The images usually bring different kinds of noise in the process of receiving, coding and transmission. In this paper the Curvelet transform is used for de-noising of image. Two digital implementations of the Curvelet transform (a multiscale transform) viz the Unequally Spaced Fast Fourier Transform (USFFT) and the Wrapping Algorithm are used to de-noise images degraded by different types of noises such as Random, Gaussian, Salt and Pepper, Speckle and Poisson noise. This paper aims at the effect the Curvelet transform has in Curvelet shrinkage assuming different types of noise models. A signal to noise ratio as a measure of the quality of de-noising was preferred. The experimental results show that the conventional Curvelet shrinkage approach fails to remove Poisson noise in medical images.

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This paper introduces a novel approach for accomplishing Poisson noise removal in biomedical images by multiresolution representation. Methods of denoising are described based on three classical methods: (1) Fast Discrete Curvelet Transform (FDCT) with simple soft thresholding, (2) Variance Stabilizing Transform (VST) combined with FDCT where hypothesis tests are made to detect the significant coefficients and (3) The proposed method where the FDCT is integrated with Rudin–Osher–Fatemi (ROF) model. Much of the literature has focused on developing algorithms for the removal of Gaussian noise where the estimation is often done by finding a Curvelet and by thresholding the noisy coefficients. However not much has been done to remove Poisson noise in biomedical images. But in most of the medical images, the recorded data are not modeled by Gaussian noise but is the realization of Poisson process. Hence, in this work, FDCT integrated with ROF model based on VST is proposed. The VST is applied so that the transformed data are homoscedastic and Gaussian. A classical hypothesis testing framework is used to detect the significant coefficients and an iterative scheme is used to reconstruct the final estimate. A central difference total variation term in the discrete ROF model is used. The model is experimented on a large number of clinical images like Computed Tomography (CT) images, X-Ray images, Positron Emission Tomography (PET) images and Single Photon Emission Computed Tomography (SPECT) images and the performances are evaluated in terms of Peak Signal to Noise Ratio (PSNR) and the Universal Quality Index (UQI). The results are compared with those obtained by the other two existing algorithms proposed in the literature. Numerical results show that the proposed algorithm obtains higher PSNR and UQI than the other two methods.

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