diff --git a/libavcodec/jpeg2000dec.c b/libavcodec/jpeg2000dec.c
index d13eedfaf7..2e09b279dc 100644
--- a/libavcodec/jpeg2000dec.c
+++ b/libavcodec/jpeg2000dec.c
@@ -391,6 +391,9 @@ static int get_siz(Jpeg2000DecoderContext *s)
         } else if (ncomponents == 1 && s->precision == 8) {
             s->avctx->pix_fmt = AV_PIX_FMT_GRAY8;
             i = 0;
+        } else if (ncomponents == 1 && s->precision == 12) {
+            s->avctx->pix_fmt = AV_PIX_FMT_GRAY16LE;
+            i = 0;
         }
     }
 
@@ -2204,7 +2207,7 @@ static inline int tile_codeblocks(const Jpeg2000DecoderContext *s, Jpeg2000Tile
                 Jpeg2000Band *band = rlevel->band + bandno;
                 int cblkno = 0, bandpos;
                 /* See Rec. ITU-T T.800, Equation E-2 */
-                int magp = quantsty->expn[subbandno] + quantsty->nguardbits - 1;
+                int M_b = quantsty->expn[subbandno] + quantsty->nguardbits - 1;
 
                 bandpos = bandno + (reslevelno > 0);
 
@@ -2212,8 +2215,8 @@ static inline int tile_codeblocks(const Jpeg2000DecoderContext *s, Jpeg2000Tile
                     band->coord[1][0] == band->coord[1][1])
                     continue;
 
-                if ((codsty->cblk_style & JPEG2000_CTSY_HTJ2K_F) && magp >= 31) {
-                    avpriv_request_sample(s->avctx, "JPEG2000_CTSY_HTJ2K_F and magp >= 31");
+                if ((codsty->cblk_style & JPEG2000_CTSY_HTJ2K_F) && M_b >= 31) {
+                    avpriv_request_sample(s->avctx, "JPEG2000_CTSY_HTJ2K_F and M_b >= 31");
                     return AVERROR_PATCHWELCOME;
                 }
 
@@ -2234,7 +2237,7 @@ static inline int tile_codeblocks(const Jpeg2000DecoderContext *s, Jpeg2000Tile
                             ret = ff_jpeg2000_decode_htj2k(s, codsty, &t1, cblk,
                                                            cblk->coord[0][1] - cblk->coord[0][0],
                                                            cblk->coord[1][1] - cblk->coord[1][0],
-                                                           magp, comp->roi_shift);
+                                                           M_b, comp->roi_shift);
                         else
                             ret = decode_cblk(s, codsty, &t1, cblk,
                                               cblk->coord[0][1] - cblk->coord[0][0],
diff --git a/libavcodec/jpeg2000htdec.c b/libavcodec/jpeg2000htdec.c
index d8fd062a63..c47c8d61fe 100644
--- a/libavcodec/jpeg2000htdec.c
+++ b/libavcodec/jpeg2000htdec.c
@@ -122,7 +122,7 @@ static void jpeg2000_init_mel(StateVars *s, uint32_t Pcup)
 
 static void jpeg2000_init_mag_ref(StateVars *s, uint32_t Lref)
 {
-    s->pos       = Lref - 2;
+    s->pos       = Lref - 1;
     s->bits      = 0;
     s->last      = 0xFF;
     s->tmp       = 0;
@@ -145,9 +145,10 @@ static void jpeg2000_init_mel_decoder(MelDecoderState *mel_state)
 static int jpeg2000_bitbuf_refill_backwards(StateVars *buffer, const uint8_t *array)
 {
     uint64_t tmp = 0;
-    int32_t position = buffer->pos - 4;
     uint32_t new_bits = 32;
 
+    buffer->last = array[buffer->pos + 1];
+
     if (buffer->bits_left >= 32)
         return 0; // enough data, no need to pull in more bits
 
@@ -157,9 +158,24 @@ static int jpeg2000_bitbuf_refill_backwards(StateVars *buffer, const uint8_t *ar
      *  the bottom most bits.
      */
 
-    for(int i = FFMAX(0, position + 1); i <= buffer->pos + 1; i++)
-        tmp = 256*tmp + array[i];
-
+    if (buffer->pos >= 3) {  // Common case; we have at least 4 bytes available
+         tmp = array[buffer->pos - 3];
+         tmp = (tmp << 8) | array[buffer->pos - 2];
+         tmp = (tmp << 8) | array[buffer->pos - 1];
+         tmp = (tmp << 8) | array[buffer->pos];
+         tmp = (tmp << 8) | buffer->last;  // For stuffing bit detection
+         buffer->pos -= 4;
+    } else {
+        if (buffer->pos >= 2)
+            tmp = array[buffer->pos - 2];
+        if (buffer->pos >= 1)
+            tmp = (tmp << 8) | array[buffer->pos - 1];
+        if (buffer->pos >= 0)
+            tmp = (tmp << 8) | array[buffer->pos];
+        buffer->pos = 0;
+        tmp = (tmp << 8) | buffer->last;  // For stuffing bit detection
+    }
+    // Now remove any stuffing bits, shifting things down as we go
     if ((tmp & 0x7FFF000000) > 0x7F8F000000) {
         tmp &= 0x7FFFFFFFFF;
         new_bits--;
@@ -176,13 +192,11 @@ static int jpeg2000_bitbuf_refill_backwards(StateVars *buffer, const uint8_t *ar
         tmp = (tmp & 0x0000007FFF) + ((tmp & 0xFFFFFF0000) >> 1);
         new_bits--;
     }
-
-    tmp >>= 8; // Remove temporary byte loaded
+    tmp >>= 8;  // Shifts away the extra byte we imported
 
     /* Add bits to the MSB of the bit buffer */
     buffer->bit_buf |= tmp << buffer->bits_left;
     buffer->bits_left += new_bits;
-    buffer->pos = FFMAX(0, position);
     return 0;
 }
 
@@ -406,6 +420,7 @@ static void recover_mag_sgn(StateVars *mag_sgn, uint8_t pos, uint16_t q, int32_t
             E[n] = 32 - ff_clz(v[pos][i] | 1);
             mu_n[n] = (v[pos][i] >> 1) + 1;
             mu_n[n] <<= pLSB;
+            mu_n[n] |= (1 << (pLSB - 1)); // Add 0.5 (reconstruction parameter = 1/2)
             mu_n[n] |= ((uint32_t) (v[pos][i] & 1)) << 31; // sign bit.
         }
     }
@@ -414,7 +429,7 @@ static void recover_mag_sgn(StateVars *mag_sgn, uint8_t pos, uint16_t q, int32_t
 static int jpeg2000_import_bit(StateVars *stream, const uint8_t *array, uint32_t length)
 {
     int cond = stream->pos < length;
-    int pos = FFMIN(stream->pos, length);
+    int pos = FFMIN(stream->pos, length - 1);
     if (stream->bits == 0) {
         stream->bits = (stream->tmp == 0xFF) ? 7 : 8;
         stream->pos += cond;
@@ -426,14 +441,22 @@ static int jpeg2000_import_bit(StateVars *stream, const uint8_t *array, uint32_t
 
 static int jpeg2000_peek_bit(StateVars *stream, const uint8_t *array, uint32_t length)
 {
+    uint8_t bit;
+
     if (stream->bits == 0) {
-        int cond = stream->pos < length;
-        int pos = FFMIN(stream->pos, length);
-        stream->bits = (stream->tmp == 0xFF) ? 7 : 8;
-        stream->pos += cond;
-        stream->tmp = cond ? array[pos] : 0xFF;
+        stream->bits = (stream->last == 0xFF) ? 7 : 8;
+        if (stream->pos < length) {
+            stream->tmp = array[stream->pos];
+            stream->pos++;
+        } else {
+            stream->tmp = 0;
+        }
+        stream->last = stream->tmp;
     }
-    return (stream->tmp >> stream->bits) & 1;
+    bit = stream->tmp & 1;
+    stream->tmp >>= 1;
+    stream->bits--;
+    return  bit;
 }
 
 static int jpeg2000_decode_mel_sym(MelDecoderState *mel_state,
@@ -994,39 +1017,18 @@ static void jpeg2000_calc_mbr(uint8_t *mbr, const uint16_t i, const uint16_t j,
                               const uint32_t mbr_info, uint8_t causal_cond,
                               uint8_t *block_states, int stride)
 {
-    int local_mbr = 0;
+    uint8_t *state_p0 = block_states + i * stride + j;
+    uint8_t *state_p1 = block_states + (i + 1) * stride + j;
+    uint8_t *state_p2 = block_states + (i + 2) * stride + j;
 
-    local_mbr |= jpeg2000_get_state(i - 1, j - 1, stride, HT_SHIFT_SIGMA, block_states);
-    local_mbr |= jpeg2000_get_state(i - 1, j + 0, stride, HT_SHIFT_SIGMA, block_states);
-    local_mbr |= jpeg2000_get_state(i - 1, j + 1, stride, HT_SHIFT_SIGMA, block_states);
-
-    local_mbr |= jpeg2000_get_state(i + 0, j - 1, stride, HT_SHIFT_SIGMA, block_states);
-    local_mbr |= jpeg2000_get_state(i + 0, j + 1, stride, HT_SHIFT_SIGMA, block_states);
-
-    local_mbr |= jpeg2000_get_state(i + 1, j - 1, stride, HT_SHIFT_SIGMA, block_states) * causal_cond;
-    local_mbr |= jpeg2000_get_state(i + 1, j + 0, stride, HT_SHIFT_SIGMA, block_states) * causal_cond;
-    local_mbr |= jpeg2000_get_state(i + 1, j + 1, stride, HT_SHIFT_SIGMA, block_states) * causal_cond;
-
-    local_mbr |= jpeg2000_get_state(i - 1, j - 1, stride, HT_SHIFT_REF, block_states) *
-                 jpeg2000_get_state(i - 1, j - 1, stride, HT_SHIFT_SCAN, block_states);
-    local_mbr |= jpeg2000_get_state(i - 1, j + 0, stride, HT_SHIFT_REF, block_states) *
-                 jpeg2000_get_state(i - 1, j - 1, stride, HT_SHIFT_SCAN, block_states);
-    local_mbr |= jpeg2000_get_state(i - 1, j + 1, stride, HT_SHIFT_REF, block_states) *
-                 jpeg2000_get_state(i - 1, j + 1, stride, HT_SHIFT_SCAN, block_states);
-
-    local_mbr |= jpeg2000_get_state(i + 0, j - 1, stride, HT_SHIFT_REF, block_states) *
-                 jpeg2000_get_state(i + 0, j - 1, stride, HT_SHIFT_SCAN, block_states);
-    local_mbr |= jpeg2000_get_state(i + 0, j + 1, stride, HT_SHIFT_REF, block_states) *
-                 jpeg2000_get_state(i + 0, j + 1, stride, HT_SHIFT_SCAN, block_states);
-
-    local_mbr |= jpeg2000_get_state(i + 1, j - 1, stride, HT_SHIFT_REF, block_states) *
-                 jpeg2000_get_state(i + 1, j - 1, stride, HT_SHIFT_SCAN, block_states) * causal_cond;
-    local_mbr |= jpeg2000_get_state(i + 1, j + 0, stride, HT_SHIFT_REF, block_states) *
-                 jpeg2000_get_state(i + 1, j + 0, stride, HT_SHIFT_SCAN, block_states) * causal_cond;
-    local_mbr |= jpeg2000_get_state(i + 1, j + 1, stride, HT_SHIFT_REF, block_states) *
-                 jpeg2000_get_state(i + 1, j + 1, stride, HT_SHIFT_SCAN, block_states) * causal_cond;
-
-    *mbr |= local_mbr;
+    uint8_t mbr0 = state_p0[0] | state_p0[1] | state_p0[2];
+    uint8_t mbr1 = state_p1[0] | state_p1[2];
+    uint8_t mbr2 = state_p2[0] | state_p2[1] | state_p2[2];
+    *mbr  = mbr0 | mbr1 | (mbr2 & causal_cond);
+    *mbr |= (mbr0 >> HT_SHIFT_REF) & (mbr0 >> HT_SHIFT_SCAN);
+    *mbr |= (mbr1 >> HT_SHIFT_REF) & (mbr1 >> HT_SHIFT_SCAN);
+    *mbr |= (mbr2 >> HT_SHIFT_REF) & (mbr2 >> HT_SHIFT_SCAN) & causal_cond;
+    *mbr &= 1;
 }
 
 static void jpeg2000_process_stripes_block(StateVars *sig_prop, int i_s, int j_s,
@@ -1060,6 +1062,18 @@ static void jpeg2000_process_stripes_block(StateVars *sig_prop, int i_s, int j_s
             jpeg2000_modify_state(i, j, stride, modify_state, block_states);
         }
     }
+    // decode sign
+    for (int j = j_s; j < j_s + width; j++) {
+        for (int i = i_s; i < i_s + height; i++) {
+            uint8_t bit;
+            int32_t *sp = &sample_buf[j + (i * (stride))];
+            uint8_t *state_p = block_states + (i + 1) * stride + (j + 1);
+            if ((state_p[0] >> HT_SHIFT_REF) & 1) {
+                bit = jpeg2000_peek_bit(sig_prop, magref_segment, magref_length);
+                *sp |= (int32_t)bit << 31;
+            }
+        }
+    }
 }
 
 /**
@@ -1130,7 +1144,8 @@ jpeg2000_decode_magref_segment( uint16_t width, uint16_t block_height, const int
     uint16_t height             = 4;
     uint16_t i_start            = 0;
     int32_t *sp;
-
+    int32_t bit;
+    int32_t tmp;
     jpeg2000_init_mag_ref(&mag_ref, magref_length);
 
     for (int n1 = 0; n1 < num_v_stripe; n1++) {
@@ -1141,9 +1156,13 @@ jpeg2000_decode_magref_segment( uint16_t width, uint16_t block_height, const int
                  *  Rec. ITU-T T.814, Figure 7.
                  */
                 sp = &sample_buf[j + i * stride];
-                if (jpeg2000_get_state(i, j, width, HT_SHIFT_SIGMA, block_states) != 0) {
-                    jpeg2000_modify_state(i, j, width, 1 << HT_SHIFT_REF_IND, block_states);
-                    *sp |= jpeg2000_import_magref_bit(&mag_ref, magref_segment, magref_length) << pLSB;
+                if (jpeg2000_get_state(i, j, stride, HT_SHIFT_SIGMA, block_states) != 0) {
+                    jpeg2000_modify_state(i, j, stride, 1 << HT_SHIFT_REF_IND, block_states);
+                    bit = jpeg2000_import_magref_bit(&mag_ref, magref_segment, magref_length);
+                    tmp = 0xFFFFFFFE | (uint32_t)bit;
+                    tmp <<= pLSB;
+                    sp[0] &= tmp;
+                    sp[0] |= 1 << (pLSB - 1); // Add 0.5 (reconstruction parameter = 1/2)
                 }
             }
         }
@@ -1153,9 +1172,13 @@ jpeg2000_decode_magref_segment( uint16_t width, uint16_t block_height, const int
     for (int j = 0; j < width; j++) {
         for (int i = i_start; i < i_start + height; i++) {
             sp = &sample_buf[j + i * stride];
-            if (jpeg2000_get_state(i, j, width, HT_SHIFT_SIGMA, block_states) != 0) {
-                jpeg2000_modify_state(i, j, width, 1 << HT_SHIFT_REF_IND, block_states);
-                *sp |= jpeg2000_import_magref_bit(&mag_ref, magref_segment, magref_length) << pLSB;
+            if (jpeg2000_get_state(i, j, stride, HT_SHIFT_SIGMA, block_states) != 0) {
+                jpeg2000_modify_state(i, j, stride, 1 << HT_SHIFT_REF_IND, block_states);
+                bit = jpeg2000_import_magref_bit(&mag_ref, magref_segment, magref_length);
+                tmp = 0xFFFFFFFE | (uint32_t)bit;
+                tmp <<= pLSB;
+                sp[0] &= tmp;
+                sp[0] |= 1 << (pLSB - 1); // Add 0.5 (reconstruction parameter = 1/2)
             }
         }
     }
@@ -1233,6 +1256,9 @@ ff_jpeg2000_decode_htj2k(const Jpeg2000DecoderContext *s, Jpeg2000CodingStyle *c
     }
     Dcup = cblk->data;
     Dref  = cblk->data + Lcup; // Dref comes after the refinement segment
+
+    cblk->data[cblk->length] = 0xFF; // an extra byte for refinement segment (buffer->last)
+
     S_blk = p0 + cblk->zbp;
     cblk->zbp = S_blk - 1;
     pLSB  = 30 - S_blk;
diff --git a/libavcodec/jpeg2000htdec.h b/libavcodec/jpeg2000htdec.h
index 572d095c92..8d6919a0de 100644
--- a/libavcodec/jpeg2000htdec.h
+++ b/libavcodec/jpeg2000htdec.h
@@ -29,6 +29,6 @@
 
 int ff_jpeg2000_decode_htj2k(const Jpeg2000DecoderContext *s, Jpeg2000CodingStyle *codsty,
                             Jpeg2000T1Context *t1, Jpeg2000Cblk *cblk, int width,
-                            int height, int magp, uint8_t roi_shift);
+                            int height, int M_b, uint8_t roi_shift);
 
 #endif /* AVCODEC_JPEG2000HTDEC_H */