On the noise-resolution duality, Heisenberg uncertainty and Shannon's information

Several variations of the Heisenberg uncertainty inequality are derived on the basis of "noise-resolution duality" recently proposed by the authors. The same approach leads to a related inequality that provides an upper limit for the information capacity of imaging systems in terms of the number of imaging quanta (particles) used in the experiment. These results can be useful in the context of biomedical imaging constrained by the radiation dose delivered to the sample, or in imaging (e.g. astronomical) problems under "low light" conditions

On the efficiency of computational imaging with structured illumination

A generic computational imaging setup is considered which assumes sequential illumination of a semi-transparent object by an arbitrary set of structured illumination patterns. For each incident illumination pattern, all transmitted light is collected by a photon-counting bucket (single-pixel) detector. The transmission coefficients measured in this way are then used to reconstruct the spatial distribution of the object's projected transmission. It is demonstrated that the squared spatial resolution of such a setup is usually equal to the ratio of the image area to the number of linearly independent illumination patterns. If the noise in the measured transmission coefficients is dominated by photon shot noise, then the ratio of the spatially-averaged squared mean signal to the spatially-averaged noise variance in the "flat" distribution reconstructed in the absence of the object, is equal to the average number of registered photons when the illumination patterns are orthogonal. The signal-to-noise ratio in a reconstructed transmission distribution is always lower in the case of non-orthogonal illumination patterns due to spatial correlations in the measured data. Examples of imaging methods relevant to the presented analysis include conventional imaging with a pixelated detector, computational ghost imaging, compressive sensing, super-resolution imaging and computed tomography.Comment: Minor corrections and clarifications compared to the original versio

CT dose reduction factors in the thousands using X-ray phase contrast

Phase-contrast X-ray imaging can improve the visibility of weakly absorbing objects (e.g. soft tissues) by an order of magnitude or more compared to conventional radiographs. Previously, it has been shown that combining phase retrieval with computed tomography (CT) can increase the signal-to-noise ratio (SNR) by up to two orders of magnitude over conventional CT at the same radiation dose, without loss of image quality. Our experiments reveal that as radiation dose decreases, the relative improvement in SNR increases. We discovered this enhancement can be traded for a reduction in dose greater than the square of the gain in SNR. Upon reducing the dose 300 fold, the phase-retrieved SNR was still almost 10 times larger than the absorption contrast data. This reveals the potential for dose reduction factors in the tens of thousands without loss in image quality, which would have a profound impact on medical and industrial imaging applications

A general few-projection method for tomographic reconstruction of samples consisting of several distinct materials

We present a method for tomographic reconstruction of objects containing several distinct materials, which is capable of accurately reconstructing a sample from vastly fewer angular projections than required by conventional algorithms. The algorithm is more general than many previous discrete tomography methods, as: (i) a priori knowledge of the exact number of materials is not required; (ii) the linear attenuation coefficient of each constituent material may assume a small range of a priori unknown values. We present reconstructions from an experimental x-ray computed tomography scan of cortical bone acquired at the SPring-8 synchrotron

Phase-and-amplitude computer tomography

A tomographic technique is proposed for reconstruction under specified conditions of the three-dimensional distribution of complex refractive index in a sample from a single projection image per view angle, where the images display both absorption contrast and propagation-induced phase contrast. The algorithm achieves high numerical stability as a consequence of the complementary nature of the absorption and phase contrast transfer functions. The method is pertinent to biomedical imaging and nondestructive testing of samples exhibiting weak absorption contrast

Clinical application of low-dose phase contrast breast CT: methods for the optimization of the reconstruction workflow

Results are presented of a feasibility study of three-dimensional X-ray tomographic mammography utilising in-line phase contrast. Experiments were performed at SYRMEP beamline of Elettra synchrotron. A specially designed plastic phantom and a mastectomy sample containing a malignant lesion were used to study the reconstructed image quality as a function of different image processing operations. Detailed evaluation and optimization of image reconstruction workflows have been carried out using combinations of several advanced computed tomography algorithms with different pre-processing and post-processing steps. Special attention was paid to the effect of phase retrieval on the diagnostic value of the reconstructed images. A number of objective image quality indices have been applied for quantitative evaluation of the results, and these were compared with subjective assessments of the same images by three experienced radiologists and one pathologist. The outcomes of this study provide practical guidelines for the optimization of image processing workflows in synchrotron-based phase-contrast mammo-tomography