A single-photon sampling architecture for solid-state imaging

Advances in solid-state technology have enabled the development of silicon photomultiplier sensor arrays capable of sensing individual photons. Combined with high-frequency time-to-digital converters (TDCs), this technology opens up the prospect of sensors capable of recording with high accuracy both the time and location of each detected photon. Such a capability could lead to significant improvements in imaging accuracy, especially for applications operating with low photon fluxes such as LiDAR and positron emission tomography. The demands placed on on-chip readout circuitry imposes stringent trade-offs between fill factor and spatio-temporal resolution, causing many contemporary designs to severely underutilize the technology's full potential. Concentrating on the low photon flux setting, this paper leverages results from group testing and proposes an architecture for a highly efficient readout of pixels using only a small number of TDCs, thereby also reducing both cost and power consumption. The design relies on a multiplexing technique based on binary interconnection matrices. We provide optimized instances of these matrices for various sensor parameters and give explicit upper and lower bounds on the number of TDCs required to uniquely decode a given maximum number of simultaneous photon arrivals. To illustrate the strength of the proposed architecture, we note a typical digitization result of a 120x120 photodiode sensor on a 30um x 30um pitch with a 40ps time resolution and an estimated fill factor of approximately 70%, using only 161 TDCs. The design guarantees registration and unique recovery of up to 4 simultaneous photon arrivals using a fast decoding algorithm. In a series of realistic simulations of scintillation events in clinical positron emission tomography the design was able to recover the spatio-temporal location of 98.6% of all photons that caused pixel firings.Comment: 24 pages, 3 figures, 5 table

Adaptive Measurement Network for CS Image Reconstruction

Conventional compressive sensing (CS) reconstruction is very slow for its characteristic of solving an optimization problem. Convolu- tional neural network can realize fast processing while achieving compa- rable results. While CS image recovery with high quality not only de- pends on good reconstruction algorithms, but also good measurements. In this paper, we propose an adaptive measurement network in which measurement is obtained by learning. The new network consists of a fully-connected layer and ReconNet. The fully-connected layer which has low-dimension output acts as measurement. We train the fully-connected layer and ReconNet simultaneously and obtain adaptive measurement. Because the adaptive measurement fits dataset better, in contrast with random Gaussian measurement matrix, under the same measuremen- t rate, it can extract the information of scene more efficiently and get better reconstruction results. Experiments show that the new network outperforms the original one.Comment: 11pages,8figure

Solving Phase Retrieval with a Learned Reference

Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by leveraging some prior knowledge about the structure of the unknown image. The inherent ambiguities about shift and flip in the Fourier measurements make this problem especially difficult; and most of the existing methods use several random restarts with different permutations. In this paper, we assume that a known (learned) reference is added to the signal before capturing the Fourier amplitude measurements. Our method is inspired by the principle of adding a reference signal in holography. To recover the signal, we implement an iterative phase retrieval method as an unrolled network. Then we use back propagation to learn the reference that provides us the best reconstruction for a fixed number of phase retrieval iterations. We performed a number of simulations on a variety of datasets under different conditions and found that our proposed method for phase retrieval via unrolled network and learned reference provides near-perfect recovery at fixed (small) computational cost. We compared our method with standard Fourier phase retrieval methods and observed significant performance enhancement using the learned reference.Comment: Accepted to ECCV 2020. Code is available at https://github.com/CSIPlab/learnPR_referenc

Necessary and sufficient conditions of solution uniqueness in ℓ1\ell_1 minimization

This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other $\ell_1$ models that either minimize $f(Ax-b)$ or impose the constraint $f(Ax-b)\leq\sigma$, where $f$ is a strictly convex function. For these models, this paper proves that, given a solution $x^*$ and defining I=\supp(x^*) and s=\sign(x^*_I), $x^*$ is the unique solution if and only if $A_I$ has full column rank and there exists $y$ such that $A_I^Ty=s$ and $|a_i^Ty|_\infty<1$ for $i\not\in I$. This condition is previously known to be sufficient for the basis pursuit model to have a unique solution supported on $I$. Indeed, it is also necessary, and applies to a variety of other $\ell_1$ models. The paper also discusses ways to recognize unique solutions and verify the uniqueness conditions numerically.Comment: 6 pages; revised version; submitte

Image reconstruction in optical interferometry: Benchmarking the regularization

With the advent of infrared long-baseline interferometers with more than two telescopes, both the size and the completeness of interferometric data sets have significantly increased, allowing images based on models with no a priori assumptions to be reconstructed. Our main objective is to analyze the multiple parameters of the image reconstruction process with particular attention to the regularization term and the study of their behavior in different situations. The secondary goal is to derive practical rules for the users. Using the Multi-aperture image Reconstruction Algorithm (MiRA), we performed multiple systematic tests, analyzing 11 regularization terms commonly used. The tests are made on different astrophysical objects, different (u,v) plane coverages and several signal-to-noise ratios to determine the minimal configuration needed to reconstruct an image. We establish a methodology and we introduce the mean-square errors (MSE) to discuss the results. From the ~24000 simulations performed for the benchmarking of image reconstruction with MiRA, we are able to classify the different regularizations in the context of the observations. We find typical values of the regularization weight. A minimal (u,v) coverage is required to reconstruct an acceptable image, whereas no limits are found for the studied values of the signal-to-noise ratio. We also show that super-resolution can be achieved with increasing performance with the (u,v) coverage filling. Using image reconstruction with a sufficient (u,v) coverage is shown to be reliable. The choice of the main parameters of the reconstruction is tightly constrained. We recommend that efforts to develop interferometric infrastructures should first concentrate on the number of telescopes to combine, and secondly on improving the accuracy and sensitivity of the arrays.Comment: 15 pages, 16 figures; accepted in A&

Image feature extraction using compressive sensing

In this paper a new approach for image feature extraction is presented. We used the Compressive Sensing (CS) concept to generate the measurement matrix. The new measurement matrix is different from the measurement matrices in literature as it was constructed using both zero mean and nonzero mean rows. The image is simply projected into a new space using the measurement matrix to obtain the feature vector. Another proposed measurement matrix is a random matrix constructed from binary entries. Face recognition problem was used as an example for testing the feature extraction capability of the proposed matrices. Experiments were carried out using two well-known face databases, namely, ORL and FERET databases. System performance is very promising and comparable with the classical baseline feature extraction algorithms. © Springer International Publishing Switzerland 2014

Minimizing Acquisition Maximizing Inference -- A demonstration on print error detection

Is it possible to detect a feature in an image without ever looking at it? Images are known to have sparser representation in Wavelets and other similar transforms. Compressed Sensing is a technique which proposes simultaneous acquisition and compression of any signal by taking very few random linear measurements (M). The quality of reconstruction directly relates with M, which should be above a certain threshold for a reliable recovery. Since these measurements can non-adaptively reconstruct the signal to a faithful extent using purely analytical methods like Basis Pursuit, Matching Pursuit, Iterative thresholding, etc., we can be assured that these compressed samples contain enough information about any relevant macro-level feature contained in the (image) signal. Thus if we choose to deliberately acquire an even lower number of measurements - in order to thwart the possibility of a comprehensible reconstruction, but high enough to infer whether a relevant feature exists in an image - we can achieve accurate image classification while preserving its privacy. Through the print error detection problem, it is demonstrated that such a novel system can be implemented in practise

Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure