Renal Dynamic Image Compression using Singular Value Decomposition

Jagrati Chaudhary; Anil Kumar Pandey; Param Dev Sharma; Chetan Patel; Rakesh Kumar

doi:10.4103/ijnm.ijnm_59_22

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Original Article

37 (

); 343-349

doi:

10.4103/ijnm.ijnm_59_22

Renal Dynamic Image Compression using Singular Value Decomposition

Jagrati Chaudhary, Anil Kumar Pandey^,, Param Dev Sharma¹, Chetan Patel, Rakesh Kumar

Department of Nuclear Medicine, All India Institute of Medical Sciences, New Delhi, India

1Department of Computer Science, SGTB Khalsa College, University of Delhi, New Delhi, India

Address for correspondence: Dr. Anil Kumar Pandey, Department of Nuclear Medicine, New Delhi - 110 029, India. E-mail: akpandeyaiims@gmail.com

Received: 2022-03-29, Accepted: 2022-06-14, Published: 2022-12

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Disclaimer:
This article was originally published by Wolters Kluwer - Medknow and was migrated to Scientific Scholar after the change of Publisher.

Abstract

Aims and Objective:

The objective of this study was to evaluate the compression of renal dynamic (RD) study images using singular value decomposition (SVD) technique.

Materials and Methods:

4600 images of fifty RD study were compressed by using SVD technique. Two Nuclear Medicine (NM) Physicians compared compressed images with their corresponding input images and labeled these as acceptable or unacceptable. The SVD computation time and compression ratio were calculated for each image. The quality of compressed image was also assessed objectively using the following image quality metrics: Error, structural similarity (SSIM), Brightness, global contrast factor, contrast per pixel (CPP), and blur. The error in split function (i.e., the error between split function calculated from compressed image and split function calculated from original image) was computed for every RD study. Wilcoxon signed-rank test with continuity correction was applied to find a statistically significant difference in ROI counts on compressed and original image at.

Results:

As per NM physicians compressed image frames look identical to the original image frames. Objectively the compressed images were brighter, less noisy, and also have better CPP. Based on the visual assessment, time activity curve generated from original and compressed image frames was identical. There was insignificant difference of ROI counts between the input and compressed image frames of 99m-Tc LLEC RD Study. There was no significant difference between the split renal function estimated from original and its compressed RD study. The average SSIM value, average compression ratio, and SVD computation time were found to be 0.7521, 1.475, and 0.1200.

Conclusions:

Visually, compressed image was identical to the original image. The percentage compression achieved was found to be up to 58% (compression factor achieved = 1.57). The SVD computation time was approximately 0.12 s for 64 × 64 matrix size image frame.

Keywords

Image compression

renal dynamic study

singular value decomposition

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Introduction

The renal dynamic (RD) study using 99m-Tc LLEC/MAG3/DTPA is usually performed for the evaluation of nephron-urological conditions and renal allografts. RD study helps the nuclear medicine (NM) physicians to examine the blood flow through the kidneys (renal perfusion), uptake of radiopharmaceuticals in renal parenchyma (relative and absolute kidney functions), transport of radiopharmaceutical through the kidney, renal calyces, and pelvis into the ureters and urinary bladder (to rule out obstructions).[1] Out of these, the measurement of relative renal functions and upper outflow tract evaluation are the major contributions of radionuclide studies to the practice of nephron-urology.[2]

We need to store the RD study image data since follow-up study requires the comparison of the current study with the previous one. When data (RD study image data) is compressed, relatively large number of studies (compared to uncompressed RD study image data) can be stored on a storage device. There are two types of image compression schemes: lossless or lossy. In lossless compression schemes, there is no loss of data and thus original and compressed images are identical; however, there is only a little compression. Lossy compression schemes provide large compression, but the compressed image quality may be degraded. The criteria for acceptable compressed image quality depend on the type of task to be performed with the compressed images. In NM, specifically related to RD study image data, we intend to make the diagnosis by visually inspecting the compressed image, thus clinical details of the original image should be preserved in the compressed image (in other words, the compressed image should be identical to the original image). Besides this, we also quantify the split renal function, thus, the quantitative parameters derived from the compressed image and the original image should be equal or the difference between these should be within an acceptable limit.

There are several lossy image compression techniques that utilize various strategies to achieve higher compression. The motivation for using singular value decomposition (SVD) based image compression (a lossy image compression scheme) was the following: (1) the SVD is numerically stable and is an efficient method of extracting the patterns from the data, and (2) the technique is data driven in that patterns are discovered purely from data without the addition of expert knowledge or intuition. In fact, when NM Physicians review the images for diagnosis they look for patterns in the image data (which is retained and even it might become prominent in the compressed image).

In this study, we compressed RD study images using SVD and the quality of compressed images was compared with the corresponding original images both subjectively and objectively. The SVD computation time for every image and error between compressed image and original image were also calculated. Renal split function was calculated from both compressed image and original image. We report here the result of this investigation.

Materials and Methods

Singular value decomposition

99m-Tc LLEC RD study is a collection of a number of images frame acquired at different point times. Individual image frame is the image of spatial distribution of radiopharmaceutical present inside the human body at the time of acquisition of the image. Mathematically, this distribution can be described by a function I (x,y). We sample this function I (x,y) at the intersection points of a two-dimensional uniformly spaced grid such that (x, y) take on countable values (n Δ x, m Δ y) (for example: x and y ranges from 1 to 128, in case of 128 × 128 acquisition matrix). The sampled image is then quantized to a sufficiently finite number of brightness values (usually, 2¹⁶ = 65536 brightness values) to allow minimal quantization noise in the process, or quantized to 2⁸ = 256 brightness values so that image can be faithfully displayed on most commonly used display monitors. This later image is also called a gray scale image. The result of sampling and quantization is an array of positive numbers which we denote as matrix [I].

The matrix [I] can be represented in a space defined by orthogonal matrices [U] and [V] as

where [λ] is a diagonal matrix, whose entries are the singular values of [I], [U] is the row eigenvector system of [I] and [V] is the column eigenvector system of [I].[3] The expansion [I] of the matrix can be represented in vector outer product notation as

where u_i,v_i and λ_i respectively, are the column vectors of [U], [V], and diagonal terms of [λ]. The limit of the summation K represents the rank (number of nonzero singular values) of [I]. If [I] is nonsingular, K will equal N, the dimension of [I]. Thus, the value of K depends on the image (the distribution of recorded counts at each grid location (that is, a pixel); in case of 99m-Tc LLEC individual frame images, this distribution is usually different for different image frames).

The SVD of each image was computed using the SVD function with economy option,[4] and the computation time was recorded for each image. To determine the value of R (the optimum threshold for truncating smaller singular values), we used the algorithm developed by Gavish and Donoho, and during the process of finding optimum value of R, the error between the approximated and original image was calculated using the nuclear norm.[5] The compressed image was reconstructed with the remaining singular values after truncating the smaller singular values.

This retrospective study was approved by ethical committee of our institute (approval no: IECPG-711/25.11.2021). Fifty RD studies performed as a part of routine NM investigation were exported in DICOM format from NM image processing computer. The rest of the experiments were performed on a personal computer, on Windows 7 Home Basic 64-bit operating system, 2GB of random-accessed memory, and an Intel Core i3-2120 central processing unit with a 3.30-GHz processor.

Image acquisition protocol

These RD studies were acquired withdual head SPECT gamma camera (SymbiaE, Siemens Medical Solutions USA, Inc.) fitted with low-energy high-resolution collimator. Before administration of 99m-Tc LLEC, patients were instructed to drink at least 300–500 mL of water to be properly hydrated to ensure radiotracer clearance, avoiding any appearance of obstruction or decreased function, void their bladder before injection and, frequently void their bladder at the end of the study to reduce the radiation burden in the body. 111–185 MBq (3–5 mCi) 99m-Tc LLEC was administered with Lasix (F + 0 technique) intravenously on table and acquisition started ensuring that both the kidneys are in field of view. Scan was acquired in flow phase (taken total 32 frames [2 sec/frame], zoom 1.23 and resolution of 64 × 64 pixels) and in uptake phase (taken total 60 frames [15 sec/frame] at zoom 1.23 and resolution of 64 × 64 pixels).

Image processing protocol

We read and displayed the DICOM study using MATLAB's inbuilt function. The SVD of every frame of a RD study was computed using SVD function with economy option, and smaller singular values were truncated with respect to the threshold value obtained using Gavish and Donoho algorithm and with the remaining larger singular values, the compressed image was reconstructed.[5] The SVD computation time was recorded. The compression ratio was calculated using the equation:

The above shows, compression ratio will depend on choice of k. The percentage compression is calculated using the formula:

Frames of a study were inspected to select a frame in which the size of the kidneys was maximum. On the selected frame, irregular region of interest was drawn on the left and right kidney to create mask for the left and right kidneys. The mask was multiplied with each frame image (of original and compressed image data) to extract the counts from the left and right kidney and time activity curves (TAC) for left and right kidneys were generated. The split kidney functions were computed by summing the kidney counts of uptake phase of the TAC using the following equations:

The error in the split function of the RD study was calculated from compressed image and original image using the following equation:

Error in split kidney function =

Image quality assessment

Visual assessment

Two NM physicians visually compared the compressed images with the corresponding input images and labelled the compressed images as either acceptable or unacceptable. The compressed images which had loss of clinical details and presence of artifacts were considered as unacceptable.

Objective assessment

The quality of images was also assessed using structural similarity (SSIM) index,[6] Brightness (the mean value of image pixel value was considered as the measure of brightness of the image). The brightness was computed by taking the mean value of the original pixel value.), Global Contrast Factor (GCF),[7] Contrast per pixel (CPP)[8] and Blur[9] and the Error (the value of which was calculated by dividing the 2-norm of (original minus compressed image vector) with the 2-norm of the original image vector). The 2-normof a vector v with N element is defined as

The SSIM index is reference image quality metric. The quality of compressed image was measured taking original image as the reference image. Higher the value of SSIM better is the quality of compressed image. Brightness was estimated as mean intensity of the image which measures the perceived brightness of the image. GCF is the average local contrast of smaller image fractions. Higher GCF indicates more detailed and variation rich image. CPP is defined as the average of absolute difference of luminance value with the adjacent pixels. Higher the CPP value, more the CPP. Blur is the nonreference perceptual blur metric with values ranging from 0 to 1. A zero value of smoothness indicates no smoothing while 1 indicates heavy smoothing. Minimum the value of Error is, the compressed image is closer to the original image.

Statistical analysis

The Wilcoxon signed-rank test was used to find the significance of difference between renal split function, blur, GCF, CPP, and Brightness estimated from original image frame and compressed image frame of the RD study at level of significance, alpha = 0.05. For statistical analysis, open-source software R was used.

Results

On visual inspection, compressed image frames were found to be identical to the original image frames of the RD studies. Figure 1 shows the alternate image frames (total 45 image frames) of an original and the compressed study RD study (study had 92 frames, first two frames are dropped). Evidently, there is no appreciable difference in the compressed and original image frames (they look identical, Figure 1).

Left side: original image frames, right side: Compressed image frames. No loss of clinical detail is seen in the compressed image

TAC generated from original and its compressed image frames were also found to be identical (based on visual inspection, Figure 2).

Time activity curve generated from the original RD study (left side) and its compressed RD study (right side). RD: Renal dynamic

There was insignificant difference between the split renal function estimated from original and its compressed RD study [Table 1]. The boxplot of left and right kidney function is shown in Figure 3.

Table 1 Statistical analysis shows kidney functions calculated on original and compressed image

	Summary statistics						P
	I	II	III	IV	V	VI	P
Left kidney
Original	5.067	40.302	50.270	53.729	71.694	96.567	0.1058
Compressed	5.054	40.220	50.271	53.719	71.752	96.549	0.1058
Right kidney
Original	3.433	28.306	49.730	46.271	59.698	94.933	0.09182
Compressed	3.451	28.248	49.729	46.281	59.780	94.946	0.09182

I: Minimum, II: 1^st quartile, III: Median, IV: Mean, V: 3^rd quartile, VI: Maximum

Boxplot of Renal split function, Top left: Original left kidney, Top right: Compressed left kidney, Bottom left: original right kidney and, Bottom right: compressed right kidney

The summary statistics of SVD computation time, error between compressed image and original image, SSIM, compression ratio and percentage compression are shown in Table 2. Table 2 shows that up to 58% compression was achieved and the maximum error was equal to 0.07. The SVD computation time was approximately 0.12 s. The SSIM value of compressed image measured by considering the original image as the reference image was found to be between 0.63 and 0.79.

Table 2 Summary statistics of compression ratio, singular value decomposition computation time, percentage compression, error, and structural similarity

	Summary statistics
	Minimum	1^st quartile	Median	Mean	3^rd quartile	Maximum
Compression ratio	1.23	1.32	1.47	1.57	1.76	2.40
SVD computation time	0.12	0.12	0.12	0.12	0.14	0.15
Percentage compression	18.80	24.42	32.22	33.98	43.18	58.37
Error	0.005	0.007	0.021	0.027	0.042	0.079
SSIM	0.63	0.72	0.75	0.74	0.76	0.79

SSIM: Structural similarity, SVD: Singular value decomposition

Compressed images were significantly brighter compared to the input images at P < 0.001 (the median brightness of compressed images {14.167} is greater than the median brightness of the original images {12.732}: Table 3). Compressed images had significantly better CPP at P < 0.001 (the median CPP of compressed images [1.829] is greater than the median CPP of the original images {1.597}: Table 3). Compressed images were also found to be significantly less noisy at P < 0.001 (the median blur of compressed images [0.3622] is greater than the median blur of the original images [0.31749]: Table 3). However, there was insignificant difference in GCF of compressed and original image frames at P = 0.5018 (the median GCF of compressed images {2589.4} is slightly greater than the median GCF of the original images {2577.0}: Table 3).

Table 3 Statistical summary of blur, global contrast factor, contrast per pixel, and brightness for objective image quality assessment of compressed image and original image

	Summary statistics						P
	I	II	III	IV	V	VI	P
Blur
Original	0.01852	0.15877	0.31749	0.25687	0.32988	0.35127	<2.2e-16
Compressed	0.1013	0.2178	0.3622	0.3081	0.3752	0.3954	<2.2e-16
Global contrast factor
Original	363.9	2325.4	2577.0	2604.7	3002.5	3881.1	0.5018
Compressed	360.6	2343.7	2589.4	2600.9	3015.4	3906.0	0.5018
Contrast per pixel
Original	0.330	1.433	1.597	1.550	1.763	2.223	<2.2e-16
Compressed	1.315	1.590	1.829	2.058	2.304	3.901	<2.2e-16
Brightness
Original	2.241	11.422	12.732	12.341	14.075	17.634	<2.2e-16
Compressed	8.618	12.462	14.167	15.597	17.534	27.875	<2.2e-16

I: Minimum, II: 1^st quartile, III: Median, IV: Mean, V: 3^rd quartile, VI: Maximum

Discussion

In this study, the image compression of 99m-Tc LLEC RD Study using SVD was investigated. The compressed image quality was assessed both subjectively and objectively. NM Physicians found the compressed image identical to the original image. There was no loss of clinical details in the compressed image. The SVD based image compression technique did not generate any artifacts in the compressed image. Objectively the compressed images were brighter, less noisy, and had better CPP. There was insignificant difference in the split renal function calculated from the compressed image and the corresponding original image. The percentage compression achieved was found to be up to 58% (i.e., CR = 1.57:1). The SVD computation took approximately 0.12 s for 64 × 64 matrix size image frame.

The SSIM index ranged between 0.63 and 0.79 which indicates significant loss of data. It is clear from the statistical analysis presented in Table 3, that following SVD blur increases and so does the CPP increase; signifying at one end reduction of low pixel values but also increase in local inhomogeneities. The apparent better performance of SVD in renal image data is due to suppression of low counts/statistical noise.

Very few researchers have worked on image compression of RD study, specifically using SVD compression. Several image compression techniques have been discussed in literature.[10] There is continuous research going on in this field to achieve higher and higher compression.[11]

David S Wack et al., have used complex SVD to reduce noise in Dynamic PET images and have also quantified the uptake value on the denoised image. The error between the uptake quantified on denoised image and original image was within approximately 5% and the error was greater in case of noisy image. In this study we have used real SVD on RD Study image frames instead.[12]

Merina S Rebelo, et al. have investigated the application of a lossy compression method using discrete cosine transforms (DCT) on cardiac NM images. They have applied the DCT compression algorithm (with the threshold 10, 20, 30, 40 and 50% of the mean energy) to the group of 23 normal heart sequence images. The ejection fraction was computed before and after compression. As a result, they found that images compressed with a threshold of up to 30% of the mean energy were considered reliable for visual inspection and no significant difference was found in the value of ejection fraction before and after compression.[13] Zhou et al. investigated the usefulness of JPEG2000 compression for NM image. In their study normal and abnormal static images were compressed using a JPEG2000 plug-in. For lossless algorithm, the compressing ratio (CR) was calculated. For lossy algorithm, images were visually analysed by NM physicians and ROC curves were generated.[14] Comparison between the original and the compressed images revealed no significant difference for 10:1 CR but significant difference for bigger CRs. They have concluded that lossless compression has little usefulness for NM image because of very low CR. When lossy compression is used, the diagnostic quality of static NM images is preserved at CRs 50: 1,40: 1, 30: 1,20: 1 up to 10: 1.

However, the SVD method compared poorly to the wavelet transform methods as in our study we got the compression ratio of 1.57:1.

The uniqueness of the study is the focus on image compression of only one kind of dynamic study performed in NM (99m-Tc LLEC RD Study) using SVD. The study had relatively large number of images (4600 image frames in 50 RD studies) on which the image compression scheme has been evaluated. The entire experiment was performed on personal computer in MATLAB programming environment and for statistical analysis open source software R was used.

A minor significance of this study is that this study demonstrates that image compression research can be performed on personal computer (cost-effective compared to vendor image processing computer). Usually, vendor's image processing computers are costly and also highly busy in routine clinical tasks at a facility. This study also points that by simply truncating the smaller singular values and then approximating the compressed image provides up to 58% compression and the compression is functionally near lossless (but lossy mathematically, since we discard same information to achieve compression).

The limitation of the SVD-based image compression technique is that amount of compression achieved is lesser than some other techniques. However, it may be possible to achieve more compression by using the pipelined application of certain schemes for image enhancement and compression in a way that loss is even lesser and compression is better. In future, an image compression pipeline, we would like to investigate for clinical acceptability by NM physician specifically for 99m-Tc LLEC RD study, might consists of (1) image denoizing using block matching 3D filter, (2) Application of dynamic stochastic resonance to improve count per pixels, (3) SVD compression scheme applied in this study, and (4) then reconstructing the compressed image using the higher bit planes of the image (image obtained from the application of SVD compression scheme applied in this study).

Conclusions

The 99m-Tc LLEC RD study compressed image frames obtained using SVD-based image compression scheme were found to be identical to the uncompressed original image frames on visual inspection. On objective assessment, the compressed image frames were less noisy and sharper compared to its original image. The split renal functions estimated from the compressed study were found to be approximately equal to the split functions estimated from original study and have insignificant difference at P < 0.001. The percentage compression factor achieved was up to 58%.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.

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