A Log-Exponential Shrinkage Technique for De-Noising of Ultrasound Images for Breast Cancer

doi:10.21203/rs.3.rs-803890/v1

Ultrasound in diagnostic imaging is well known for its safety and accessibility. But its efficiency for diagnosis is always limited by the presence of noise. So, in this study, a Log-Exponential shrinkage technique is presented for denoising of ultrasound images. A Combinational filter was designed for the removal of additive noise without losing any details. The speckle noise after homomorphic transformation follows Gaussian distribution and the conventional median estimator has very low accuracy for Gaussian distribution. The scale parameter calculated from the sub-band coefficients after homomorphic transformation was utilized to design the estimator. For shrinkage of wavelet coefficients, a multi-scale thresholding function was designed, with better flexibility. The proposed technique was tested for both medical and standard images. A significant improvement was observed in the estimation of speckle noise variance. For quantitative evaluation of the proposed technique with existing denoising methods, Mean Squared Error (MSE), Structural Similarity Index (SSIM), and Peak Signal to Noise Ratio (PSNR) were used. At the highest noise variance, the minimum improvement achieved by the proposed denoising technique in PSNR, SSIM, and MSE was 10.65%, 23.21%, and 30.46% respectively.

Biomedical Engineering

Ultrasound

Mean Squared Error (MSE)

SSIM

diagnostic

homomorphic transformation

Table 1 - Previous approaches to reduce speckle noise

Ref	First author surname	Description
[13]	Chen et al	A 3D Gabor transform was applied over image in iterative manner until the mean absolute error falls below a threshold
[7]	Zhou et al	Divided image into overlapping patches then applied an iterative filter for every patch until its match the optimum patch calculated using Bayesian nonlocal mean filter
[16]	Cheng et al	Suggested a versatile feature weighted system for estimation of the dense motion field from a sequence of ultrasound image. The neighbouring frames were registered and deformed to contest a frame of reference followed by averaging of frames for the final compound image
[17]	Randhawa et al	Proposed to a novel method to calculate the threshold and then applied soft thresholding for speckle denoising
[18]	Elyasi et al	Applied a homogeneity modified BayesShrink (HMBS) for a sub-band dependent threshold. Before applying thresholding operation, a mean filter was applied all over the image.
[19]	Andria et al	A multiscale thresholding operator was preferred to avoid impulsive distribution because of universal thresholding. Exponential function with fall degree of exponential was utilized as the thresholding operator
[20]	Rajalaxmi et al	Proposed a straight kernel entropy filtering a unique methodology to reduce speckle noise from ultrasound image, uses minimum and maximum intensity pixels for calculation of entropy and then apply combination of entropy and linear regression for pixel modification
[21]	Kaur et al	Proposed a modification in BayesShrink and in which threshold was better adaptive because it is sub-band data dependent.
[23]	Donoho et al	The VisuShrink also known as universal threshold is known to yield overly smoothed images due to its dependence on the number of samples
[22]	Donoho et al	Another method for threshold calculation was proposed by using generalized Gaussian distribution and called BayesShrink, procured by minimizing Bayesian risk
[14]	Donoho et al	SureShrink the threshold value is calculated by minimizing Stein’s Unbiased Risk Estimator (SURE) [28]
[15]	Perona et al	Proposed a diffusion filter which runs according to an edge stopping function to remove noise from image and at the same time preserves edges

Table 2 The estimated Noise variance value by both MAD [24] and the proposed estimator

Image	Breast ultrasound		Lena		Barbara		Liver ultrasound
Original	MAD	Proposed	MAD	Proposed	MAD	Proposed	MAD	Proposed
0.02	0.02	0.02	0.02	0.01	0.03	0.02	0.01	0.02
0.04	0.04	0.04	0.05	0.03	0.05	0.03	0.03	0.04
0.06	0.07	0.06	0.07	0.04	0.07	0.05	0.04	0.05
0.08	0.09	0.08	0.09	0.06	0.10	0.06	0.05	0.07
0.10	0.12	0.10	0.12	0.07	0.12	0.08	0.09	0.09
0.12	0.15	0.12	0.15	0.09	0.15	0.09	0.11	0.11
0.14	0.17	0.14	0.18	0.11	0.18	0.11	0.15	0.13
0.16	0.20	0.16	0.21	0.12	0.21	0.12	0.17	0.15
0.18	0.23	0.18	0.24	0.14	0.24	0.14	0.20	0.17
0.20	0.27	0.21	0.27	0.16	0.28	0.16	0.23	0.19
0.22	0.31	0.23	0.31	0.18	0.32	0.18	0.26	0.21
0.24	0.36	0.25	0.36	0.20	0.36	0.20	0.29	0.23
0.26	0.40	0.27	0.41	0.22	0.40	0.22	0.33	0.25
0.28	0.48	0.30	0.46	0.24	0.47	0.24	0.36	0.28
0.30	0.54	0.31	0.53	0.27	0.52	0.27	0.41	0.30

Table 3 Comparison table for PSNR value of different denoising techniques for breast ultrasound mages

Noise Variance	HMBS[18]	Exponential[19]	Normal[21]	Wiener[12]	Proposed
0.02	31.74	28.17	26.37	29.73	32.84
0.04	30.04	27.80	23.60	27.86	30.96
0.06	28.84	27.84	22.03	26.47	30.09
0.08	27.93	27.46	21.01	25.46	29.48
0.10	27.12	26.79	20.31	24.61	28.86
0.12	26.57	26.22	19.72	23.96	28.46
0.14	25.95	25.46	19.33	23.36	27.94
0.16	25.48	24.92	18.95	22.92	27.61
0.18	25.06	24.20	18.83	22.47	27.20
0.20	24.59	23.42	18.52	22.08	26.82
0.22	24.28	22.84	18.41	21.72	26.54
0.24	23.93	22.20	18.35	21.41	26.25
0.26	23.70	21.59	18.25	21.17	26.12
0.28	23.33	20.84	18.05	20.83	25.72
0.30	23.09	20.33	18.18	20.67	25.55

Table 4: Comparison table for SSIM value of different techniques for breast ultrasound mages

Noise Variance	HMBS[18]	Exponential[19]	Normal[21]	Wiener[12]	Proposed
0.02	0.88	0.78	0.72	0.89	0.91
0.04	0.84	0.77	0.61	0.75	0.86
0.06	0.80	0.78	0.54	0.71	0.84
0.08	0.77	0.76	0.49	0.69	0.83
0.10	0.74	0.75	0.46	0.66	0.81
0.12	0.72	0.73	0.43	0.64	0.79
0.14	0.69	0.70	0.42	0.63	0.78
0.16	0.67	0.68	0.40	0.61	0.76
0.18	0.66	0.65	0.39	0.60	0.75
0.20	0.64	0.63	0.38	0.58	0.74
0.22	0.62	0.60	0.37	0.57	0.73
0.24	0.61	0.58	0.37	0.56	0.72
0.26	0.59	0.55	0.37	0.55	0.72
0.28	0.58	0.52	0.36	0.54	0.70
0.30	0.56	0.50	0.37	0.53	0.69

Table 5: Comparison table for MSE value of different techniques for breast ultrasound mages

Noise Variance	HMBS[18]	Exponential[19]	Normal[21]	Wiener[12]	Proposed
0.02	43.60	99.03	149.88	69.12	39.89
0.04	64.50	107.81	283.55	106.50	53.51
0.06	84.88	106.87	407.33	146.42	66.99
0.08	104.77	116.68	514.75	184.88	79.10
0.10	126.15	136.15	605.17	224.77	93.65
0.12	143.34	155.10	693.37	261.40	104.58
0.14	165.27	184.77	758.57	299.97	119.48
0.16	184.19	209.51	829.00	331.84	131.51
0.18	202.99	247.03	851.00	368.39	144.31
0.20	226.19	295.69	914.93	402.48	159.39
0.22	242.58	337.78	937.34	437.53	171.88
0.24	263.10	391.93	949.76	470.09	185.25
0.26	277.47	451.23	972.40	496.53	193.35
0.28	301.83	536.34	1018.33	537.01	210.64
0.30	319.13	603.27	987.74	557.45	221.91

Table 6: Percentage improvement in performance at higher noise variance (0.3) by the proposed method

Parameters	HMBS[18]	Exponential[19]	Normal[21]	Wiener[12]	MAD[24]
PSNR	10.65	25.71	40.51	23.61	-
SSIM	23.21	38.23	86.5	30.1	-
MSE	30.46	63.21	77.5	60.19	-
Estimation error	-	-	-	-	95.8

A Log-Exponential Shrinkage Technique for De-Noising of Ultrasound Images for Breast Cancer

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