Fig. 1. PC-bzip2 framework for high-speed lossless LFM data compression. (a) Schematic of the light-field microscopy system and LFM data structure. (b) Schematic of the predictors based on spatial continuity, angular continuity, and 4D phase-space continuity. (c) A complete framework including PC-bzip2 compression and decompression process. The compression pipeline consists of prediction part, 2D image entropy criterion, multicore CPU accelerated bzip2 coding, and packing header information and coded data. The decompression pipeline consists of unpacking header information, multicore CPU-accelerated bzip2 decoding, and inverse prediction.

Fig. 2. Main functions used in this work for LFM data compression. (a) Schematic of LFM data structure. S1, S2, S3, and X are adjacent in the spatial plane; A1, A2, A3, and X are adjacent in the angular plane. (b) The functions used in the predictors. The first four are common prediction functions in JPEG based on adjacent pixel information and the last one is to map all predicted values to a positive interval. (c) Lossless predictors for X based on the schematic in (a). Phase-space function means to use 4D phase-space continuity to predict X, angle function means that only angle continuity is used to predict X, and space function means using spatial continuity alone to predict X.

Fig. 3. The schematic of the 2D image entropy calculation. In BWT transformation, the realigned 16-bit image sequence is regarded as an 8-bit image sequence by splitting each 16-bit value into high and low 8 bits. After BWT transformation, every two adjacent 8 bits will be formed into 16 bits for histogram statistics.

Fig. 4. Comparing different compression ratios on images of different specimens with different SNRs. (a) Two groups of samples are captured at different exposure time (the change of the exposure time results in different SNRs on images). The beads images are obtained by imaging green fluorescent beads with the LFM, and MCF-10A images are obtained by imaging MCF-10A cells with the LFM. The image in the lower-right corner is a close-up marked by the yellow box. (b) The performance comparison on MCF-10A images with different predictors. The automatic criterion can accurately choose (A+B)/2 as the optimal predictor method and find the optimal compression ratio as well. Compared with the compression ratio without the prediction, the maximum improvement is up to 0.77 bits/dim. (c) The performance comparison on beads images with different predictors. The predictor did not improve the compression ratio but the automatic criterion could always locate the best compression ratio. (d) The performance comparison of angle prediction (ac-bzip2), space prediction (sc-bzip2), and phase-space prediction (PC-bzip2) on MCF-10A images. Obviously, the phase-space prediction works best. (e) The performance comparison of KLB and PC-bzip2 in compression time, decompression time, and compress ratio, respectively, on MCF-10A images. The location of the rectangle corresponds to the compression ratio, its size corresponds to the sum of compression and decompression time (as indicated by the numbers next to it), the light color corresponds to the compression time, and the dark color corresponds to the decompression time.

Fig. 5. Compression performance by extending PC-bzip2 to the time dimension. (a) Two sets of 20-frame videos are obtained by imaging larval zebrafish with different laser powers using the LFM [Fig. 1(a)]. The low excitation power is 3.2mWmm−2 (488 nm) and the high excitation power is 16.1mWmm−2 (488 nm). The image in the lower-right corner is a close-up marked by the yellow box. (b) Comparing the compression ratios on the video shown in (a) using angle prediction (ac-bzip2), space prediction (sc-bzip2), phase-space prediction (PC-bzip2), and, respectively, adding time dimension prediction to them (ac-bzip2+time, sc-bzip2+time, and PC-bzip2+time). (c) Comparing the compression ratios of KLB, PC-bzip2, and PC-bizp2 with temporal extension (PC-bzip2+time).

Fig. 6. Comparison of PC-bzip2 compression performance on image data and time series image data. (a) Comparison of lossy compression and lossless compression on biomedical image data captured by light-field microscope. The left column shows the decompressed larval zebrafish image by B3D lossy compression, and the right column shows the decompressed larval zebrafish image by PC-bzip2 lossless compression. The upper right corner shows the magnified areas marked by the yellow box, and the gray-scale histogram of the areas marked by the yellow box is shown below. (b) Comparison of PC-bzip2 decompressed results and PC-bzip2 compression input image of MCF-10A cells image data with an exposure time of 1024 ms. The left column shows the PC-bzip2 compression input image and its gray-scale histogram. The right column shows the PC-bzip2 decompressed image and its gray-scale histogram. (c) and (d) The performance of PC-bzip2 extended to the time dimension, where the images are randomly selected from the time series. (c) A larval zebrafish image with laser power of 16.1mWmm−2 (488 nm). (d) A larval zebrafish image with laser power of 3.2mWmm−2 (488 nm). The left column of each part is the PC-bzip2 compression input images and their gray-scale histogram. The right column of each part is the PC-bzip2 decompressed image and its gray-scale histogram.