An Image Denoising Algorithm Based On Curvelet Transform

Aiming at the limitations of the wavelet transform in image denoising, this paper proposes a new image denoising algorithm based on curvelet transform mathematical method. In this paper, the feasibility of this method is proved by the experimental results. The experiment result shows that, using the proposed new algorithm can get high peak signal to noise ratio, visual effect is very good image

Satellite Image Denoising Using Discrete Cosine Transform

The process of adding and removing the noises to an image is said to be as Image denoising. The process can be used in many image applications. This paper presents a method of satellite image denoising scheme using a wavelet transform called as Discrete Cosine Transform (DCT). The noise that is added in this scheme is the salt and pepper noise. By using hard thresholding method in the noise image the co-ordinates of the image can be changed and the original image can be retrieved by removing the noise. This can be done by Inverse Discrete Cosine Transform (IDCT). The performance measures of the proposed system can be done by measuring the PRNR values of the denoised image

DENOISING OF HIGH RESOLUTION REMOTE SENSING DATA USING STATIONARY WAVELET TRANSFORM

An image is often corrupted by a noise in its acquisition and transmission. A high resolution remote sensing data will be seen more roughly if it is corrupted by a noise. Wavelet is one of the fascinating denoising manners that will be used to solve this problem. The main application of the Stationary Wavelet Transform (SWT) is denoising. The principle is the average of several denoised signals. Each of them is obtained by using the usual denoising scheme, but it is applied to the coefficients of a ε-decimated DWT. The stationary wavelet transform (SWT) is to make the wavelet decomposition time invariant. This improves the power of wavelet in the signal denoising. In this research, we apply the SWT method to preprocess the remote sensing data for removing the noise. The Worldview-1 satellite data is used in this research. The sensor resolution is 0.55 meters and Ground Sample Distance (GSD) at 20º off-nadir. The Area of Interest (AoI) is Monas, Jakarta and the acquisition of the data was done on March 13th, 2008. For the data analysis, the Worldview-1 satellite data is added by the noise. The result of this research is that the noise can be removed by SWT method. By using structural similarity index (SSIM), the quality of the denoised images by SWT, Wavelet Transform 2D and Wavelet Packet 2D are 0.2666, 0.1912, and 0.1927, respectively. Thus, the SWT provides a better performance in denoising the remote sensing data than Wavelet Packet 2 D and Wavelet 2D methods. Keyword: Denoising, Remote sensing data, Stationary wavelet transfor

Reduced Cycle Spinning Method for the Undecimated Wavelet Transform

[EN] The Undecimated Wavelet Transform is commonly used for signal processing due to its advantages over other wavelet techniques, but it is limited for some applications because of its computational cost. One of the methods utilized for the implementation of the Undecimated Wavelet Transform is the one known as Cycle Spinning. This paper introduces an alternative Cycle Spinning implementation method that divides the computational cost by a factor close to 2. This work develops the mathematical background of the proposed method, shows the block diagrams for its implementation and validates the method by applying it to the denoising of ultrasonic signals. The evaluation of the denoising results shows that the new method produces similar denoising qualities than other Cycle Spinning implementations, with a reduced computational cost.This research was funded by grants number PGC2018-09415-B-I00 (MCIU/AEI/FEDER, UE) and TEC2015-71932-REDT.Rodríguez-Hernández, MA. (2019). 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The discrete wavelet transform: wedding the a trous and Mallat algorithms. IEEE Transactions on Signal Processing, 40(10), 2464-2482. doi:10.1109/78.157290Li, M., & Ghosal, S. (2015). Fast Translation Invariant Multiscale Image Denoising. IEEE Transactions on Image Processing, 24(12), 4876-4887. doi:10.1109/tip.2015.2470601Hazarika, D., Nath, V. K., & Bhuyan, M. (2016). SAR Image Despeckling Based on a Mixture of Gaussian Distributions with Local Parameters and Multiscale Edge Detection in Lapped Transform Domain. Sensing and Imaging, 17(1). doi:10.1007/s11220-016-0141-8Sakhaee, E., & Entezari, A. (2017). Joint Inverse Problems for Signal Reconstruction via Dictionary Splitting. IEEE Signal Processing Letters, 24(8), 1203-1207. doi:10.1109/lsp.2017.2701815Ong, F., Uecker, M., Tariq, U., Hsiao, A., Alley, M. T., Vasanawala, S. S., & Lustig, M. (2014). Robust 4D flow denoising using divergence-free wavelet transform. 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Wavelet Cycle Spinning Denoising of NDE Ultrasonic Signals Using a Random Selection of Shifts. Journal of Nondestructive Evaluation, 34(1). doi:10.1007/s10921-014-0270-8Rodriguez-Hernandez, M. A., & Emeterio, J. L. S. (2015). Noise reduction using wavelet cycle spinning: analysis of useful periodicities in the z-transform domain. Signal, Image and Video Processing, 10(3), 519-526. doi:10.1007/s11760-015-0762-8Rodriguez-Hernandez, M. A. (2016). Shift selection influence in partial cycle spinning denoising of biomedical signals. Biomedical Signal Processing and Control, 26, 64-68. doi:10.1016/j.bspc.2015.12.002Beylkin, G., Coifman, R., & Rokhlin, V. (1991). Fast wavelet transforms and numerical algorithms I. Communications on Pure and Applied Mathematics, 44(2), 141-183. doi:10.1002/cpa.3160440202Beylkin, G. (1992). On the Representation of Operators in Bases of Compactly Supported Wavelets. SIAM Journal on Numerical Analysis, 29(6), 1716-1740. doi:10.1137/0729097Donoho, D. 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Using wavelet denoising and mathematical morphology in the segmentation technique applied to blood cells images

Accurate image segmentation is used in medical diagnosis since this technique is a noninvasive pre-processing step for biomedical treatment. In this work we present an efficient segmentation method for medical image analysis. In particular, with this method blood cells can be segmented. For that, we combine the wavelet transform with morphological operations. Moreover, the wavelet thresholding technique is used to eliminate the noise and prepare the image for suitable segmentation. In wavelet denoising we determine the best wavelet that shows a segmentation with the largest area in the cell. We study different wavelet families and we conclude that the wavelet db1 is the best and it can serve for posterior works on blood pathologies. The proposed method generates goods results when it is applied on several images. Finally, the proposed algorithm made in MatLab environment is verified for a selected blood cells.Boix García, M.; Cantó Colomina, B. (2013). Using wavelet denoising and mathematical morphology in the segmentation technique applied to blood cells images. Mathematical Biosciences and Engineering. 10(2):279-294. doi:10.3934/mbe.2013.10.279S27929410

Blind Curvelet based Denoising of Seismic Surveys in Coherent and Incoherent Noise Environments

The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a combination of the curvelet transform and a whitening filter along with procedure for noise variance estimation. The whitening filter is added to get the best performance of the curvelet transform under coherent and incoherent correlated noise cases, and furthermore, it simplifies the noise estimation method and makes it easy to use the standard threshold methodology without digging into the curvelet domain. The proposed method is tested on pseudo-synthetic data by adding noise to real noise-less data set of the Netherlands offshore F3 block and on the field data set from east Texas, USA, containing ground roll noise. Our experimental results show that the proposed algorithm can achieve the best results under all types of noises (incoherent or uncorrelated or random, and coherent noise)

Denoising the temperature data using wavelet transform

Wavelets transform are effectively used in data compression and denoising such as in signal and image compression and denoising. One of the advantages of wavelets method is there exist fast algorithm in order to use wavelet for various applications. In this paper we will apply Discrete Wavelet Transform (DWT) to denoise the temperature data using symlet 16 with 32 corresponding filters (low-pass and high-pass). We apply various thresholding approaches e.g., Heuristic SURE, SURE, Minimax and Fixed-Form method. We utilized temperature data in Kuala Lumpur from January 1948 until July 2010. We also discuss the advantages of wavelet as compared with Fast Fourier Transform (FFT). Several numerical results will be presented by using Matlab

The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a` trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement

Compressive Imaging via Approximate Message Passing with Image Denoising

We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and runtime. To pursue our objective, we propose compressive imaging algorithms that employ the approximate message passing (AMP) framework. AMP is an iterative signal reconstruction algorithm that performs scalar denoising at each iteration; in order for AMP to reconstruct the original input signal well, a good denoiser must be used. We apply two wavelet based image denoisers within AMP. The first denoiser is the "amplitude-scaleinvariant Bayes estimator" (ABE), and the second is an adaptive Wiener filter; we call our AMP based algorithms for compressive imaging AMP-ABE and AMP-Wiener. Numerical results show that both AMP-ABE and AMP-Wiener significantly improve over the state of the art in terms of runtime. In terms of reconstruction quality, AMP-Wiener offers lower mean square error (MSE) than existing compressive imaging algorithms. In contrast, AMP-ABE has higher MSE, because ABE does not denoise as well as the adaptive Wiener filter.Comment: 15 pages; 2 tables; 7 figures; to appear in IEEE Trans. Signal Proces