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In order to clustering data to reduce the noise, we can use the simple k-means clustering algorithm. The idea of k-means is quite simple. Here is the step of the k-means algorithm. 1. Randomly pick samples (depending on how many groups we want to cluster) as the references. 2. Compute the distance between each data point and references. 3. Comparing the distance to each reference, grouping the data points from the shortest distance. 4. Compute the centroid of each group as the new reference. 5. Repeat 2-4, until the centroids are the same with the previous result. Here is the Matlab code: ======================================= % An example for k-means clustering % % Renfong 2018/12/19 % % create test data % There are 3 types of sigal % 1-20, 36-70, 91-100 are the group 1 % 21-35 are group 2 % 71-90 are group 3 xx=0:1:1024; cen=[120, 360, 780]; amp=[100, 60, 55]; sig=[50, 10, 30]; % peak 1+3 for i=1:20     sp(i,:)=amp(1)*exp((-...

The difficulties limit the direct application to electron tomography The tilt range has to be from -90 degree to +90 degree The number of projections in a tilt series needs to be 2N for an N*N object The grid points past the resolution circle cannot be experimentally determined These limitations are overcome by combining the PPFFT with an iterative process. Ref: http://www.physics.ucla.edu/research/imaging/EST/index.html

Coherent Diffractive Imaging [1] Also known as lensless imaging , is based on the retrieval of a complex sample structure (phase) from a measurement of scattered radiation intensity from a coherently illuminated sample out of the imaging plane. [2] Coherent diffractive imaging (CDI) is an alternative technique that promises, in theory, to allow imaging of specimens at a resolution limited only by the wavelength of the illuminating radiation. CDI replaces the imaging optics and their associated imperfections, with a solution to an inverse problem (phase problem) . The inversion step involves determining the complex exit-surface wave function from the recorded intensity, which in the case of diffractive imaging is in the far field.  Reconstruction of the full complex exit wave recovers the amplitude and phase of the specimen transmission function, related to physical properties of the specimen. CDI involves a non-linear inverse problem and the consequent issue of the...