Signal Processing: Image Communication 96 (2021) 116306
Contents lists available at ScienceDirect
Signal Processing: Image Communication
journal homepage: www.elsevier.com/locate/image
Efficient coding of experimental holograms using speckle denoising
Marco V. Bernardo a ,∗, Elsa Fonseca c,b , António M.G. Pinheiro c,a , Paulo T. Fiadeiro c,b ,
Manuela Pereira c,a
a
Instituto de Telecomunicações (IT), Covilhã, Portugal
Fiber Materials and Environmental Technologies (FibEnTech-UBI), Covilhã, Portugal
c
Universidade da Beira Interior (UBI), R. Marquês D’Ávila e Bolama, 6201-001 Covilhã, Portugal
b
ARTICLE
Keywords:
Digital Holography
Data compression
Coding efficiency
Speckle noise
INFO
ABSTRACT
Lossy compression for Experimental Holograms (EH) and Computer-Generated Holograms (CGH) using
standardized coding solutions is a highly efficient process provided that these solutions can be applied to
the object plane. This compression efficiency reveals to be more relevant in CGH. Speckle noise mainly affects
reconstructed EH, and to less extent reconstructed CGH. In the current work, the reduction of speckle noise of
EH is proposed to improve the coding efficiency of the hologram compression scheme. The compression scheme
defines a base layer where a 2D version of the object is coded with an image codec standard. When speckle
noise reduction is performed before any compression, efficient compression is obtained for both CGH and EH.
Since speckle noise reduction is performed only on amplitude data, without affecting the phase information
of the reconstructed hologram, it is still possible to render 3D features such as depth map, multi-view or to
recover holographic interference patterns for further 3D visualization.
1. Introduction
Bringing the display technology closer to the human’s natural visual
perception, by adding a third dimension, is one of the most challenging
quests among the emerging imaging modalities. Digital Holography
(DH) created the possibility of developing impressive dynamic 3D
displays, capable of presenting visual depth cues [1,2]. When compared
to classical stereoscopic or autostereoscopic light field displays, DH has
a significant amount of advantages, since it allows both vertical and
horizontal parallax for several simultaneous viewers, and without the
visual discomfort produced by the accommodation-vergence rivalry.
A digital hologram is usually obtained by recording the interference
pattern between a reference wavefront and an object wavefront, reflected from or transmitted through an object, with a digital camera.
Since it provides the means for amplitude and phase encoding of the
light wave, DH is capable of high depth resolution, which is particularly
relevant for microscopy or non-destructive evaluation in industrial and
biomedical applications [3].
Given the fact that high-resolution interference patterns need to
be stored and processed for holographic display rendering, the data
storage requirements associated with this technology are rapidly increasing. This leads to the need of developing advanced solutions for
holographic data representation and coding. However, the quality of
the reconstructed holographic image is always degraded due to the
presence of speckle noise which has a negative impact on compression
performance. The speckle phenomenon is due to the use of coherent
radiation during DH acquisition and, to get a high-quality reconstructed
image, speckle denoising is mandatory before further processing can
be applied. Despite this fact, there is a lack of studies on the relation
between speckle characteristics and their effect on DH compression [4].
Furthermore, little has been reported about the way speckle reduction
filters may impact the behavior of coding schemes.
Several methods were proposed for the compression of holographic
data on the hologram plane. The lossless and lossy data compression
and quantization effects were analyzed in the context of phase-shifting
digital holography [5–7]. Histogram quantization for digital holograms
of 3-D real-world objects was presented in [7]. Scalar and vector
quantization were analyzed using two different representations, the
amplitude-phase data and the difference data of the complex object
wave [8].
The application of transforms adapted to the holographic data was
analyzed. The directional wavelet transforms with a packet decomposition scheme for off-axis holographic recordings were applied in
[9,10]. Authors in [8] proposed a nonseparable vector lifting scheme
to exploit the two-dimensional characteristics of holographic data.
The wavelet-bandelets transform was applied in [11]. The bandelets
transform was used to analyze wavelet transformed hologram fringes.
The wave atom transform was applied in [12]. A mode dependent
directional transform-based using standardized coding solutions was
∗ Corresponding author.
E-mail address: mbernardo@ubi.pt (M.V. Bernardo).
https://doi.org/10.1016/j.image.2021.116306
Received 12 August 2020; Received in revised form 16 April 2021; Accepted 30 April 2021
Available online 12 May 2021
0923-5965/© 2021 Elsevier B.V. All rights reserved.
M.V. Bernardo, E. Fonseca, A.M.G. Pinheiro et al.
Signal Processing: Image Communication 96 (2021) 116306
also considered [13,14]. The authors in [15] provided a design of
a Morlet wavelet and explained an efficient discretization method to
transform a hologram and reconstructing parts of a scene based on
the viewer position. The Gabor wavelets, which obtain an optimal
compromise between spatial and angular resolution, permitted by the
Heisenberg principle, were also used on holographic data compression.
A matching pursuit algorithm using an overcomplete Gabor’s dictionary
was proposed in [16]. The suitability of Gabor wavelets for an adaptive
partial reconstruction of holograms based on the viewer position was
verified in [17].
Compression of holographic data on the object plane was also
analyzed. The Fresnelets, an alternative to common wavelet bases,
demonstrated good compression capabilities [18–21]. In [22] it was
shown that the increased spatial correlation apparent at the reconstruction plane can be effectively exploited to obtain high compression, even
with relatively simple methods such as the quantization followed by
lossless coding. A comparison of HEVC coding efficiency between the
object plane and hologram plane was presented in [14].
The direct application of image and video coding standards was also
tested for hologram compression [23–27]. A benchmark over different
coding standards suggested that HEVC intra main coding profile is the
best standardized coding solution for both the hologram plane [13] and
object plane [27].
A coding method for digital hologram video, using a threedimensional scanning method and a two-dimensional video compression technique, was presented in [28]. Other solutions for dynamic
hologram coding were recently proposed in [29]. A detailed state
of the art on compression of digital holographic data can be found
in [4,30,31].
To the best of the author’s knowledge, there are no DH compression
studies where the effect of speckle suppression before image compression is analyzed. Therefore, some related imaging modalities where
speckle noise is typically an issue and image compression are necessary,
such as Synthetic Aperture Radar (SAR), Ultrasound (US), and Optical
Coherence Tomography (OCT), will be briefly reviewed. In a very
recent study on compression of DH [32], the authors introduced a new
lossless compression algorithm, applied to the hologram plane, based
on the directionality of the interference fringes. They referred to the
advantages of lossless compression methods when compared to lossy
algorithms, by stressing the fact that lossy compression methods may
lead to increased speckle, even when it is not noticeable in the original
uncompressed hologram.
In [33,34], the authors proposed a compression scheme where
speckle noise reduction is performed by soft-threshold of multi-wavelets
based techniques applied to SAR images, before encoding. In this
work, compression was performed with classical set partitioning in
hierarchical trees (SPIHT) algorithm. In [35], the authors also performed denoising in SAR imaging, before image compression with
the SPIHT scheme. They reduced the speckle noise using the Kuan
filter after applying the k-nearest neighbor (K-NN) algorithm for filter
improvement.
Other applications, such as US, take advantage of noise suppression
features of coding algorithms to simultaneously compress and denoise
the reconstructed image. In [36], the authors proposed an adaptive subband (wavelet) coder that denoises the input ultrasound image based
on the compression rate desired. In another work on US imaging [37],
the authors applied a threshold to the contourlet transform. After the
threshold, the coefficients are quantized and Huffman coding is applied
to the quantized coefficients.
Also in the context of OCT, wavelet transforms were used to simultaneously compress and reduce the speckle. In [38], a dual tree
complex wavelet transform (DTCWT) based image compression is proposed to solve factors such as low image contrast and speckle noise.
Ophthalmic OCT, SD-OCT (Spectral Domain OCT), and secondary images were compressed by the proposed DTCWT. Another scheme for
Ophthalmic OCT was proposed by [39]. The authors proposed a 3D
adaptive sparse representation based compression algorithm for 3DOCT that exploits correlations among adjacent OCT images to improve
compression performance. The proposed method presented an inherent
denoising mechanism.
This paper is organized as follows: Section 2 discusses the objectives
of the present research concerning previous work, describes the speckle
reduction technique and the proposed compression approach; Section 3
describes the used data characteristics and the image coding settings;
Section 4 presents the results and the performance evaluation using
objective metrics; finally, Section 5 presents the concluding remarks.
2. Coding scheme
2.1. Hologram reconstruction
Optically acquired digital holograms are recorded as interference
patterns where the information regarding the amplitude and the phase
of the wave field scattered by the object is encoded. Numerical reconstruction refers to the process of retrieving this information from
the interference pattern and involves a simulation of the diffraction
of light as it propagates through the hologram to the diffraction or
image plane (see Fig. 1). Although for clarity, the image plane is
depicted as the result of forward propagation, the numerical reconstruction usually simulates the back-propagation to the original object
plane location. Depending on the setup parameters, different numerical
reconstruction methods may be applied. For macroscopic objects, in
the paraxial approximation, which is valid for the used database, the
Fresnel Transform (FTM) method is usually applied [40]. Let 𝑂0 (𝑥0 , 𝑦0 )
be the complex object wave field at the hologram plane, ℎ(𝑥, 𝑦; 𝑧) be the
free-space point spread function (PSF), and 𝑂(𝑥, 𝑦; 𝑧) be the numerical
reconstruction at distance 𝑧 from the hologram plane. Assuming a
collimated beam is used as the reference wave, the object field can be
computed from the Rayleigh–Sommerfeld (RS) integral and expressed
as a convolution:
(1)
𝑂(𝑥, 𝑦; 𝑧) = 𝑂0 (𝑥0 , 𝑦0 ) ⋆ ℎ(𝑥, 𝑦; 𝑧)
where, the paraxial approximation of the PSF can be written as
[
)]
𝜋 ( 2
𝑒𝑗2𝜋𝑧∕𝜆
exp 𝑗
𝑥 + 𝑦2
ℎ(𝑥, 𝑦; 𝑧) =
𝑗𝜆𝑧
𝜆𝑧
(2)
where 𝜆 is the wavelength of the laser light source. This allows the RS
integral to be expressed as a single Fourier transform:
𝑂(𝑥, 𝑦; 𝑧) =
𝑒
[
)]
1 ( 2
𝑗 2𝜋𝑧
𝑥 +𝑦2
𝑧+ 2𝑧
𝜆
𝑗𝜆𝑧
{

𝑂0 (𝑥0 , 𝑦0 )𝑒
(
)}
𝜋
𝑥20 +𝑦20
𝑗 𝜆𝑧
𝑦
(3)
𝑥
𝑓𝑥 = 𝜆𝑧
,𝑓𝑦 = 𝜆𝑧
The holograms used in this work were acquired using the phase-shifting
technique [41], where four holograms 𝐼𝛼𝑖 , are sequentially acquired
with reference phases 𝛼𝑖 separated by 𝜋∕2 steps. The complex object
field at the hologram plane can be obtained by the following algebraic
combination:
(
)
(
)
𝐼0 − 𝐼𝜋 − 𝑗 𝐼𝜋∕2 − 𝐼3𝜋∕2
.
(4)
𝑂0 (𝑥0 , 𝑦0 ) =
4
This method removes unwanted components, namely the twin-image
and DC terms, from the reconstructed field. The compression step can
then proceed, once the hologram plane 𝑂0 (𝑥, 𝑦) and back-propagated
object plane 𝑂(𝑥, 𝑦; 𝑧) complex fields become available, using the numerical reconstruction process.
2.2. Previous work
In a previous work [42], a digital hologram compression scheme
for representation on the object plane was proposed. The two layers
coding scheme was based on standardized codecs. First, the amplitude
computed in the object plane was coded in the base layer. This can be
later decoded, yielding a direct 2D representation of the image. In a second layer, a suitable representation of the phase, needed to recover the
2
M.V. Bernardo, E. Fonseca, A.M.G. Pinheiro et al.
Signal Processing: Image Communication 96 (2021) 116306
In this method, the image is decomposed in heterogeneous patches
following a procedure named grouping and collaborative filtering. During the grouping stage, similar blocks sharing similar noise distributions
are identified and stacked together in 3D arrays. There are many
parameters involved in this process, such as the search window size, the
similarity metric between patches, the similarity threshold, etc. Then,
collaborative filtering is applied to all grouped blocks by filtering them
jointly, leading to individual estimates of these groups. Since these
3D arrays are highly correlated, a 3D decorrelating unitary transform
is applied and the noise is attenuated by shrinkage of the transform
coefficients. The filtered matched blocks are then obtained through
inverse 3D transformation. This process is repeated in a sliding manner
until the whole image has been scanned. The final estimate is computed
as the weighted sum of all stacked patches, in a similar way as in the
non-local means method [55].
In this work, a freely available implementation1 of the BM3D
method that is suitable for attenuation of additive white Gaussian noise
from grayscale images is used [56]. Despite the DH reconstruction’s
different noise characteristics, the referred implementation has been
successfully tested in holograms by other authors [52,53].
The BM3D filter relies on the optimization of many parameters and
their re-optimization for DH would be a complex task that is out of the
scope of this paper. Therefore, most of the parameters suggested by the
authors for the BM3D filter were kept constant and only the variable 𝜎,
denoting the standard deviation of the noise, was adjusted. The 𝜎 values
selected in this work are the most performing ones found in a previous
study [54]. In Fig. 2, two numerical reconstructions of an experimental
hologram, before and after BM3D filtering, are presented side-by-side
for comparison purposes.
Fig. 1. Coordinate system for the numerical reconstruction of a digital hologram.
3D features of the object field, was coded. It was observed in previous
studies that the phase information requires much higher bitrates than
the amplitude information because of their intrinsic properties that
are not the aim of the common standards codecs. Thus, an alternative
model was proposed, where the phase was represented by encoding
the real information and the signal of the imaginary information.
Optionally, the imaginary information could also be coded but it was
observed that the lossless binary coding of the signal produces a lower
bit rate. The reconstruction of the complex signal uses the amplitude
of the base layer, plus the real part and the signal of the imaginary
part of the second layer. Hence, this second layer combined with the
base layer defines the holographic information, suitable to be used in
applications like holographic displaying, hologram printing, or if other
rendering applications such as depth map, extended depth of focus, or
multiple perspectives would be required.
The efficiency of the base layer compression is much higher in case
of CGH when compared with EH.
The objective of the present work is to demonstrate that using
speckle noise reduction improves the coding efficiency of the hologram
compression scheme described above.
2.4. Proposed scheme
The proposed compression approach is based on a two layers
scheme [42]. The general coding scheme is presented in Fig. 3.
The amplitude (A) coded in the base layer is filtered with the BM3D
method presented above, before being coded with the Standardized
Image Codec (SIC). Performing speckle noise reduction before the compression should improve the compression efficiency of experimental
holograms.
In a 3D enhancement layer, the data required to recover the complex amplitudes in the hologram plane is coded. The phase is represented by encoding the real component and the signal of the imaginary
component. The real component is also encoded using a SIC, while the
imaginary signal is lossless encoded with the binary codec JBIG2 [57].
Notably, it is not possible to apply BM3D filtering to the real part
because of its nature. The filtering operation might have strong repercussions at the phase reconstruction, with the possible loss of the
hologram 3D features.
The decoding of the base layer provides a denoised direct 2D
representation of the hologram. Decoding the base and enhancement
layers provides the amplitude and the phase data.
The scheme presented in Fig. 3 also represents the objective quality
assessment metric that will be discussed in the Results section. The
metrics PSNR and VIFP were chosen because they revealed a high
correlation with a subjective evaluation [58].
In the proposed coding scheme, the speckle noise reduction is applied to amplitude data, while the phase component is left unchanged.
Therefore, it is still possible to render 3D features or to recover holographic interference patterns for further 3D applications. This can be
done by gathering the filtered amplitude and the original phase of the
Complex Object Field (COF) and, subsequently, propagate it back to
the hologram plane. This yields a restored version of the DH. Fig. 4
illustrates the preservation of parallax information by presenting a pair
of views that have been numerically reconstructed from such restored
hologram.
2.3. Speckle reduction
Recording a digital hologram of macroscopic objects usually requires a coherent source, such as a laser, to preserve the phase relations
between the reference beam and the wavefront scattered by the object.
When a coherent light source is reflected from a surface with a
certain degree of roughness, a signal dependent multiplicative noise,
called speckle, occurs. Speckle noise degrades the image quality of
numerically reconstructed digital holograms in conventional 2D displays as well as the optical quality in holographic displays, imposing
severe limitations in spatial resolution, signal-to-noise ratio, and phase
accuracy. Although other sources of noise might be present, such as
additive noise [43] and shot noise [44], speckle noise [45] seems to
have the most hindering effect since, being a multiplicative kind of
noise, it is quite difficult to remove using common filtering techniques.
Several speckle reduction (SR) techniques have been proposed [46–
48] and can be divided into two main categories: optical and digital
methods. The first is performed during the acquisition process by
combining multiple decorrelated holograms obtained, for example, by
rotating rough diffusers, diversifying the polarization angle or the
illumination direction. The second category of methods is applied to
the reconstructed holograms using signal processing techniques.
The block matching 3D filter, BM3D [49], falls on the second type
of methods and will be used in this work. Since its introduction by
Dabov et al. [50], it has been used by several authors for hologram
despeckling [51–53] and, according to several objective quality metrics, it is considered one of the best models for image denoising.
Furthermore, in [54], the BM3D was also one of the preferred filters
when a subjective quality assessment was applied.
1
3
https://www.cs.tut.fi/~foi/GCF-BM3D/.
M.V. Bernardo, E. Fonseca, A.M.G. Pinheiro et al.
Signal Processing: Image Communication 96 (2021) 116306
Fig. 2. Example of experimental acquired hologram. (a) Before speckle reduction. (b) After speckle reduction.
Fig. 3. Flowchart of the complete compression scheme and objective quality assessment between reference and the coded component, on the Complex Object Field (COF).
Fig. 4. Left and right views of the astronauts, obtained after SR, and their absolute differences.
3. Performance analysis
the aforementioned CMOS camera (model F-503B) was used, differing
only by a pixel of 2.2 μm side length, and a resolution of 2588 × 1940
pixels.
According to the phase-shifting technique, four interference patterns
separated by a constant phase shift of 𝜋∕2, produced by a piezo electric
mirror, are sequentially optically recorded. By algebraically combining
these frames, a complex object field free from the DC and twin image
terms can be reconstructed.
The numerical reconstruction of a hologram consists of propagating
the recorded object complex field amplitude at the digital camera plane
to its original position, using the Scalar Diffraction theory. The FTM,
Eq. (3), was used to obtain the reconstructed complex object fields.
The corresponding amplitudes were then denoised using the already
mentioned BM3D filter to suppress the speckle noise, while the phase
is left unchanged. The value of noise standard deviation 𝜎 = 9.0 was
found to give the best results for both digital hologram subsets.
The characteristics of each of the above mentioned holograms are
presented in Table 1. The Distance parameter corresponds to the reconstruction distance between the object and the digital camera.
This section presents the used data, the choice for the image coding
standard and used parameters.
3.1. Used data
Eight EH were selected from the EmergImg-HoloGrail database,
available online 2 and presented in Fig. 5. These holograms were
acquired at ‘‘Universidade da Beira Interior’’ using a four-step phaseshifting DH [59] technique. The recording setup comprises a Mach–
Zehnder type interferometer working in reflection mode and using an
in-line configuration. According to this setup, a HeNe laser, with 5 mW
and 632.8 nm wavelength, generates a linearly polarized beam which is
separated into the reference and the object arms of the interferometer
through a variable beam splitter. The light reflected by the object is
then combined with the reference beam, using a second beam splitter,
that is digitally recorded with a CMOS based camera.
The set of EH’s can be further divided into two groups of four
holograms each, recorded by different camera models. Specifically, the
first group was produced by a color Guppy Pro (model F-503C) CMOS
camera with a square effective pixel size of 4.4 μm side length, and an
acquisition mode of 1296 × 972 pixels of resolution and 8 bit-depth.
The Car2575 was acquired with lower resolution (800 × 600 pixels)
since it was part of a set of holograms that were recorded to generate
a video sequence. For the second subset, a monochromatic version of
2
3.2. Image coding standard and parameters definition
The HEVC codec has proven to be the most effective standardized
codec for the compression of holographic data [13,27]. Based on these
previous works, the coding scheme proposed in this study considered the HEVC Intra mode as the SIC. The latest reference software
HM-16.20 was selected for HEVC.3
3
http://emergimg.di.ubi.pt/HoloGrail_DB.html
4
https://hevc.hhi.fraunhofer.de/.
M.V. Bernardo, E. Fonseca, A.M.G. Pinheiro et al.
Signal Processing: Image Communication 96 (2021) 116306
Fig. 5. Experimental acquired holograms from EmergImg-HoloGrail-v1 in first line, and from EmergImg-HoloGrail-v2 in second line.
Table 1
Hologram characteristics.
Horse
King
Cube
Car2575
Astronaut
Dice1
Dice2
Skull
Resolution
(pixel)
Pitch
(μm)
Distance
(m)
Wavelength
(nm)
972 × 972
972 × 972
972 × 972
600 × 600
2588 × 2588
2588 × 2588
2588 × 2588
2588 × 2588
4.4
4.4
4.4
4.4
2.2
2.2
2.2
2.2
0.1400
0.1400
0.1350
0.2450
0.1721
0.1400
0.1595
0.2450
632.8
632.8
632.8
632.8
632.8
632.8
632.8
632.8
the object plane was very low and still outperforms encoding in the
hologram plane. However, the increase of adding the amplitude for EH
was much higher when comparing with CGH. In the present work, the
proposed method is compared with the method presented in [42].
Improved compression performance can be observed for the bitrate/PSNR relations for the amplitudes (2D version) that have been
denoised by the BM3D filter. This result was expected since the speckle
noise has a high negative influence on compression efficiency when
using a SIC, as explained in [14]. When comparing the bitrate/PSNR
and the bitrate/VIFp relations for the holograms from two different
versions of the database, presented in Figs. 6 and 7, it can be noted that
the gain is much higher for the older version, where lower resolutions
lead to increased speckle levels.
For the complex amplitudes, the gain is more evident for higher
bitrates. For low bit rates, it is not so evident because the compression
of the signal results in a higher contribution. Moreover, at low bit
rates and for both A and COF curves, the differences between the
two compression schemes tend to vanish, since compression has a
smoothing effect that acts as a speckle noise filter.
The proposed coding scheme combines the advantage of being
backward-compatible with HEVC and offering the ability to encode
information to render further viewing angles and other 3D features.
In case a single perspective for conventional 2D display is required,
the proposed solution has the additional benefit of saving significant
computational time at the rendering stage since no further speckle
suppression is necessary.
The Bjontegaard delta peak-signal-to-noise ratio (BD-PSNR) and the
Bjontegaard delta rate (BD-Rate) metrics [60] were also used to assess
and compare the coding efficiency of the proposed coding scheme with
the coding scheme presented in [42]. The Bjontegaard model is used
to calculate the average PSNR and bitrate differences between two
R-D curves obtained from the PSNR measurement when encoding a
content at different bitrates. The model reports two values, the BDPSNR, which corresponds to the average PSNR difference in dB for the
same bitrate, and the BD-Rate, which corresponds to the average bitrate
difference in percent for the same PSNR. This method estimates thirdorder logarithmic polynomial fitting curves for the PSNR and the bit
rate. The Bjontegaard metrics are the average difference between the
two R-D curves and it is proportional to the difference between the
integrals of the fitting curves [61].
The Bjontegaard metrics are computed for A and the COF. The
obtained BD-PSNR and the BD-Rate are presented in Table 2. The BDPSNR and BD-Rate for the amplitude compare the coding efficiency
when considering only the base layer of both schemes. This base
The HEVC Intra mode can be used for image coding. The larger
input bit rate allowed in this profile is 16 bits. This is the only case
of the ‘‘intra main rext’’ that corresponds to an extension of the Intra
coding profile. In this work, this extension of the HM software: Encoder
Version 16.14 was used. The reason behind this choice is related to
the propagation process between the two planes. When 8 bits representation is used, the propagation numerical error tends to increase.
Moreover, the behavior of the bitrate quality relation with 8 and 16
bits is similar, as was verified in [14].
4. Results
In the present work, the hologram quality assessment is based on
the PSNR metric. Specifically, the PSNR of the amplitude images and
the PSNR of the COF were computed, as illustrated in the scheme of
Fig. 3. The PSNR of amplitude images (2D version) is computed in the
usual manner. On the other hand, the PSNR of the COF is computed
from the mean of the individual PSNR values of the real and imaginary
parts.
The plots in Figs. 6 and 7 represent the PSNR and VIFp versus bitrate
(logarithmic scale) relations of one EH from each of the two groups of
the EmergImg-HoloGrail database. The relations for the other EH are
very similar. The subfigures (a) and (c) for both Figs. 6 and 7 present
the PSNR and VIFp versus bitrate (logarithmic scale) relations for the
2D version coded on the base layer. The subfigures (b) and (d) for both
Figs. 6 and 7 present the bitrate/PSNR and bitrate/VIFp relations for
the COF recovery from the base plus the 3D enhancement layer.
In [14] authors show that the HEVC intra compression in the object
plane outperforms encoding in the hologram plane commonly used in
the state of the art [8,13,31]. Moreover, in [42] authors verify that
the increase of adding the amplitude to the real imaginary coding on
5
M.V. Bernardo, E. Fonseca, A.M.G. Pinheiro et al.
Signal Processing: Image Communication 96 (2021) 116306
Fig. 6. The bitrate/PSNR and bitrate/VIFp relations of A and COF for Horse hologram from EmergImg-HoloGrail-v1.
Fig. 7. The bitrate/PSNR and bitrate/VIFp relations of A and COF for Astronaut hologram from EmergImg-HoloGrail-v2.
Table 2
Bjontegaard metric for experimental holograms coded with HEVC. Average coding
efficiency with SR over without SR.
A
H orse
King
Cube
Car2575
Astronaut
Dice1
Dice2
Skull
to obtain the Bjontegaard metrics for A and the COF. The obtained BDPSNR and the BD-Rate are presented in Table 3. As already verified in
previous works, there is an important gain of coding in the object plane
comparing with a similar coding in the hologram plane. This gain is still
observed although it includes in the proposed work the growth on bit
rate caused by the layered coding scheme.
COF
BD-PSNR [dB]
BD-Rate [%]
BD-PSNR [dB]
BD-Rate [%]
19.75
31.51
24.93
11.94
28.77
28.45
26.57
29.25
−90.18
−98.00
−98.26
−90.96
−99.36
−99.62
−99.19
−99.18
2.90
0.56
0.09
3.31
0.93
1.02
2.04
0.55
−23.96
−10.30
−9.31
−27.85
−10.38
−11.48
−12.70
−0.03
5. Conclusions
In the present work, speckle noise reduction of experimentally
acquired holograms was used to improve the coding efficiency of a
hologram compression scheme. The analysis aims at contributing to
fulfilling a gap that has been noticed by several authors concerning the
characterization of the effects of speckle noise, as well as of methods
of speckle denoising, on the efficiency of digital hologram compression
methods. In digital holography, a related discussion on the advantages
of the compression in the object plane, as compared to compression
in the hologram plane, can also benefit from the analysis presented
herein. The suppression of speckle noise is usually applied to hologram
reconstructions, which is particularly tailored to a compression scheme
performed in the object plane, such as the one proposed in this work.
Standard image and video codecs are inappropriate for the coding
of holograms on hologram plane. However, they demonstrated good
compression capabilities when applied to the object plane, mainly
for computer generated holograms where the gain on BD-rate is of
the order of 50% when compared with the application of the same
codec to hologram. For experimentally acquired holograms, the direct
application of the standard image and video codecs the gain is less
than 10%, and this difference in coding efficiency is partially explained
by the fact that computer generated holograms are less affected by
speckle noise that is a characteristic of experimental holograms. The
proposed coding scheme yields an amplitude gain higher than 90%
when compared with a similar scheme without speckle removal. The
results presented in this work show that standard image and video
codecs also demonstrate good compression capabilities when applied
to the object plane for experimentally acquired holograms if they are
combined with speckle filtering of 2D version of the object. Moreover,
with the proposed scheme, the base layer provides a denoised direct
2D representation of the hologram, suitable for conventional displays.
Table 3
Bjontegaard metric for experimental holograms coded with HEVC. Average coding
efficiency with proposed method over method proposed in [13].
A
H orse
King
Cube
Car2575
Astronaut
Dice1
Dice2
Skull
COF
BD-PSNR [dB]
BD-Rate [%]
BD-PSNR [dB]
BD-Rate [%]
47.32
44.70
42.99
42.36
65.26
57.45
62.55
60.79
−97.37
−99.51
−99.54
−98.16
−99.82
−99.87
−99.76
−99.76
6.55
1.68
0.25
6.00
2.13
1.39
0.36
0.16
−41.36
−18.49
−18.86
−57.43
−31.37
−26.56
−7.91
−10.60
layer allows using a standard codec to decode a 2D version. The BDPSNR and BD-Rate for the COF compare the coding efficiency when
considering that all the base and enhancement layers were decoded. Improved compression performance can be observed for the bitrate/PSNR
relations of the proposed scheme. Fig. 8 shows an example where the
compression distortions can be observed. For that two cropped areas of
the Astronaut hologram are shown, coded with the HEVC quantization
parameter 𝑞 = 40 and 𝑞 = 30, and also the original. The compression
distortions are more visible without speckle reduction, although the bit
rate is much higher than the bit rate obtained with speckle reduction.
We also compared the proposed method with the proposed by
Peixeiro et al. [13]. For that, we adapt the method presented in [13]
6
M.V. Bernardo, E. Fonseca, A.M.G. Pinheiro et al.
Signal Processing: Image Communication 96 (2021) 116306
Fig. 8. Compression distortion example of the Astronaut hologram with cropped areas signalized. (a) Original. From (b) to (d) signalized cropped areas without speckle reduction.
From (e) to (g) with speckle reduction respectively for the reference, and coded with quantization parameter 𝑞 = 30 and 𝑞 = 40 (d).
Declaration of competing interest
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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Acknowledgments
This research was funded by the Portuguese FCT-Fundação para
a Ciência e Tecnologia and co-funded by FEDER–PT2020 partnership
agreement under the project PTDC/EEI-PRO/2849/ 2014 - POCI-010145-FEDER-016693, under the project UIDB/EEA/50008/2020, PLive
X-0017-LX-20, and by operation Centro-01-0145-FEDER-000019 - C4
- Centro de Competências em Cloud Computing, cofinanced by the
European Regional Development Fund (ERDF) through the Programa
Operacional Regional do Centro (Centro 2020), in the scope of the
Sistema de Apoio à Investigação Científica e Tecnológica - Programas
Integrados de IC&DT.
The authors are very grateful for the support given by Fiber Materials and Environmental Technologies (FibEnTech-UBI) on the extent of
the project reference UIDB/00195/2020, funded by the Fundação para
a Ciência e a Tecnologia (FCT).
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8