I do not think mine will be a complete answer, but I'll offer what I know and since this is a community edited site, I hope somebody will give a complimentary answer soon :)
Adaptive thresholding methods are those that do not use the same threshold throughout the whole image.
But, for some simpler usages, it is sometimes enough to just pick a threshold ...
You can find a paper containing a comparison of a number of thresholding methods here:
M. Sezgin, B. Sankur - Survey over image thresholding techniques and quantitative performance evaluation, Journal of Electronic Imaging, 2004 - pdf
Here's another paper evaluating binarization methods:
P. Stathis, E. Kavallieratou and N. Papamarkos - An Evaluation ...
Following on from the above excellent answer, here is how to do it in python using scikit funcitons.
from skimage.feature import hessian_matrix, hessian_matrix_eigvals
#assume you have an image img
hxx, hxy, hyy = hessian_matrix(img, sigma=3)
i1, i2 = hessian_matrix_eigvals(hxx, hxy, hyy)
#i2 is the variable you want.
#Visualise the result
I'm by no means an expert in this, but I find the subject of compressed sensing very interesting, so I thought it'd be fun to play around with this.
I believe your error is in the generation of your sampling matrix, $\Phi$. According to the paper you reference "The convergence of this algorithm was proven in  under the condition that $\|\Phi\|_2 < 1$ ....
This question has been answered very well from different perspectives, and I just want to summarize my experience and also emphasize some problems related to adaptive binarization.
Adaptive binarization can be divided into three categories:
1) Global method: with this method first of the background of the image is estimated; after that a normalized image ...
First, you'll probably have better luck posting this on dsp.stackexchange. That's a more specialized group that does stuff like this all the time.
In terms of your problem, here's a couple of options.
One is a machine learning approach. e.g. create a training set by taking a bunch of data and hand marking the points that are good versus bad (like you've ...
Low-pass filtering is based on the assumption that "natural" images have more energy in the low-frequency coefficients than in the high frequency coefficients ; while noise will affect equally all coefficients. Thus, removing the high frequency coefficients will comparatively eliminate more noise than signal. The problem is that there are "legit" high-...
Disclaimer: What I am about to say is a general rule of the thumb, there are exceptions.
In short: Linear space is more useful for computer vision while non-linear space is more useful for showing the final image to humans, without outputing a quantitative analysis.
This highly depends on your problem.
Linear space is more related to physical ...
Thresholding in the Fourier domain is an archaic method sometimes called spectral subtraction, used for background noise removal in speech. Bad results in image processing can be due to several factors:
Misinterpretation: you say "The Fourier denoising hard threshold method just uses threshold value to keep high frequency coefficients". Not quite. You keep "...
It seems your problem is that you don't have enough measurements ($n$ is too large) or, conversely, your sparsity level is too large ($k$ is too large).
I get the following results running your code with n=650 and k=50:
iter# = 0 MSE = 0.00812474693295
iter# = 1 MSE = 0.00271708140753
iter# = 2 MSE = 0.000356259110511
iter# = 3 MSE = 6.21904907643e-05
This topic has always attracted a lot of interest, and yet no real consensus exists on the topic. Therefore I decided to drop a few words.
My answers to previously asked similar questions on stackexchange (Q1 and Q2) involved a subpixel curvilinear structure extraction algorithm by Steger. This method performed reasonably well in many cases and luckily, ...
i'm avoiding labels light and dark because you could say that we choose 128 as threshold which perfectly separate light and dark pixels but consider you have a picture with only two gray levels which are 240 and 250 and you want to label them but both seems to be light.
now consider an example which you have a part of x-ray image which composed of soft ...
To summarize you have two distributions with unknown parameters and a measurement which may have originated from either stochastic process. This is typically referred to as a data association problem and it is very common, and widely studied, within the tracking community. You might consider using a Probability Data Association Filter (PDAF) or Multi-...
You can locate the local maxima for a given radius. For example, you scan the Hough image taking peaks as maxima only when they are maximal in a $3\times 3$ window.
The second step could be refining the peak position to sub-pixel accuracy. This can be done by parabola fitting.
Suppose the value in Hough image is $f(x)$ where $x$ is the 2D position. Now you ...
This code on the File Exchange will help you find all the local maxima.
If you have some knowledge about how many lines you want to find (in this case five), you simply select the five local maxima with the highest Hough scores.
Your question has received quite few contributions, probably because of a lacking content. During a recent conference , I came across the PhD thesis: Détection en Environnement non Gaussien (Detection in a non-Gaussian environment). Since it is in French, I reproduce the abstract here:
For a long time, radar echoes coming from the various returns of the
Circle hough transforms from the OpenCV library are well-suited for this application. You will have to run a number of radii but the best hough response will give you the pills' boundaries and centers. Note that you would have to use generalized hough transforms to find non-circular pills. It will work even if the pills have occluded or missing edge points.
If you want to use the thresholding approach, you should use an adaptive thresholding method if there are big lighting variations like in the 3rd example image (dsp question here).
Also, you should experiment with colorspaces, it's easy: the script to decompose the image into different colorspaces should be no more than a few lines long, and a lot of image ...
compute RMS from audio signal to get power
do AGC (automatic gain control)
perform "discrete differentiation" (the simplest is 1st order: $y[i] = x[i] - x[i-1]$)
if the value is greater than certain threshold, it means we have an onset. You have to determinate the threshold experimentally or use adaptive algorithm. Obviously you also need some kind of ...
Your question is broadly answered here: How to extract traffic signs from a photograph?
Your specific case is a little more complicated because the signs are not particularly distinguishing, however the same suggested techniques of cross correlating the images with clean images of original signs (you will probably want a library of images containing all ...
Otsu threshold assumes a bi-modal (e.g. two-class) histogram. Nobuyuki Otsu shows that in such a case, minimizing the within-class variance is the same as maximizing between-class variance. To separate the bi-modal histogram, that is actually what you need to do. It would correspond to maximizing the distance between the clusters, which would give you the ...
Some guidelines for using Thresholding:
Stretch the image to use the whole Dynamic Range (DR).
Apply some Denoising (Very very gentle).
Median with small radius would be a good idea.
Unless you hand tweak the Threshold, Otsu's Method generally yields good results for this kind of tasks (Text on background).
If one use Adaptive Local Methods (Mean / Gaussian ...
You added noise with Variance of 0.01 in the spatial domain.
Now you need to calculate what's the variance of the Noise per each bin in the DFT.
It's not the same, there are gains in the DFT domain, otherwise no one would use it.
By the way, there are much faster methods to apply "Hard Threshold" than the loop in your program. Use logical indexing to do it ...
If you calculate the standard deviation of the blocks (from the average) it could serve as a good measure to the smoothness of a block (assuming there is no an extraordinary value and the specific use of the "system")
A Matlab code and illustration is given below, with the discrete cosine transform (DCT):
nSample = 512;
pDataThreshold = 90/100 ; % percentage, as a float in [0 1]
time = linspace(0,1,nSample)';
data = sin(2*pi*4*sqrt(time));
dataTrans = dct(data);
dataThreshold = quantile(abs(dataTrans),pDataThreshold);
dataTransThreshold = dataTrans;
I think you could specify a higher DPI for higher 'resolution' (which effectively changes the pixel number of your image) in loading the data.
Resizing the data will usually cause small changes to your data that are usually irreversible (unless you know exactly the correct parameters for resizing).