Multilevel bidimensional empirical mode decomposition: a new speckle reduction method in digital holography Marco Leo, a, * Roberta Piccolo, a Cosimo Distante, a Pasquale Memmolo, b Melania Paturzo, b and Pietro Ferraro b a National Institute of Optics–CNR, via della Libertà 3, Arnesano LE 73014, Italy b National Institute of Optics–CNR via Campi Flegrei 34, Pozzuoli NA 80078, Italy Abstract. The paper presents a new automatic technique for speckle reduction in the context of digital holog- raphy. Speckle noise is a superposition of unwanted spots over objects of interest, due to the behavior of a coherence source of radiation with the object surface characteristics. In the proposed denoising method, bidi- mensional empirical mode decomposition is used to decompose the image signal, which is then filtered through the Frost filter. The proposed technique was preliminarily tested on the “Lena” image for quality assessment in terms of peak signal-to-noise ratio. Then, its denoising capability was assessed on different holographic images on which also the comparison (using both blind metrics and visual inspection) with the leading strategies in the state of the art was favorably performed. © 2014 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.OE.53.11 .XXXXXX] Keywords: digital holography; bidimensional empirical mode decomposition; speckle reduction; image denoising; Frost filter. Paper 140257SSP received Feb. 14, 2014; revised manuscript received May 23, 2014; accepted for publication May 28, 2014. 1 Introduction In 1971, the Hungarian–British physicist Dennis Gabor was awarded with the Nobel Prize in Physics for the invention and development of the holographic method. 1 This method is a means for recording and reconstructing the whole information contained in an optical wavefront, namely amplitude and phase, and not just intensity as in photogra- phy: this allows a three-dimensional (3-D) reconstruction of the object. In digital holography (DH), 2 a charge coupled device (CCD) camera is used to record the holograms. Unfortunately, these reconstructed structures are corrupted by speckle noise. A speckle pattern results when an object is illuminated by a coherent source of radiation and the object has a surface structure that is roughly of the order of a wavelength of the incident radiation. In the image plane, the presence of speckle is evident as a collection of spots superimposed upon the actual object. Speckle noise makes image quality lower and its removal is challenging since, often, the removing process destroys important structures in the image that are in the same scale of a speckle pattern. Several speckle-removing approaches have been pro- posed in the last decades and they can be divided into two main categories: image-processing techniques 3 and optical techniques. 4 Optical techniques are based on the def- inition of specific acquisition setup. Instead, digital image- processing techniques do not affect the acquisition setup but they try to reduce the noise by numerical processing of the recorded data. Nonadaptive filters (e.g., mean or median filters 3 ) have been largely used for this purpose. To reduce the impact of filtering in image areas containing texture and edges, adaptive filters have also been introduced [e.g., Frost filter, 5 Lee filter, 6 discrete Fourier filtering, 7 nonlocal means filter- ing (NLM) 8 ]. To reduce noise, empirical mode decomposition method (EMD) and bidimensional empirical mode decomposition (BEMD) method were also pro- posed. 9–11 In this paper, a multiresolution technique is introduced to analyze the input signal at different scales: it makes use of an automatic reconstruction process that, on the basis of image quality indicators, is able to evaluate which portion of fre- quency bands (in the multiresolution framework) can be suppressed to the aim of reducing the speckle and to preserve the image contents. The proposed multiresolution framework is based on the BEMD procedure and, in particular, it exploits a recently introduced, modified version of the classical BEMD that allows multilevel decomposition. 12,13 The key idea is to ana- lyze the reconstructed digital holograms by using the afore- said multilevel BEMD and then to perform an automatic sub- band decimation stage guided by speckle index indicators. This introduces a twofold level of innovation with respect to state-of-the-art techniques: on the one side, BEMD is first time used for denoising reconstructed holograms (it was only already used in DH for fringe pattern denois- ing 14–17 ). On the other side, it introduces a multilevel strategy which is able to automatically select the speckle noise sub- band, making it suitable to be easily exploited when different acquisition setups are used. 2 Bidimensional Empirical Mode Decomposition BEMD is a two-dimensional (2-D) extension of the classical EMD. In general, EMD 18 is a fully data-driven method used to remove the noise produced in transform process without making any assumptions on the initial data. Since it provides more advantages when processing complex signals, EMD has been used in a wide range of fields, including biology, 19 geophysics, 20 radar, 21 and medicine. 22 *Address all correspondence to: Marco Leo, E-mail: marco.leo@ino.it 0091-3286/2014/$25.00 © 2014 SPIE Optical Engineering XXXXXX-1 November 2014 • Vol. 53(11) Optical Engineering 53(11), XXXXXX (November 2014)