Spatial bandwidth-optimized compression of image plane oﬀ-axis holograms with image and video codecs – unoﬃcial supplement

This document contains the unoﬃcial supplementary materials for the paper “Spatial bandwidth-optimized compression of image plane oﬀ-axis holograms with image and video codecs”.

• For lossy compression, plots showing distortion in function of achieved bitrate. Distortion is given in terms of complex wavefield SNR and unwrapped phase RMSE. SNR performance is summarized with the BD-SNR metric.
• In Supplement E, the summary of SNR distortion plots with the BD-SNR metric.
• In Supplement F, the summary of the RMSE distortion plots by providing the bitrate achieved for the target distortion level. The target unwrapped phase distortion is RMSE = 0.05 rad.
• In Supplement G, the bitrates achieved in lossless compression schemes, both static and video-like.

Supplement A Codecs description
PNG PNG [1] was introduced as an improved and patent-free replacement for the GIF standard and is one of the most widely used lossless image compression standard in the world. The compression consists of a prediction step, which predicts the current pixel based on the neighbouring pixels, and an entropy coding step which encodes the prediction residual using the DEFLATE algorithm.
JPEG JPEG [2] is the most widely used format by digital cameras and other image capturing devices as well as the most popular image standard used on the World Wide Web. At the heart of the JPEG standard is the discrete cosine transform applied on spatial blocks of size 8 × 8, followed by entropy coding using either arithmetic or Huffman coding.

JPEG LS
JPEG LS [3] is an image codec introduced for lossless/near lossless compression of continous tone images, and is designed to be implemented with low complexity hardware while offering state of the art lossless compression performance. Unlike transform based codecs, the LOCO-I algorithm (introduced in 1996) used in JPEG LS utilizes a context based model to predict pixels based on previously encountered pixels. The prediction residuals are encoded using Golomb coding.

JPEG 2000
JPEG 2000 [4], introduced as the successor of JPEG, provides several improvements over the older standard. Fundamentally, JPEG 2000 encoding comprises of a discrete wavelet transform stage suitable for natural images and a two-tiered embedded block coding by optimized truncation (EBCOT) stage for compressing the wavelet coefficients.

JPEG DAPD
JPEG DAPD (JPEG 2000 with Directional Wavelet and Full Packet Decomposition) [5] is an extension to JPEG 2000 designed for holographic data while retaining the rich feature set of JPEG 2000. It allows for truly arbitrary packet decomposition suited for holographic data where information resides in higher frequency sub-bands. The directional wavelet transform can locally adapt the direction of wavelet transform so that the strongly oriented fringes in the off-axis hologram can be efficiently captured.

JPEG XS
JPEG XS [6] is a lightweight low latency image compression standard intended for visually lossless compression and designed to be efficiently implemented on a variety of platforms like FPGAs, ASICs, CPUs and GPUs. It is a wavelet based codec, which is designed with low latency in mind.

H.264/AVC
Advanced Video Coding (AVC) [7] is one of the most widely used standards for storage and broadcast of video content. The input frame to be compressed is initially divided into macroblocks, where the encoder will try to predict the macroblocks using either intra mode, which means that consecutive frames are compressed separately, or inter mode which exploits also the redundancy between consecutive frames using motion estimation and compensation techniques.

H.265/HEVC
High Efficiency Video Coding (HEVC) [8] was introduced in 2013 as the successor to AVC and can produce files that are up to half the size of AVC, but with the same visual quality. HEVC uses coding tree units that can offer larger degrees of freedom when compared to AVC, as well as refinements in intra/inter prediction.

Supplement B Compression function calls with specified parameters
The common inputs used in the compression function calls are given below • <input>-Array containing image to be written • <inputfile>-Location of the input file containing image • <outputfile>-Location of the output file to be written imwrite(<input>,'<outputfile>','jpg','Quality',<sclr>) Parameter <sclr> is used for rate control in lossy compression is a scalar value between 0 and 100 representing the quality of the output file. 0 represents lowest quality and maximal compression while 100 represents highest quality and minimal compression.

JPEG LS
The libjpeg codec, available via official repository is used for JPEG LS. For lossless compression jpeg -ls 0 -c <inputfile> <outputfile> <err> is used for rate control in lossy compression and represents the maximal allowed integer absolute valued error for a pixel jpeg -ls 0 -m <err> -c <inputfile> <outputfile>

JPEG DAPD
JPEG DAPD [5] requires the executable file that will be disclosed upon contact with the author, Dr. David Blinder (dblinder@etrovub.be).

Supplement F Bitrate performance of lossy compression
The following tables present acheived bitrate for the target distortion of unwrapped phase (0.05 rad RMSE).