![]() We first retrieve the input image from our folder using the uigetfile function and read it using the imread function. The denoised image is obtained when IFDCT is performed on these thresholded coefficients. It then analyzes the threshold for the detailed coefficients. This scheme takes the noisy images as the input, performs FDCT to obtain the approximation coefficients cA and detailed coefficients cD. ![]() The image below shows the approximated coefficients:īelow is the curvelet-based denoising scheme: This is how Curvelets are efficient in capturing coefficients along the curvature. ![]() They kept changing since the number of edges was 16. The white colors are the Curvelet coefficients of scale 2 at different orientations. The square coefficients are then displayed using the imshow function one by one: These extracted coefficients are resized to a square dimension of 512 using the imresize function. The detailed coefficient at the second decomposition level is extracted using the varying k. K is the number of edges, ranging from 1-16. LEVEL is a positive integer less than or equal to floor (log2 (min ( M N))), where M and N are the row and column sizes of the image. IMDEN wdenoise2 (IM,LEVEL) denoises the image IM down to resolution level LEVEL. %Showing all the detailed coefficients at scale 2. To denoise an RGB image in the original color space, use the ColorSpace name-value pair. This curvelet transform is usually expressed in the frequency domain, as shown below: $\varphi$: Is the Curvelet function.į: This is the input image with a size of MxN. $k_1$ and $k_2$: They are the spatial location of the Curvelet. It is because the Curvelet is arranged in the spatial domain. $\theta$: This is the Curvelet orientation. For example, if j is 3, we have three levels of decomposition of the image using a Curvelet. In general, Discrete Curvelet transform can be expressed as follows:Ĭ: is the Curvelet coefficients which are the function of j, $\theta, k_1$, and $k_2$. Wrapping-based FDCT is faster than USFFT, which makes it widely used. Unequally spaced Fast Fourier transform(USFFT). This newly implemented version, also known as Fast discrete curvelet transform (FDCT), is implemented in two ways: Later, a fast and less redundant Curvelet transform version was introduced. It is highly redundant, thus giving a poor output.It is not optimal for sparse approximation of curve features beyond C-square singularity.However, this generation suffered two main drawbacks: It is also efficient in representing curve-like edges. The 2nd generation Curvelet transform is an efficient tool in numerous applications including image processing, seismic data exploration, fluid mechanics, and solving partial differential equations. In 2000, they introduced 1st and 2nd generation Curvelet transform, called Ridgelet transform-based Curvelet transform. It was regarded as an anisotropic geometric wavelet transform. Ridgelet transform was proposed by Candes and Donoho in 1999. ![]() However, it is difficult to design complex wavelets with perfect reconstruction properties and filter characteristics. The complex transform is one way to improve directional selectivity. Wavelets are effective in capturing coefficients along the horizontal, vertical, and diagonal axes but poor in determining coefficients along the curvature. A huge disadvantage of wavelets is that they are not directional. Theoretical background of Curvelet transformĬurvelet transform is a geometric scale transform, used to represent edges and curves more efficiently than traditional wavelets. A clear understanding of Matlab basics.Theoretical background of Curvelet transform.We will also discuss the application of the Curvelet toolbox. This tutorial will look into the Curvelet transform analysis and denoising of images using Matlab. This is the removal of noise signals in an image. It is useful when it comes to feature extraction and pattern recognition.Ĭurvelet transform is also efficient in image denoising. It should be easy to port my Python script to MATLAB, though.Curvelet transform is a powerful tool that can capture details along the curvature in images. Magnitude_spectrum_no_vertical = 20*np.log(np.abs(fshift))įeel free to play around with different approaches: Applying a gaussian filter before FFT to improve the outcome, masking background and so on. horizontal lines) in the frequency domain # remove the high frequency signals (i.e. # smoothen the vertical lines in the spatial domain = Magnitude_spectrum = 20*np.log(np.abs(fshift)) There are tons of sources you can inform yourself about it, so I leave this part to you. The frequency domain can be used to smoothen particular noises (vertical lines in your case) in the spatial domain by removing the corresponding high frequency signals. This is a perfect use case for the Fast Fourier Transform (FFT).įFT converts an image in the spatial domain to its frequency domain.
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