Lecture 4: Denoising & Deconvolution Flashcards
Why do we need image restoration?
To recover an image that has been degraded by using a priori knowledge of the degradation
How does image restoration differ from image enhancement?
Image restoration is the operation of taking a corrupt/noisy image and estimating the clean original image. Corruption may come in many forms such us motion blur, noise and camera mis-focus.
The purpose of image enhancement is to improve the contrast and sharpening the image to enable for further processing and analysis. It is the purpose of adjusting digital images so that the results are more suitable for display or further image analysis.
Schematically sketch the image formation process including degradations
Degradation: f(x,y) -> Degratation function -> + -> Restoration filter(s) -> f-~(x,y)-> : Restoration.
Noise psi(x,y) to +
How to artificially distrupt an input image with a certain type of noise?
Convolved with the noise h(x,y). h(x,y) can be salt and pepper noise.
Name few type of noise models
- Gaussian noise model:
- z: mean value
- delta: standard deviation
- 68% of value reside wihtin a range of z+delta
- 95% of the value reside within of z + 2*delta. - Rayleigh noise model:
- delta^2: variance
- Displacement form the origin controlled by parameter alpha.
- Skewed appearence, suitable for modeling skewed histogram (non symmetric data distribution graphs).
- Used to characterize noise in range imaging. - Exponential noise model:
- Applicable in laser imaging application - Poisson or shot noise model:
- k = delta^2 = lambda: mean and variance
- Probability of measuring k photons when lambda photons are expected.
- Poisson noise is particularly useful for modeling stochastic processes like x-ray sources, electric charge or photon counting devices - Uniform noise model
- Salt and pepper noise model:
- > Model quick, defective pixels or faulty switching happening during the imaging.
Given a raw input image, what possibilites do you have to identify which noise model is most appropriate?
- Crop the region S of more or less constant intensity and compute the normalized histogram
- Estimate the variance and the mean value from the patches.
- Capturing a “flat” image may serve for the noise estimation.
How would you approximate the parameters of noise distribution
??
Can you explain how basic linear and non-linear filtering can be used for noise removal? when would you use a specific filter?
- Basic linear filtering:
At each pixel of the original image, the intenstiy values of the neighboring pixel are weighted with the filter kernel and summed to forrm a new pixel value in the output image.
example: Basic linear filtering algorithm (Mean filter)
-> The mean filter smooths local variations It reduces noise but at the same time causes blurring - Non-linear filtering:
a. Sort image intensities in a specified neighborhood in ascending order.
b. Extract statistical quantities like media, minimum or maximum from the sorted list.
c. Replace the original intensities value with the desired quantity.
Examples:
2.1 Median filter: Exhibit less blurring compared to linear filters and effectively removes salt & pepper noise.
2.2 Min and Max filter: Can be used to dilate and erode dark regions respectively
2.3 Midpoint filter: Uses the arithmetic mean of minimum and maximum (suited for gaussian or uniform random noise).
How do adaptive techniques work in general?
Adaptive filters try to alter the behaviour based on the statistical characteristic of the local neighborhood S_xy
They take the actual image characteristic into account
What is image deconvolution and what is it useful for microscopy images?
Deconvolution is used to enhance the contrast and resolution of digital image captured with the microscope. It tries to remove or reverse the blurring present in mircroscope images.
3D images which are stacked together out of 2D images, has the problem of the out of focus blurring from the other focal planes.
Can you explain how the convolution theorem can be employed for deconvolution?
In deconvolution, the reconstructed original object will be generated through the convolution of the Point Spread Function (SPF) and the input image.
Point Spread Function: Shape of an idealized point imaged trough the optical system.
What’s the problem with naive inverse filtering?
- Possible instability in regions where OTF values are close to or at zero.
Solution: Usage of sufficiently large frequencies. - Additive noise.
This could lead to amplification by inverse filtering, especially in regions where the signal is weak.
How does Wiener filter work?
Wiener filter solved the problem of unknown additive noise.
- The calculated filtered image is dependeing on the inverse of the SNR
- So if the noise increases at certain frequencies, the SNR decreases, the factor decreases. t´The filter attenuates the frequencyíes depending on their signal to noise ratio.
How about Lucy-Richardson and other iterative deconvolution algortihms?
The Iterative methods:
- Initialize estimate f0 (uniform image or observed image)
- Blurring with known PSF
- Compute error and the required correction
- Update the estimate and repeat 2-4 until convergence
Iterative methods are the Lucy Richardson and the VanCittert’s methods.
Lucy Richardson : Current image multiplied by the correlation of PSF and the degraded image divided
by PSF conv. current image.
VanCittert’s: Current image plus the degraded image subtracted by the convolution of PSF and
Current image.
What can be done if the PSF cannot be accurately determined?
Iterative scheme can also be extended to estimate the PSF along with the deconvolved
image, starting with initial guesses for both
