Towards real-time image deconvolution: application to confocal and STED microscopy

Abstract

Although deconvolution can improve the quality of any type of microscope, the high computational time required has so far limited its massive spreading. Here we demonstrate the ability of the scaled-gradient-projection (SGP) method to provide accelerated versions of the most used algorithms in microscopy. To achieve further increases in efficiency, we also consider implementations on graphic processing units (GPUs). We test the proposed algorithms both on synthetic and real data of confocal and STED microscopy. Combining the SGP method with the GPU implementation we achieve a speed-up factor from about a factor 25 to 690 (with respect the conventional algorithm). The excellent results obtained on STED microscopy images demonstrate the synergy between super-resolution techniques and image-deconvolution. Further, the real-time processing allows conserving one of the most important property of STED microscopy, i.e the ability to provide fast sub-diffraction resolution recordings.

Limited-memory scaled gradient projection methods for real-time image deconvolution in microscopy

“…With the above settings for the scaling matrix and the step-length parameter, SGP has been compared against the RL algorithm on many imaging problems, providing a remarkable convergence rate acceleration without losing accuracy in the reconstruction. In particular, in [12] a special SGP implementation for GPU devices has been successfully exploited, providing a step ahead toward real-time deconvolution of microscopy images. Thus, further improvements of the SGP performance can be a crucial key for developing more effective deconvolution tools.…”

“…The slow convergence seriously limits the use of the RL algorithm, especially in case of large-scale imaging problems, and the design of accelerated iterative schemes have received growing interest in the last years. For microscopy images deconvolution, a very promising accelerated reconstruction approach has been recently proposed in [12], based on the general constrained minimization scheme called Scaled Gradient Projection (SGP) method introduced in [5]. The SGP scheme is a gradient method able to exploit essentially four key elements: the scaled gradient directions, a parameter for controlling the step-length along the scaled gradient directions, a projection step for generating feasible descent directions and a line search strategy for ensuring sufficient reduction of the objective function during the iterations.…”

“…By combining an efficient step-length selection based on the adaptive alternation of the two BB rules [13,14] and a scaling strategy similar to that used by the RL algorithm, SGP has shown significant convergence rate improvements in comparison with RL, without excessive growth of the cost per iteration and loss of reconstruction accuracy [5]. These abilities allowed the GPU version of SGP designed in [12] to show interesting performance as real-time deconvolution algorithm. In order to efficiently equip SGP with the new step-length rule presented in [3], crucial aspects concerning with the presence of scaled gradient directions and nonnegativity constraints need to be discussed.…”

“…Given that we are interested in evaluating the advantages of the algorithm in terms of iterations and computational time, while maintaining a sufficiently good reconstruction (that is to say, an image/volume reconstruction having an error level comparable to the one of other reference methods for the application field), we use synthetic phantoms. Even if they are randomly generated, these phantoms are properly designed to correctly simulate realworld situations and have already been tested and validated by experts in the field [12]. Seeking completeness, the next subsection summarizes the generation process.…”

“…Since in the last years promising image reconstruction algorithms have been designed by exploiting BB-based rules within gradient methods [5,6,7,8,9,10,11], it is worthwhile to investigate if useful acceleration can be achieved with the new step-length selection idea. In particular, we focus on the algorithm for image deconvolution in microscopy provided by the Scaled Gradient Projection (SGP) method recently developed in [12], that can be appropriately modified for managing the step-length rule proposed in [3]. SGP is a very general algorithm for minimization problems with simple constraints, able to exploit both scaled gradient directions and selection rules for the step-length parameter.…”