First-photon imaging via a hybrid penalty

Abstract

First-photon imaging is a photon-efficient, computational imaging technique that reconstructs an image by recording only the first-photon arrival event at each spatial location and then optimizing the recorded photon information. The optimization algorithm plays a vital role in image formation. A natural scene containing spatial correlation can be reconstructed by maximum likelihood of all spatial locations constrained with a sparsity regularization penalty, and different penalties lead to different reconstructions. The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m1"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> -norm penalty of wavelet transform reconstructs major features but blurs edges and high-frequency details of the image. The total variational penalty preserves edges better; however, it induces a “staircase effect,” which degrades image quality. In this work, we proposed a hybrid penalty to reconstruct better edge features while suppressing the staircase effect by combining wavelet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m2"> <mml:mrow> <mml:msub> <mml:mi>l</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> -norm and total variation into one penalty function. Results of numerical simulations indicate that the proposed hybrid penalty reconstructed better images, which have an averaged root mean square error of 12.83%, 5.68%, and 10.56% smaller than those of the images reconstructed by using only wavelet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m3"> <mml:mrow> <mml:msub> <mml:mi>l</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> -norm penalty, total variation penalty, or recursive dyadic partitions method, respectively. Experimental results are in good agreement with the numerical ones, demonstrating the feasibility of the proposed hybrid penalty. Having been verified in a first-photon imaging system, the proposed hybrid penalty can be applied to other noise-removal optimization problems.

Topics & Concepts