Spatial Shift Invariance Research Articles

Different channels to transmit information in scattering media

A communication channel should be built to transmit information from one place to another. Imaging is 2 or higher dimensional information communication. Conventionally, an imaging channel comprises a lens with free space at its both sides, whose transfer function is usually known and hence the response of the imaging channel can be well defined. Replacing the lens with a thin scattering medium, the image can still be extracted from the detected optical field, suggesting that the scattering medium retains or reconstructs not only energy but also information transmission channels. Aided by deep learning, we find that unlike the lens system, there are different channels in a scattering medium: the same scattering medium can construct different channels to match the manners of source coding. Moreover, it is found that without a valid channel, the convolution law for a spatial shift-invariant system (the output is the convolution of the point spread function and the input object) is broken, and in this scenario, information cannot be transmitted onto the detection plane. Therefore, valid channels are essential to transmit information through even a spatial shift-invariant system. These findings may intrigue new adventures in imaging through scattering media and reevaluation of the known spatial shift-invariance in various areas.

Accelerating computed tomographic imaging spectrometer reconstruction using a parallel algorithm exploiting spatial shift-invariance

Computed tomographic imaging spectrometers capture hyperspectral images in realtime. However, postprocessing the imagery can require enormous computational resources; thus, limiting its application to nonrealtime scenarios. To overcome these challenges, we developed a highly parallelizable algorithm that exploits spatial shift-invariance. To demonstrate the versatility of our algorithm, we developed implementations on a desktop and an embedded graphics processing unit. To our knowledge, our results show the fastest image reconstruction times reported.

Physical picture of the optical memory effect

The optical memory effect is an interesting phenomenon that has attracted considerable attention in recent decades. Here, we present a new physical picture of the optical memory effect, in which the memory effect and the conventional spatial shift invariance are united. Based on this picture we depict the role of thickness, scattering times, and anisotropy factor and derive equations to calculate the ranges of the angular memory effect (AME) of different scattering components (ballistic light, singly scattered, doubly scattered, etc.), and hence a more accurate equation for the real AME ranges of volumetric turbid media. A conventional random phase mask model is modified according to the new picture. The self-consistency of the simulation model and its agreement with the experiment demonstrate the rationality of the model and the physical picture, which provide powerful tools for more sophisticated studies of the memory-effect-related phenomena and wavefront-sensitive techniques, such as wavefront shaping, optical phase conjugation, and optical trapping in/through scattering media.

The Nature of Single Round Hole Neutron Penumbral Imaging

The relationship and differences between pinhole imaging and penumbral imaging are explained and discussed in detail. A Monte Carlo (MC) model for a practical fusion neutron penumbral imaging system, which is expected to be used as one of the diagnostics of the nuclear facilities in China, was established. The source consists of many assumed discrete elements whose sizes equal the minimum resolution of the imaging system and that are identical to the point source in general concept. The point spread functions (PSFs) of two assumed discrete elements, located in the center and at the edge of a 200-μm field of view (FOV) in the neutron source face, were obtained for two cases, respectively: imaging in geometrical near-optics and the more real case of an MC numerical experiment. A series of PSFs of points in the diameter of FOV were obtained, and the PSF spatial shift invariance tolerances were tested within ~20 μm accuracy. Using mathematical analysis convolution and MC numerical experiments, “penumbral images” of a neutron source, which consists of just four discrete elements in 20-μm space, were obtained. Employing the same program, the two penumbral images were reconstructed, and the obtained original source images were basically the same. This allows the nature of encoding and decoding by the neutron penumbral imaging aperture prototype, which was designed by our work group, to be visualized and realized.

Parallel beamforming using synthetic transmit beams

Parallel beamforming is frequently used to increase the acquisition rate of medical ultrasound imaging. However, such imaging systems will not be spatially shift invariant due to significant variation across adjacent beams. This paper investigates a few methods of parallel beam-forming that aims at eliminating this flaw and restoring the shift invariance property. The beam-to-beam variations occur because the transmit and receive beams are not aligned. The underlying idea of the main method presented here is to generate additional synthetic transmit beams (STB) through interpolation of the received, unfocused signal at each array element prior to beamforming. Now each of the parallel receive beams can be aligned perfectly with a transmit beam--synthetic or real--thus eliminating the distortion caused by misalignment. The proposed method was compared to the other compensation methods through a simulation study based on the ultrasound simulation software Field II. The results have been verified with in vitro experiments. The simulations were done with parameters similar to a standard cardiac examination with two parallel receive beams and a transmit-line spacing corresponding to the Rayleigh criterion, wavelength times f-number (lambda x f#). From the results presented, it is clear that straightforward parallel beamforming reduces the spatial shift invariance property of an ultrasound imaging system. The proposed method of using synthetic transmit beams seems to restore this important property, enabling higher acquisition rates without loss of image quality.

From Bounded Families of Localized Cosines to Bi-Orthogonal Riesz Bases via Shift-Invariance

The notion of bi-inner product functionals\(P(f,g) = \sum\limits_n{ }\)generated by two Bessel sequences {fn} and {gn} of functions from L2was introduced in our earlier work as a vehicle to identify dual frames and bi-orthogonal Riesz bases of L2. The objective was to find conditions under which P is a constant mu of L2. A necessary and suffici condition derived in is that P is both spatial shift-invariant and phase shift-invariant. A<hough these two shift-invariance properties are, in general, unrelated, it could happen that one is a consequence of the other for certain clases of Bessel sequences {fn} and {gn}. In this paper, we show that, indeed, for localized cosines with two-overlapping windoes (i.e., only adjacent window functions are allowed to overlap), spatial shift-invariance of P is already sufficient to guarantee that P is a constant mu<iple of the inner product, while phase shift-invariance is not. Hence, phase shift-invariance of P for two-overlapping localized cosine Bessel sequences is a consequence of spatial shift-invariance, but the converse is not valid. As an application, we also show that two families of localized cosines with uniformly bounded and two-overlapping windows are bi-orthogonal Riesz bases of L2, if and only if P is spatial shift-invariant. In addition, we apply this resu< to generalize a resu< on characterization of dual localized cosine bases in our earlier work in to the mu<ivariate setting. A method for computing the dual windows is also given in this paper.

A true order recursive algorithm for two-dimensional mean squared error linear prediction and filtering

In this paper a novel algorithm is presented for the efficient two-dimensional (2-D), mean squared error (MSE), FIR filtering and system identification. Filter masks of general boundaries are allowed. Efficient order updating recursions are developed by exploiting the spatial shift invariance property of the 2-D data set. Single-step-order updating recursions are developed. During each iteration, the filter coefficients set is augmented by a single new element. The single-step-order updating formulas allow for the development of an efficient, true order recursive algorithm for the 2-D MSE linear prediction and filtering. In contrast to the existing column(row)wise 2-D recursive schemes based on the Levinson–Wiggins–Robinson multichannel algorithm, the proposed technique offers the greatest maneuverability in the 2-D index space in a computational efficient way. This flexibility can be taken into advantage if the shape of the 2-D mask is not a priori known and has to be dynamically configured. The recursive character of the algorithm allows for a continuous reshaping of the filter mask. Search for the optimal filter mask, essentially reconfigures the filter mask to achieve an optimal match. The optimum determination of the mask shape offers important advantages in 2-D system modeling, filtering and image restoration. An illustrative example from 2-D autoregressive spectrum estimation is also supplied.

Scale and the differential structure of images

Why and how one should study a scale-space is prescribed by the universal physical law of scale invariance, expressed by the so-called Pi-theorem. The fact that any image is a physical observable with an inner and outer scale bound, necessarily gives rise to a ‘scale-space representation’, in which a given image is represented by a one-dimensional family of images representing that image on various levels of inner spatial scale. An early vision system is completely ignorant of the geometry of its input. Its primary task is to establish this geometry at any available scale. The absence of geometrical knowledge poses additional constraints on the construction of a scale-space, notably linearity, spatial shift invariance and isotropy, thereby defining a complete hierarchical family of scaled partial differential operators: the Gaussian kernel (the lowest order, resettling operator) and its linear partial derivatives. They enable local image analysis through the detection of local differential structure in a robust way, while at the same time capturing global features through the extra scale degree of freedom. In this paper we show why the operations of scaling and differentiation cannot be separated. This framework permits us to construct in a systematic way multiscale, cartesian differential invariants, i.e. true image descriptors that exhibit manifest invariance with respect to a change of cartesian coordinates. The scale-space operators closely resemble the receptive field profiles found in mammalian frontend visual systems.