bits + cpi->switchable_restore_cost[RESTORE_BILATERAL]) >> 4, err);
    }
  }
  // Find cost for combined configuration
  bits = frame_level_restore_bits[rsi.frame_restoration_type]
         << AV1_PROB_COST_SHIFT;
  for (j = 0; j < ntiles * BILATERAL_SUBTILES; ++j) {
    rsi.bilateral_level[j] = bilateral_level[j];
    if (rsi.bilateral_level[j] >= 0) {
      bits += bilateral_level_bits << AV1_PROB_COST_SHIFT;
    }
#if BILATERAL_SUBTILES
    bits +=
        av1_cost_bit(RESTORE_NONE_BILATERAL_PROB, rsi.bilateral_level[j] >= 0);
#endif
  }
  err = try_restoration_frame(src, cpi, &rsi, partial_frame);
  cost_bilateral = RDCOST_DBL(x->rdmult, x->rddiv, (bits >> 4), err);

  aom_free(rsi.bilateral_level);

  aom_yv12_copy_y(&cpi->last_frame_uf, cm->frame_to_show);
  if (cost_bilateral < cost_norestore) {
    if (best_cost_ret) *best_cost_ret = cost_bilateral;
    return 1;
  } else {
    if (best_cost_ret) *best_cost_ret = cost_norestore;
    return 0;
  }
}

static int search_filter_bilateral_level(const YV12_BUFFER_CONFIG *src,
                                         AV1_COMP *cpi, int partial_frame,
                                         int *filter_best, int *bilateral_level,
                                         double *best_cost_ret,
                                         double *best_tile_cost) {
  const AV1_COMMON *const cm = &cpi->common;
  const struct loopfilter *const lf = &cm->lf;
  const int min_filter_level = 0;
  const int max_filter_level = av1_get_max_filter_level(cpi);
  int filt_direction = 0;
  int filt_best;
  double best_err;
  int i, j;
  int *tmp_level;
  int bilateral_success[MAX_LOOP_FILTER + 1];

  const int ntiles =
      av1_get_rest_ntiles(cm->width, cm->height, NULL, NULL, NULL, NULL);
  double *tile_cost = (double *)aom_malloc(sizeof(*tile_cost) * ntiles);

  // Start the search at the previous frame filter level unless it is now out of
  // range.
  int filt_mid = clamp(lf->filter_level, min_filter_level, max_filter_level);
  int filter_step = filt_mid < 16 ? 4 : filt_mid / 4;
  double ss_err[MAX_LOOP_FILTER + 1];
  // Set each entry to -1
  for (i = 0; i <= MAX_LOOP_FILTER; ++i) ss_err[i] = -1.0;

  tmp_level =
      (int *)aom_malloc(sizeof(*tmp_level) * ntiles * BILATERAL_SUBTILES);

  bilateral_success[filt_mid] = search_bilateral_level(
      src, cpi, filt_mid, partial_frame, tmp_level, &best_err, best_tile_cost);
  filt_best = filt_mid;
  ss_err[filt_mid] = best_err;
  for (j = 0; j < ntiles * BILATERAL_SUBTILES; ++j) {
    bilateral_level[j] = tmp_level[j];
  }

  while (filter_step > 0) {
    const int filt_high = AOMMIN(filt_mid + filter_step, max_filter_level);
    const int filt_low = AOMMAX(filt_mid - filter_step, min_filter_level);

    // Bias against raising loop filter in favor of lowering it.
    double bias = (best_err / (1 << (15 - (filt_mid / 8)))) * filter_step;

    if ((cpi->oxcf.pass == 2) && (cpi->twopass.section_intra_rating < 20))
      bias = (bias * cpi->twopass.section_intra_rating) / 20;

    // yx, bias less for large block size
    if (cm->tx_mode != ONLY_4X4) bias /= 2;

    if (filt_direction <= 0 && filt_low != filt_mid) {
      // Get Low filter error score
      if (ss_err[filt_low] < 0) {
        bilateral_success[filt_low] =
            search_bilateral_level(src, cpi, filt_low, partial_frame, tmp_level,
                                   &ss_err[filt_low], tile_cost);
      }
      // If value is close to the best so far then bias towards a lower loop
      // filter value.
      if (ss_err[filt_low] < (best_err + bias)) {
        // Was it actually better than the previous best?
        if (ss_err[filt_low] < best_err) {
          best_err = ss_err[filt_low];
        }
        filt_best = filt_low;
        for (j = 0; j < ntiles * BILATERAL_SUBTILES; ++j) {
          bilateral_level[j] = tmp_level[j];
        }
        memcpy(best_tile_cost, tile_cost, sizeof(*tile_cost) * ntiles);
      }
    }

    // Now look at filt_high
    if (filt_direction >= 0 && filt_high != filt_mid) {
      if (ss_err[filt_high] < 0) {
        bilateral_success[filt_high] =
            search_bilateral_level(src, cpi, filt_high, partial_frame,
                                   tmp_level, &ss_err[filt_high], tile_cost);
      }
      // If value is significantly better than previous best, bias added against
      // raising filter value
      if (ss_err[filt_high] < (best_err - bias)) {
        best_err = ss_err[filt_high];
        filt_best = filt_high;
        for (j = 0; j < ntiles * BILATERAL_SUBTILES; ++j) {
          bilateral_level[j] = tmp_level[j];
        }
        memcpy(best_tile_cost, tile_cost, sizeof(*tile_cost) * ntiles);
      }
    }

    // Half the step distance if the best filter value was the same as last time
    if (filt_best == filt_mid) {
      filter_step /= 2;
      filt_direction = 0;
    } else {
      filt_direction = (filt_best < filt_mid) ? -1 : 1;
      filt_mid = filt_best;
    }
  }
  aom_free(tmp_level);
  aom_free(tile_cost);

  // Update best error
  best_err = ss_err[filt_best];
  if (best_cost_ret) *best_cost_ret = best_err;
  if (filter_best) *filter_best = filt_best;

  return bilateral_success[filt_best];
}

static double find_average(uint8_t *src, int h_start, int h_end, int v_start,
                           int v_end, int stride) {
  uint64_t sum = 0;
  double avg = 0;
  int i, j;
  for (i = v_start; i < v_end; i++)
    for (j = h_start; j < h_end; j++) sum += src[i * stride + j];
  avg = (double)sum / ((v_end - v_start) * (h_end - h_start));
  return avg;
}

static void compute_stats(uint8_t *dgd, uint8_t *src, int h_start, int h_end,
                          int v_start, int v_end, int dgd_stride,
                          int src_stride, double *M, double *H) {
  int i, j, k, l;
  double Y[RESTORATION_WIN2];
  const double avg =
      find_average(dgd, h_start, h_end, v_start, v_end, dgd_stride);

  memset(M, 0, sizeof(*M) * RESTORATION_WIN2);
  memset(H, 0, sizeof(*H) * RESTORATION_WIN2 * RESTORATION_WIN2);
  for (i = v_start; i < v_end; i++) {
    for (j = h_start; j < h_end; j++) {
      const double X = (double)src[i * src_stride + j] - avg;
      int idx = 0;
      for (k = -RESTORATION_HALFWIN; k <= RESTORATION_HALFWIN; k++) {
        for (l = -RESTORATION_HALFWIN; l <= RESTORATION_HALFWIN; l++) {
          Y[idx] = (double)dgd[(i + l) * dgd_stride + (j + k)] - avg;
          idx++;
        }
      }
      for (k = 0; k < RESTORATION_WIN2; ++k) {
        M[k] += Y[k] * X;
        H[k * RESTORATION_WIN2 + k] += Y[k] * Y[k];
        for (l = k + 1; l < RESTORATION_WIN2; ++l) {
          double value = Y[k] * Y[l];
          H[k * RESTORATION_WIN2 + l] += value;
          H[l * RESTORATION_WIN2 + k] += value;
        }
      }
    }
  }
}

#if CONFIG_AOM_HIGHBITDEPTH
static double find_average_highbd(uint16_t *src, int h_start, int h_end,
                                  int v_start, int v_end, int stride) {
  uint64_t sum = 0;
  double avg = 0;
  int i, j;
  for (i = v_start; i < v_end; i++)
    for (j = h_start; j < h_end; j++) sum += src[i * stride + j];
  avg = (double)sum / ((v_end - v_start) * (h_end - h_start));
  return avg;
}

static void compute_stats_highbd(uint8_t *dgd8, uint8_t *src8, int h_start,
                                 int h_end, int v_start, int v_end,
                                 int dgd_stride, int src_stride, double *M,
                                 double *H) {
  int i, j, k, l;
  double Y[RESTORATION_WIN2];
  uint16_t *src = CONVERT_TO_SHORTPTR(src8);
  uint16_t *dgd = CONVERT_TO_SHORTPTR(dgd8);
  const double avg =
      find_average_highbd(dgd, h_start, h_end, v_start, v_end, dgd_stride);

  memset(M, 0, sizeof(*M) * RESTORATION_WIN2);
  memset(H, 0, sizeof(*H) * RESTORATION_WIN2 * RESTORATION_WIN2);
  for (i = v_start; i < v_end; i++) {
    for (j = h_start; j < h_end; j++) {
      const double X = (double)src[i * src_stride + j] - avg;
      int idx = 0;
      for (k = -RESTORATION_HALFWIN; k <= RESTORATION_HALFWIN; k++) {
        for (l = -RESTORATION_HALFWIN; l <= RESTORATION_HALFWIN; l++) {
          Y[idx] = (double)dgd[(i + l) * dgd_stride + (j + k)] - avg;
          idx++;
        }
      }
      for (k = 0; k < RESTORATION_WIN2; ++k) {
        M[k] += Y[k] * X;
        H[k * RESTORATION_WIN2 + k] += Y[k] * Y[k];
        for (l = k + 1; l < RESTORATION_WIN2; ++l) {
          double value = Y[k] * Y[l];
          H[k * RESTORATION_WIN2 + l] += value;
          H[l * RESTORATION_WIN2 + k] += value;
        }
      }
    }
  }
}
#endif  // CONFIG_AOM_HIGHBITDEPTH

// Solves Ax = b, where x and b are column vectors
static int linsolve(int n, double *A, int stride, double *b, double *x) {
  int i, j, k;
  double c;
  // Partial pivoting
  for (i = n - 1; i > 0; i--) {
    if (A[(i - 1) * stride] < A[i * stride]) {
      for (j = 0; j < n; j++) {
        c = A[i * stride + j];
        A[i * stride + j] = A[(i - 1) * stride + j];
        A[(i - 1) * stride + j] = c;
      }
      c = b[i];
      b[i] = b[i - 1];
      b[i - 1] = c;
    }
  }
  // Forward elimination
  for (k = 0; k < n - 1; k++) {
    for (i = k; i < n - 1; i++) {
      c = A[(i + 1) * stride + k] / A[k * stride + k];
      for (j = 0; j < n; j++) A[(i + 1) * stride + j] -= c * A[k * stride + j];
      b[i + 1] -= c * b[k];
    }
  }
  // Backward substitution
  for (i = n - 1; i >= 0; i--) {
    if (fabs(A[i * stride + i]) < 1e-10) return 0;
    c = 0;
    for (j = i + 1; j <= n - 1; j++) c += A[i * stride + j] * x[j];
    x[i] = (b[i] - c) / A[i * stride + i];
  }
  return 1;
}

static INLINE int wrap_index(int i) {
  return (i >= RESTORATION_HALFWIN1 ? RESTORATION_WIN - 1 - i : i);
}

// Fix vector b, update vector a
static void update_a_sep_sym(double **Mc, double **Hc, double *a, double *b) {
  int i, j;
  double S[RESTORATION_WIN];
  double A[RESTORATION_WIN], B[RESTORATION_WIN2];
  int w, w2;
  memset(A, 0, sizeof(A));
  memset(B, 0, sizeof(B));
  for (i = 0; i < RESTORATION_WIN; i++) {
    int j;
    for (j = 0; j < RESTORATION_WIN; ++j) {
      const int jj = wrap_index(j);
      A[jj] += Mc[i][j] * b[i];
    }
  }
  for (i = 0; i < RESTORATION_WIN; i++) {
    for (j = 0; j < RESTORATION_WIN; j++) {
      int k, l;
      for (k = 0; k < RESTORATION_WIN; ++k)
        for (l = 0; l < RESTORATION_WIN; ++l) {
          const int kk = wrap_index(k);
          const int ll = wrap_index(l);
          B[ll * RESTORATION_HALFWIN1 + kk] +=
              Hc[j * RESTORATION_WIN + i][k * RESTORATION_WIN2 + l] * b[i] *
              b[j];
        }
    }
  }
  // Normalization enforcement in the system of equations itself
  w = RESTORATION_WIN;
  w2 = (w >> 1) + 1;
  for (i = 0; i < w2 - 1; ++i)
    A[i] -=
        A[w2 - 1] * 2 + B[i * w2 + w2 - 1] - 2 * B[(w2 - 1) * w2 + (w2 - 1)];
  for (i = 0; i < w2 - 1; ++i)
    for (j = 0; j < w2 - 1; ++j)
      B[i * w2 + j] -= 2 * (B[i * w2 + (w2 - 1)] + B[(w2 - 1) * w2 + j] -
                            2 * B[(w2 - 1) * w2 + (w2 - 1)]);
  if (linsolve(w2 - 1, B, w2, A, S)) {
    S[w2 - 1] = 1.0;
    for (i = w2; i < w; ++i) {
      S[i] = S[w - 1 - i];
      S[w2 - 1] -= 2 * S[i];
    }
    memcpy(a, S, w * sizeof(*a));
  }
}

// Fix vector a, update vector b
static void update_b_sep_sym(double **Mc, double **Hc, double *a, double *b) {
  int i, j;
  double S[RESTORATION_WIN];
  double A[RESTORATION_WIN], B[RESTORATION_WIN2];
  int w, w2;
  memset(A, 0, sizeof(A));
  memset(B, 0, sizeof(B));
  for (i = 0; i < RESTORATION_WIN; i++) {
    int j;
    const int ii = wrap_index(i);
    for (j = 0; j < RESTORATION_WIN; j++) A[ii] += Mc[i][j] * a[j];
  }

  for (i = 0; i < RESTORATION_WIN; i++) {
    for (j = 0; j < RESTORATION_WIN; j++) {
      const int ii = wrap_index(i);
      const int jj = wrap_index(j);
      int k, l;
      for (k = 0; k < RESTORATION_WIN; ++k)
        for (l = 0; l < RESTORATION_WIN; ++l)
          B[jj * RESTORATION_HALFWIN1 + ii] +=
              Hc[i * RESTORATION_WIN + j][k * RESTORATION_WIN2 + l] * a[k] *
              a[l];
    }
  }
  // Normalization enforcement in the system of equations itself
  w = RESTORATION_WIN;
  w2 = RESTORATION_HALFWIN1;
  for (i = 0; i < w2 - 1; ++i)
    A[i] -=
        A[w2 - 1] * 2 + B[i * w2 + w2 - 1] - 2 * B[(w2 - 1) * w2 + (w2 - 1)];
  for (i = 0; i < w2 - 1; ++i)
    for (j = 0; j < w2 - 1; ++j)
      B[i * w2 + j] -= 2 * (B[i * w2 + (w2 - 1)] + B[(w2 - 1) * w2 + j] -
                            2 * B[(w2 - 1) * w2 + (w2 - 1)]);
  if (linsolve(w2 - 1, B, w2, A, S)) {
    S[w2 - 1] = 1.0;
    for (i = w2; i < w; ++i) {
      S[i] = S[w - 1 - i];
      S[w2 - 1] -= 2 * S[i];
    }
    memcpy(b, S, w * sizeof(*b));
  }
}

static int wiener_decompose_sep_sym(double *M, double *H, double *a,
                                    double *b) {
  static const double init_filt[RESTORATION_WIN] = {
    0.035623, -0.127154, 0.211436, 0.760190, 0.211436, -0.127154, 0.035623,
  };
  int i, j, iter;
  double *Hc[RESTORATION_WIN2];
  double *Mc[RESTORATION_WIN];
  for (i = 0; i < RESTORATION_WIN; i++) {
    Mc[i] = M + i * RESTORATION_WIN;
    for (j = 0; j < RESTORATION_WIN; j++) {
      Hc[i * RESTORATION_WIN + j] =
          H + i * RESTORATION_WIN * RESTORATION_WIN2 + j * RESTORATION_WIN;
    }
  }
  memcpy(a, init_filt, sizeof(*a) * RESTORATION_WIN);
  memcpy(b, init_filt, sizeof(*b) * RESTORATION_WIN);

  iter = 1;
  while (iter < 10) {
    update_a_sep_sym(Mc, Hc, a, b);
    update_b_sep_sym(Mc, Hc, a, b);
    iter++;
  }
  return 1;
}

// Computes the function x'*A*x - x'*b for the learned filters, and compares
// against identity filters; Final score is defined as the difference between
// the function values
static double compute_score(double *M, double *H, int *vfilt, int *hfilt) {
  double ab[RESTORATION_WIN * RESTORATION_WIN];
  int i, k, l;
  double P = 0, Q = 0;
  double iP = 0, iQ = 0;
  double Score, iScore;
  int w;
  double a[RESTORATION_WIN], b[RESTORATION_WIN];
  w = RESTORATION_WIN;
  a[RESTORATION_HALFWIN] = b[RESTORATION_HALFWIN] = 1.0;
  for (i = 0; i < RESTORATION_HALFWIN; ++i) {
    a[i] = a[RESTORATION_WIN - i - 1] =
        (double)vfilt[i] / RESTORATION_FILT_STEP;
    b[i] = b[RESTORATION_WIN - i - 1] =
        (double)hfilt[i] / RESTORATION_FILT_STEP;
    a[RESTORATION_HALFWIN] -= 2 * a[i];
    b[RESTORATION_HALFWIN] -= 2 * b[i];
  }
  for (k = 0; k < w; ++k) {
    for (l = 0; l < w; ++l) {
      ab[k * w + l] = a[l] * b[k];
    }
  }
  for (k = 0; k < w * w; ++k) {
    P += ab[k] * M[k];
    for (l = 0; l < w * w; ++l) Q += ab[k] * H[k * w * w + l] * ab[l];
  }
  Score = Q - 2 * P;

  iP = M[(w * w) >> 1];
  iQ = H[((w * w) >> 1) * w * w + ((w * w) >> 1)];
  iScore = iQ - 2 * iP;

  return Score - iScore;
}

#define CLIP(x, lo, hi) ((x) < (lo) ? (lo) : (x) > (hi) ? (hi) : (x))
#define RINT(x) ((x) < 0 ? (int)((x)-0.5) : (int)((x) + 0.5))

static void quantize_sym_filter(double *f, int *fi) {
  int i;
  for (i = 0; i < RESTORATION_HALFWIN; ++i) {
    fi[i] = RINT(f[i] * RESTORATION_FILT_STEP);
  }
  // Specialize for 7-tap filter
  fi[0] = CLIP(fi[0], WIENER_FILT_TAP0_MINV, WIENER_FILT_TAP0_MAXV);
  fi[1] = CLIP(fi[1], WIENER_FILT_TAP1_MINV, WIENER_FILT_TAP1_MAXV);
  fi[2] = CLIP(fi[2], WIENER_FILT_TAP2_MINV, WIENER_FILT_TAP2_MAXV);
}

static int search_wiener_filter(const YV12_BUFFER_CONFIG *src, AV1_COMP *cpi,
                                int filter_level, int partial_frame,
                                int (*vfilter)[RESTORATION_WIN],
                                int (*hfilter)[RESTORATION_WIN],
                                int *wiener_level, double *best_cost_ret,
                                double *best_tile_cost) {
  AV1_COMMON *const cm = &cpi->common;
  RestorationInfo rsi;
  int64_t err;
  int bits;
  double cost_wiener, cost_norestore, cost_norestore_tile;
  MACROBLOCK *x = &cpi->td.mb;
  double M[RESTORATION_WIN2];
  double H[RESTORATION_WIN2 * RESTORATION_WIN2];
  double vfilterd[RESTORATION_WIN], hfilterd[RESTORATION_WIN];
  const YV12_BUFFER_CONFIG *dgd = cm->frame_to_show;
  const int width = cm->width;
  const int height = cm->height;
  const int src_stride = src->y_stride;
  const int dgd_stride = dgd->y_stride;
  double score;
  int tile_idx, tile_width, tile_height, nhtiles, nvtiles;
  int h_start, h_end, v_start, v_end;
  int i, j;

  const int ntiles = av1_get_rest_ntiles(width, height, &tile_width,
                                         &tile_height, &nhtiles, &nvtiles);
  assert(width == dgd->y_crop_width);
  assert(height == dgd->y_crop_height);
  assert(width == src->y_crop_width);
  assert(height == src->y_crop_height);

  //  Make a copy of the unfiltered / processed recon buffer
  aom_yv12_copy_y(cm->frame_to_show, &cpi->last_frame_uf);
  av1_loop_filter_frame(cm->frame_to_show, cm, &cpi->td.mb.e_mbd, filter_level,
                        1, partial_frame);
  aom_yv12_copy_y(cm->frame_to_show, &cpi->last_frame_db);

  rsi.frame_restoration_type = RESTORE_NONE;
  err = sse_restoration_tile(src, cm, 0, cm->width, 0, cm->height);
  bits = frame_level_restore_bits[rsi.frame_restoration_type]
         << AV1_PROB_COST_SHIFT;
  cost_norestore = RDCOST_DBL(x->rdmult, x->rddiv, (bits >> 4), err);

  rsi.frame_restoration_type = RESTORE_WIENER;
  rsi.vfilter =
      (int(*)[RESTORATION_WIN])aom_malloc(sizeof(*rsi.vfilter) * ntiles);
  assert(rsi.vfilter != NULL);
  rsi.hfilter =
      (int(*)[RESTORATION_WIN])aom_malloc(sizeof(*rsi.hfilter) * ntiles);
  assert(rsi.hfilter != NULL);
  rsi.wiener_level = (int *)aom_malloc(sizeof(*rsi.wiener_level) * ntiles);
  assert(rsi.wiener_level != NULL);

  // Compute best Wiener filters for each tile
  for (tile_idx = 0; tile_idx < ntiles; ++tile_idx) {
    wiener_level[tile_idx] = 0;
    av1_get_rest_tile_limits(tile_idx, 0, 0, nhtiles, nvtiles, tile_width,
                             tile_height, width, height, 0, 0, &h_start, &h_end,
                             &v_start, &v_end);
    err = sse_restoration_tile(src, cm, h_start, h_end - h_start, v_start,
                               v_end - v_start);
    // #bits when a tile is not restored
    bits = av1_cost_bit(RESTORE_NONE_WIENER_PROB, 0);
    cost_norestore_tile = RDCOST_DBL(x->rdmult, x->rddiv, (bits >> 4), err);
    if (best_tile_cost) best_tile_cost[tile_idx] = cost_norestore_tile;

    av1_get_rest_tile_limits(tile_idx, 0, 0, nhtiles, nvtiles, tile_width,
                             tile_height, width, height, 1, 1, &h_start, &h_end,
                             &v_start, &v_end);
#if CONFIG_AOM_HIGHBITDEPTH
    if (cm->use_highbitdepth)
      compute_stats_highbd(dgd->y_buffer, src->y_buffer, h_start, h_end,
                           v_start, v_end, dgd_stride, src_stride, M, H);
    else
#endif  // CONFIG_AOM_HIGHBITDEPTH
      compute_stats(dgd->y_buffer, src->y_buffer, h_start, h_end, v_start,
                    v_end, dgd_stride, src_stride, M, H);

    if (!wiener_decompose_sep_sym(M, H, vfilterd, hfilterd)) {
      for (i = 0; i < RESTORATION_HALFWIN; ++i)
        rsi.vfilter[tile_idx][i] = rsi.hfilter[tile_idx][i] = 0;
      wiener_level[tile_idx] = 0;
      continue;
    }
    quantize_sym_filter(vfilterd, rsi.vfilter[tile_idx]);
    quantize_sym_filter(hfilterd, rsi.hfilter[tile_idx]);
    wiener_level[tile_idx] = 1;

    // Filter score computes the value of the function x'*A*x - x'*b for the
    // learned filter and compares it against identity filer. If there is no
    // reduction in the function, the filter is reverted back to identity
    score = compute_score(M, H, rsi.vfilter[tile_idx], rsi.hfilter[tile_idx]);
    if (score > 0.0) {
      for (i = 0; i < RESTORATION_HALFWIN; ++i)
        rsi.vfilter[tile_idx][i] = rsi.hfilter[tile_idx][i] = 0;
      wiener_level[tile_idx] = 0;
      continue;
    }

    for (j = 0; j < ntiles; ++j) rsi.wiener_level[j] = 0;
    rsi.wiener_level[tile_idx] = 1;

    err = try_restoration_tile(src, cpi, &rsi, partial_frame, tile_idx, 0, 0);
    bits = WIENER_FILT_BITS << AV1_PROB_COST_SHIFT;
    bits += av1_cost_bit(RESTORE_NONE_WIENER_PROB, 1);
    cost_wiener = RDCOST_DBL(x->rdmult, x->rddiv, (bits >> 4), err);
    if (cost_wiener >= cost_norestore_tile) wiener_level[tile_idx] = 0;
    if (best_tile_cost) {
      bits = WIENER_FILT_BITS << AV1_PROB_COST_SHIFT;
      best_tile_cost[tile_idx] = RDCOST_DBL(
          x->rdmult, x->rddiv,
          (bits + cpi->switchable_restore_cost[RESTORE_WIENER]) >> 4, err);
    }
  }
  // Cost for Wiener filtering
  bits = frame_level_restore_bits[rsi.frame_restoration_type]
         << AV1_PROB_COST_SHIFT;
  for (tile_idx = 0; tile_idx < ntiles; ++tile_idx) {
    bits += av1_cost_bit(RESTORE_NONE_WIENER_PROB, wiener_level[tile_idx]);
    if (wiener_level[tile_idx])
      bits += (WIENER_FILT_BITS << AV1_PROB_COST_SHIFT);
    rsi.wiener_level[tile_idx] = wiener_level[tile_idx];
  }
  // TODO(debargha): This is a pretty inefficient way to find the error
  // for the whole frame. Specialize for a specific tile.
  err = try_restoration_frame(src, cpi, &rsi, partial_frame);
  cost_wiener = RDCOST_DBL(x->rdmult, x->rddiv, (bits >> 4), err);

  for (tile_idx = 0; tile_idx < ntiles; ++tile_idx) {
    if (wiener_level[tile_idx] == 0) continue;
    for (i = 0; i < RESTORATION_HALFWIN; ++i) {
      vfilter[tile_idx][i] = rsi.vfilter[tile_idx][i];
      hfilter[tile_idx][i] = rsi.hfilter[tile_idx][i];
    }
  }

  aom_free(rsi.vfilter);
  aom_free(rsi.hfilter);
  aom_free(rsi.wiener_level);

  aom_yv12_copy_y(&cpi->last_frame_uf, cm->frame_to_show);
  if (cost_wiener < cost_norestore) {
    if (best_cost_ret) *best_cost_ret = cost_wiener;
    return 1;
  } else {
    if (best_cost_ret) *best_cost_ret = cost_norestore;
    return 0;
  }
}

static int search_switchable_restoration(
    const YV12_BUFFER_CONFIG *src, AV1_COMP *cpi, int filter_level,
    int partial_frame, RestorationInfo *rsi, double *tile_cost_bilateral,
    double *tile_cost_wiener, double *best_cost_ret) {
  AV1_COMMON *const cm = &cpi->common;
  const int bilateral_level_bits = av1_bilateral_level_bits(&cpi->common);
  MACROBLOCK *x = &cpi->td.mb;
  double err, cost_norestore, cost_norestore_tile, cost_switchable;
  int bits, tile_idx;
  int tile_width, tile_height, nhtiles, nvtiles;
  int h_start, h_end, v_start, v_end;
  const int ntiles = av1_get_rest_ntiles(cm->width, cm->height, &tile_width,
                                         &tile_height, &nhtiles, &nvtiles);

  //  Make a copy of the unfiltered / processed recon buffer
  aom_yv12_copy_y(cm->frame_to_show, &cpi->last_frame_uf);
  av1_loop_filter_frame(cm->frame_to_show, cm, &cpi->td.mb.e_mbd, filter_level,
                        1, partial_frame);
  aom_yv12_copy_y(cm->frame_to_show, &cpi->last_frame_db);

  // RD cost associated with no restoration
  rsi->frame_restoration_type = RESTORE_NONE;
  err = sse_restoration_tile(src, cm, 0, cm->width, 0, cm->height);
  bits = frame_level_restore_bits[rsi->frame_restoration_type]
         << AV1_PROB_COST_SHIFT;
  cost_norestore = RDCOST_DBL(x->rdmult, x->rddiv, (bits >> 4), err);

  rsi->frame_restoration_type = RESTORE_SWITCHABLE;
  bits = frame_level_restore_bits[rsi->frame_restoration_type]
         << AV1_PROB_COST_SHIFT;
  for (tile_idx = 0; tile_idx < ntiles; ++tile_idx) {
    av1_get_rest_tile_limits(tile_idx, 0, 0, nhtiles, nvtiles, tile_width,
                             tile_height, cm->width, cm->height, 0, 0, &h_start,
                             &h_end, &v_start, &v_end);
    err = sse_restoration_tile(src, cm, h_start, h_end - h_start, v_start,
                               v_end - v_start);
    cost_norestore_tile =
        RDCOST_DBL(x->rdmult, x->rddiv,
                   (cpi->switchable_restore_cost[RESTORE_NONE] >> 4), err);
    if (tile_cost_wiener[tile_idx] > cost_norestore_tile &&
        tile_cost_bilateral[tile_idx] > cost_norestore_tile) {
      rsi->restoration_type[tile_idx] = RESTORE_NONE;
    } else {
      rsi->restoration_type[tile_idx] =
          tile_cost_wiener[tile_idx] < tile_cost_bilateral[tile_idx]
              ? RESTORE_WIENER
              : RESTORE_BILATERAL;
      if (rsi->restoration_type[tile_idx] == RESTORE_WIENER) {
        if (rsi->wiener_level[tile_idx]) {
          bits += (WIENER_FILT_BITS << AV1_PROB_COST_SHIFT);
        } else {
          rsi->restoration_type[tile_idx] = RESTORE_NONE;
        }
      } else {
        int s;
        for (s = 0; s < BILATERAL_SUBTILES; ++s) {
#if BILATERAL_SUBTILES
          bits += av1_cost_bit(
              RESTORE_NONE_BILATERAL_PROB,
              rsi->bilateral_level[tile_idx * BILATERAL_SUBTILES + s] >= 0);
#endif
          if (rsi->bilateral_level[tile_idx * BILATERAL_SUBTILES + s] >= 0)
            bits += bilateral_level_bits << AV1_PROB_COST_SHIFT;
        }
      }
    }
    bits += cpi->switchable_restore_cost[rsi->restoration_type[tile_idx]];
  }
  err = try_restoration_frame(src, cpi, rsi, partial_frame);
  cost_switchable = RDCOST_DBL(x->rdmult, x->rddiv, (bits >> 4), err);
  aom_yv12_copy_y(&cpi->last_frame_uf, cm->frame_to_show);
  if (cost_switchable < cost_norestore) {
    *best_cost_ret = cost_switchable;
    return 1;
  } else {
    *best_cost_ret = cost_norestore;
    return 0;
  }
}

void av1_pick_filter_restoration(const YV12_BUFFER_CONFIG *src, AV1_COMP *cpi,
                                 LPF_PICK_METHOD method) {
  AV1_COMMON *const cm = &cpi->common;
  struct loopfilter *const lf = &cm->lf;
  int wiener_success = 0;
  int bilateral_success = 0;
  int switchable_success = 0;
  double cost_bilateral = DBL_MAX;
  double cost_wiener = DBL_MAX;
  // double cost_norestore = DBL_MAX;
  double cost_switchable = DBL_MAX;
  double *tile_cost_bilateral, *tile_cost_wiener;
  const int ntiles =
      av1_get_rest_ntiles(cm->width, cm->height, NULL, NULL, NULL, NULL);
  cm->rst_info.restoration_type = (RestorationType *)aom_realloc(
      cm->rst_info.restoration_type,
      sizeof(*cm->rst_info.restoration_type) * ntiles);
  cm->rst_info.bilateral_level = (int *)aom_realloc(
      cm->rst_info.bilateral_level,
      sizeof(*cm->rst_info.bilateral_level) * ntiles * BILATERAL_SUBTILES);
  assert(cm->rst_info.bilateral_level != NULL);

  cm->rst_info.wiener_level = (int *)aom_realloc(
      cm->rst_info.wiener_level, sizeof(*cm->rst_info.wiener_level) * ntiles);
  assert(cm->rst_info.wiener_level != NULL);
  cm->rst_info.vfilter = (int(*)[RESTORATION_WIN])aom_realloc(
      cm->rst_info.vfilter, sizeof(*cm->rst_info.vfilter) * ntiles);
  assert(cm->rst_info.vfilter != NULL);
  cm->rst_info.hfilter = (int(*)[RESTORATION_WIN])aom_realloc(
      cm->rst_info.hfilter, sizeof(*cm->rst_info.hfilter) * ntiles);
  assert(cm->rst_info.hfilter != NULL);
  tile_cost_wiener = (double *)aom_malloc(sizeof(cost_wiener) * ntiles);
  tile_cost_bilateral = (double *)aom_malloc(sizeof(cost_bilateral) * ntiles);

  lf->sharpness_level = cm->frame_type == KEY_FRAME ? 0 : cpi->oxcf.sharpness;

  if (method == LPF_PICK_MINIMAL_LPF && lf->filter_level) {
    lf->filter_level = 0;
    cm->rst_info.frame_restoration_type = RESTORE_NONE;
  } else if (method >= LPF_PICK_FROM_Q) {
    const int min_filter_level = 0;
    const int max_filter_level = av1_get_max_filter_level(cpi);
    const int q = av1_ac_quant(cm->base_qindex, 0, cm->bit_depth);
// These values were determined by linear fitting the result of the
// searched level, filt_guess = q * 0.316206 + 3.87252
#if CONFIG_AOM_HIGHBITDEPTH
    int filt_guess;
    switch (cm->bit_depth) {
      case AOM_BITS_8:
        filt_guess = ROUND_POWER_OF_TWO(q * 20723 + 1015158, 18);
        break;
      case AOM_BITS_10:
        filt_guess = ROUND_POWER_OF_TWO(q * 20723 + 4060632, 20);
        break;
      case AOM_BITS_12:
        filt_guess = ROUND_POWER_OF_TWO(q * 20723 + 16242526, 22);
        break;
      default:
        assert(0 &&
               "bit_depth should be AOM_BITS_8, AOM_BITS_10 "
               "or AOM_BITS_12");
        return;
    }
#else
    int filt_guess = ROUND_POWER_OF_TWO(q * 20723 + 1015158, 18);
#endif  // CONFIG_AOM_HIGHBITDEPTH
    if (cm->frame_type == KEY_FRAME) filt_guess -= 4;
    lf->filter_level = clamp(filt_guess, min_filter_level, max_filter_level);
    bilateral_success = search_bilateral_level(
        src, cpi, lf->filter_level, method == LPF_PICK_FROM_SUBIMAGE,
        cm->rst_info.bilateral_level, &cost_bilateral, tile_cost_bilateral);
    wiener_success = search_wiener_filter(
        src, cpi, lf->filter_level, method == LPF_PICK_FROM_SUBIMAGE,
        cm->rst_info.vfilter, cm->rst_info.hfilter, cm->rst_info.wiener_level,
        &cost_wiener, tile_cost_wiener);
    switchable_success = search_switchable_restoration(
        src, cpi, lf->filter_level, method == LPF_PICK_FROM_SUBIMAGE,
        &cm->rst_info, tile_cost_bilateral, tile_cost_wiener, &cost_switchable);
  } else {
    // lf->filter_level = av1_search_filter_level(
    //     src, cpi, method == LPF_PICK_FROM_SUBIMAGE, &cost_norestore);
    // bilateral_success = search_bilateral_level(
    //     src, cpi, lf->filter_level, method == LPF_PICK_FROM_SUBIMAGE,
    //     cm->rst_info.bilateral_level, &cost_bilateral, tile_cost_bilateral);
    bilateral_success = search_filter_bilateral_level(
        src, cpi, method == LPF_PICK_FROM_SUBIMAGE, &lf->filter_level,
        cm->rst_info.bilateral_level, &cost_bilateral, tile_cost_bilateral);
    wiener_success = search_wiener_filter(
        src, cpi, lf->filter_level, method == LPF_PICK_FROM_SUBIMAGE,
        cm->rst_info.vfilter, cm->rst_info.hfilter, cm->rst_info.wiener_level,
        &cost_wiener, tile_cost_wiener);
    switchable_success = search_switchable_restoration(
        src, cpi, lf->filter_level, method == LPF_PICK_FROM_SUBIMAGE,
        &cm->rst_info, tile_cost_bilateral, tile_cost_wiener, &cost_switchable);
  }
  if (cost_bilateral < AOMMIN(cost_wiener, cost_switchable)) {
    if (bilateral_success)
      cm->rst_info.frame_restoration_type = RESTORE_BILATERAL;
    else
      cm->rst_info.frame_restoration_type = RESTORE_NONE;
  } else if (cost_wiener < AOMMIN(cost_bilateral, cost_switchable)) {
    if (wiener_success)
      cm->rst_info.frame_restoration_type = RESTORE_WIENER;
    else
      cm->rst_info.frame_restoration_type = RESTORE_NONE;
  } else {
    if (switchable_success)
      cm->rst_info.frame_restoration_type = RESTORE_SWITCHABLE;
    else
      cm->rst_info.frame_restoration_type = RESTORE_NONE;