A hybrid approach to seismic deblending: when physics meets self-supervision
Authors: Nick Luiken
Matteo Ravasi
Claire Emma Birnie
Venue: NeurIPS 2022 Submitted (2022)
Keywords: Seismic deblending
self-supervised denoising
Plug-and-Play
inverse problems

Abstract: To limit the time, cost, and environmental impact associated with the acquisition
of seismic data, in recent decades considerable effort has been put into so-called
simultaneous shooting acquisitions, where seismic sources are fired at short time
intervals between each other. As a consequence, waves originating from consecu-
tive shots are entangled within the seismic recordings, yielding so-called blended
data. For processing and imaging purposes, the data generated by each individual
shot must be retrieved. This process, called deblending, is achieved by solving
an inverse problem which is heavily underdetermined. Conventional approaches
rely on transformations that render the blending noise into burst-like noise, whilst
preserving the signal of interest. Compressed sensing type regularization is then
applied, where sparsity in some domain is assumed for the signal of interest. The
domain of choice depends on the geometry of the acquisition and the properties of
seismic data within the chosen domain. In this work, we introduce a new concept
that consists of embedding a self-supervised denoising network into the Plug-and-
Play (PnP) framework. A novel network is introduced whose design extends the
blind-spot network architecture of Laine et al. (2019) for partially coherent noise
(i.e., correlated in time). The network is then trained directly on the noisy input
data at each step of the PnP algorithm. By leveraging both the underlying physics
of the problem and the great denoising capabilities of our blind-spot network,
our algorithm is shown to outperform an industry-standard method whilst being
comparable in terms of computational cost. Moreover, being independent on the
acquisition geometry, it can be easily applied to both marine and land data without
any significant modification.

33 entangled seismic data, also called blended data, where waves originating from one source tend A hybrid approach to seismic deblending: when physics meets self-supervision
Anonymous Author(s)
Affiliation
Address
email
Abstract
To limit the time, cost, and environmental impact associated with the acquisition of seismic data, in recent decades considerable effort has been put into so-called simultaneous shooting acquisitions, where seismic sources fired at short time intervals between each other. As consequence, waves originating from tive shots are entangled within the seismic recordings, yielding so-called blended data. For processing and imaging purposes. the data generated by each individual shot must be retrieved. This process, called deblending. is achieved by solving an inverse problem which is heavily underdetermined. Conventional approaches rely on transformations that render the blending noise into burst-like noise, whilst preserving the signal of interest. Compressed sensing type regularization is then applied, where sparsity in some domain is assumed for the signal of interest. The domain of choice depends the geometry of the acquisition and the properties of seismic data within the chosen domain. this work, we introduce a new concept consists embedding a sule-supe denoising network into Plug-and-Plas (PnP) framework. novel network is introduced whose design extends the blind-spol network architecture of [27] for partially coherent noise (i.c., correlated in time). The network is trained directly on the noisy input data at each step of the PnP algorithm. By leveraging both the underlying physics of the blending operator and the great denoising capabilities of our blind-spot network, the proposed algorithm is shown outperform industry-standard method whilst of computational acquisition geometry. our method can easily applied to both marine and land data without any significant modification.
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Moreover, being independent on
1 Introduction
Reflection seismology 4 is a geophysical technique uses reflected seismic waves characterize the Farth's is subsurface. comprises controlled source of scismic energy and an array of receivers 27 that record the pressure (or displacement) induced by the reflected waves. After the introduction of 3D scismic [TT]. today's 'sss conventional scismic acquisition campaigns may last several weeks up to a few months 7 25 10] In an attempt to improve acguisition efficiency, and therefore limit the time, cost, and associated environmental impact, 66 g 36 introduced a paradigm in seismic acquisition referred
sinultaneous shooting. Simply put, consecutive sources fired at short time intervals, thereby minimizing the overall acquisition time. This comes the of recording
34 overlap with those originating from previous and subsequent sources. To render such data suitable for subsequent steps of seismic processing and imaging, the interference between consecutive shots must be removed such that the contribution of each individual source (also referred to as a shot gather) is retrieved. This process is called deblending. In theory. deblending can be achieved by solving
Submitted to 36th Conference on Neural Information Processing Systems (NeurIPS 2022). Do not distribute.

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39 an inverse problem; however, as this problem is heavily underdetermined, choosing an appropriate regularization is fundamental to achieve a successful inversion. Historically, the design of suitable regularizers is motivated by the effect of the adjoint of the blending operator on the blended data. In fact, the resulting data can be seen as superposition of coherent signal (i.e. reflections from the shot whose firing time has been properly accounted for) and rracewiiee burst-like noise (i.e, reflections from all other interfering shots whose firing times have not been properly accounted for).
The recent success of deep lcarning in various scientific disciplines has attracted the interest of the 65 geophysical community, resulting in many opportunities and new challenges [T]. For example,
48 whilst training data should consist of clean, representative ground truth examples that resemble
47 the solution to the inverse problem at hand, such data is generally not available. Two approaches
48 commonly adopted to circumvent this problem are to either generate synthetic data or to use state- of-the-urt urt algorithms to produce intul- pairs to train a network on; in both cases, transfer learning [42] 33 or domain adaptation [2] [2] techniques are then required to generalize the network capabilities to unseen field data. A major drawback of the first approach is that synthetic data may not resemble field data accurately enough be considered representative dataset: this well-known
53 the geophysical community and has been a major criticism for decades when new methods are
54 tested only on synthetic data. also represents a serious roadblock to the application of deep learning
25 methods in geophysics. Additionally, in most geophysical applications the underlying physics is 58 (at least partly) well understood. Pure, end-to-end machine learning methods tend to ignore these well-studied physical principles, thereby discarding important a priori knowledge of the problem they are tasked to solve.
Our contribution We introduce novel algorithm for seismic deblending, which combines the physics of the underlying physical process with a ofate-of-thear superssp denoiser into single, well-crafted inverse process. This is specifically achieved within the framework of Plug- 52 and Play (PnP) priors. Our network architecture is inspired by blind-spot network of [27] and
83 modificd to handle trace-wise coherent noise. The network is trained on-the-fly fly at each PnP iteration
54 in a self super-uuee manner, completely bypassing the need for ground truth data. Our numerical
65 experiments illustrate that the proposed algorithm can outperform a statc-of-the-art conventional method. Finally, we show that our algorithm is independent on the underlying structure of the seismic data and can he used casily for different acquisition sct-ups clear advantage over conventional methods.
2 Background
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The seismic data layout Seismic data are commonly acquired by firing a source at a given time and 71 recording the reflections arising from the interaction between the emitted seismic wave and changes in subsurface properties. Conceptually, seismic data can be arranged as a three dimensional tensor (or a cube), having the dimensions of the number of sources n., number of receivers ni,, and number of time samples ny: d2. 2., 1). Slicing this cube in different directions gives raise to so-called scismic gathers: more specifically. when slicing across the source axis, we obtain the data recorded by all 78 receivers for a single shot, usually called Common Shot Gather (CSG); conversely, by slicing across
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77 the receiver axis we obtain the data generated by shots for a single receiver. When the receivers
78 move alongside the source (í.c., marine case) the resulting gather is called Common Channel Gather
79 (CCG). For static receivers (i.e., ocean-bottom or land acquisition). the seismic gather is know as the
80 Common Receiver Gather (CRG). Both scenarios will later he considered.
Blended acquisition In practice. to be able to collect data where no overlap exists between consecutive shots, each shot has to be fired with appropriate time delay. such that all reflections from one shot have been recorded by the receivers before the next shot is fired. This dictates the overall acquisition time and greatly limits any possible acquisition speed-up. Alternatively.
85 blended acquisition, shots are fired at shorter intervals. This means that each individual CSG
85 contains recordings from both the nominal as well as the previous and subsequent shots. In this work, oo--t-----h----- the-art in marine 89 seismic acquisition due to the fact it is easy to implement in the field. It is achieved by firing the airgun towed by the acquisition vessel at short time intervals, and continuously recording the waves returning to the receiver array as depicted in figure [[] The recorded data d, can be simply described the superposition of all of the unblended, clean, data shifted in time by the given time delay
87 we consider the so-called continuous blending setting. This approach is state-of
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4=i-T+ At, Here. the nominal firing interval and At, is a random dither applied to the nominal firing time of shot i. The blended data can thus be described as a function of the clean data
d, Bd. = [B..... B,, de = B1 + ... B.,, de...
(1)
where the blending operator horizontal stack time-shift operators B,, and the clean data a 95 vector where all vectorized shot gathers, de, = (ec(dd((s..s> wy. f]), are stacked together. Morcover, each B. time-shift operator has the property that B B, 1, and composition of time-shift operators is again time-shift operator 33
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a)
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Peeudo-debiended data: 8 (g(g)
Figure 1: Schematic illustration of seismic simultaneous shooting acquisition. a) Cartoon of scismic acquisition campaign in continuous blending mode. A single vessel towing source (red star) and array of receivers (blue triangles) moves from right left and fires energy into the ground dithered periodic time samples. For each shot, reflections originated from shallow subsurface layers are immediately recorded by the receivers, whilst those produced by deeper reflectors are recorded later in time alongside the shallow rellections from the next firing shot. This phenomenon leads to the blending of independent shot gathers. b) A short time window of the continuously blended scismic data. Dashed verticul color lines represent the nominal firing times (i.e., i T), whilst the solid color lines represent the actual firing times with dithering. Color rectangles refer to every individual shot gather that we wish separate from the other overlapping gathers. c) Pseudo-deblended data for a single receiver (white dashed line in panel
Pseudo-deblending
To better understand how to design effective regularization strategies for the dehlending problem, we first have consider the action of T on the blended data. For the 8th shot gather, the result of B Bd, can be written
B (Bide, I... B,, (h..d....) dess (Bl I I... B Bn, de...)
(2)
Therefore the action of B on the blended data produces the original 8th shot gather alongside randomly shifted versions of all the other shot gathers. Whilst these randomly shifted shot gathers are coherent and look like standard seismic signal in the CSG domain, they appear trace-wise coherent noise in the CRG (or CCG) domain shown in figure [cc). Because the application of the adjoint of the blending operator retrieves the true signal, albeit with some additional noise, action usually called pseudo-deblending. As a consequence of this, now clear that to retrieve the various deys. an effective regularization must filter the trace-wits noise in CRGs (or CCGs) whilst preserving the coherent signal. Conventional approaches identify a domain in which the signal can be
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easily discriminated from the noise, and more specifically the signal in such domain is sparse whilst the noise is pot. Examples of such a kind include the hyperbolic Radon transform for CRGs (24) the patched Fourier transform for CCGs [1, the Curvelet transform [30]
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112 Deblending by inversion
Deblending by denoising is achieved by minimizing
min lld, Bd doll1 + R(de),
(3)
d.
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whereas deblending by inversion amounts to retrieving the clean data by solving the (heavily) underdetermined inverse problem,
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min Bdl. d. + 2
(4)
115 where R(-) is any chosen regularization. The literature has shown that deblending by inversion is
118 superior to deblending by denoising in terms of the overall quality of reconstruction and will be the focus of this work. More details on both approaches are provided in the supplementary material.
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supervied denoising: Incoherent noise Self-supervised denoisers are designed in such a way 118 that noisy images can be used as both the input and label to train a neural network to act as a denoiser.
120 thereby bypassing the need for clean data as labels. Noise2Noise represents the first such method not relying on ground truth labels (28). The network is forced to infer the signal from pairs of noisy data For applications where such pairs unavailable, an alternative was proposed in the concurrent works of (26) and [S]. who introduced 2oid and Noise2Self, respectively. In both cases, the same image is used as input and label: under the assumption that the noise is incoherent whilst the signal is coherent, the network can naturally leam infer only the signal from its neighbouring pixels. More specifically, to denoise particular pixel, (26) replace the pixel the input image with a randomly selected neighbouring pixel. As this pre- pre-processing step introduces randomness in the central pixel of the receptive field of the network, the network should not learn anything from it and naturally learns to infer the signal from its neighbours (since the noise is assumed to be incoherent).
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Rather than directly replacing the pixel of interest, [5] pre-process the input image with a blind-spot convolutional filter, that the network cannot rely the central pixel to predict itself. A key limitation of both approaches lies in the fact that the self-supervised loss be evaluated only the pixels that have heen corrupted, making the training of these denoisers relatively slow. An alternative upproach blind-spol networks was introduced by [27]. Instead of corrupting the middle pixel, their network is explicitly designed to have receptive field with hole the middle. This is achieved by combining padding and cropping with a standard convolution layer (i.e., to create a causal filter) and by rotating the input image four times prior to feeding it through the network. After the rotated inputs have been fed through the network, they are rotated back, concatenated, and combined by series 130 of 1 x 1 convolutions prior to evaluating the loss ut every pixel of the output image. A schematic description of this network is depicted in figure Ph.
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Self Self-supervised denoising: Coherent noise Both Noise2 Void and Noise2Self operate under the assumption that the noise is independent and identically distributed. ([5) shows that the denoising 143 quality of Void is degraded when the noise is structured. This shortcoming of Noise2 Void is
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144 solved by masking pixels along the direction of the noise: the authors dub their method Structured Noide For the seismic deblending problem, the noise that we are interested to suppress also structured: more specifically. the blending noise shows correlation along the time axis. We, therefore.
147 extend here the efficient implementation of [27] to suppress structured noise in seismic data, by using
148 the original and flipped (over the source axis) version of the image as input. This produces a network
149 whose receptive field is masked over an entire time trace, see figure Zp. In the following, we will call
150 this network Structured Blind Spot, or StructBS for short.
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Related work
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Simultaneous shooting Simultaneous shooting was first pioneered by [6] and has gained popularity
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recent years (9) Although the first attempts deblending were mostly by means of denoising [33]
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recent research has reveled the superiority of deblending by inversion [[] Since then, research has
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been devoted to finding appropriate regularization terms. Some approaches involve median- median-fittering
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[2 21 23 renk-reduction methods [17] [55]. sparse regularization [29 [0 [56] [57]5]] [59]. and deep
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learning 43 58 49 All the deep learning approaches to date use CNNs and require pre-training. 4
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uses the RED framework introduced in [38]. which is similar to the PnP framework. The difference
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is that RED explicitly incorporates the denoiser into the objective function. The authors propose the
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use of two conventional regularization techniques as denoiser, the patched Fourier transform [I]
and the seaessse-eertteyyssste filter (17), instead of applying them sparse penalty.
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a) Goneral sate: noise incoherent along both (Laine all 2020)
Impalse reaporse
Wade
b) Our specific case; noise only incuherent along the spatial axis
Impalse
Figure 2: (a) The blind-spot network of (27). whose receptive field excludes the center pixel. (b) Our newly proposed blind-spot network, whose receptive field excludes an entire direction instead of just the middle pixel. Impulse responses are created by feeding the respective networks with unitary weights and zero biases with an image containing unitary spike in the middle.
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Self-supervised seismic denoising Seismic data are a prime example of a noisy data type where no clean, ground truth labels are available. As such, the upplication of self-supervised denoisers has recently been proposed for the suppression of different types of noise present in seismic data. Follow- ing the Noise2 methodology, [13 blind-spot networks for the suppression of random noise post-stack seismic data. Expanding on this, (32) adapted the methodology of StueturedNoise2We6
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[S] for the suppression of trace-wise noise in seismic shot gathers, originating from poorly coupled receivers and/or dead sensors. The method that is most closely related to ours is the one presented in
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49 both with respect to application and methodology. The authors propose to use a self-supervised
denoising network to deblend the data by denoising. To produce satisfactory results they require a number of additional pre- and post-pri post-prccesing steps. In our work, we incorporate deep learning based denoiser in deblending by inversion, thereby leveraging both the underlying physics and the power of neural networks. Moreover, no pre- and post-procct processing is required.
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The Plug-and- Play framework The Plug-and-Play framework was pioncered by 48 The authors considered a numher of popular denoisers, including BM3D [1]] K-SVD [19), PL.W [16] and q- GGMRF (:5) In subsequent works, the denoisers have been replaced by pre-trained neural networks,
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most notably CNN and DrCNN. Lately, (31 proposed regularization by artifact-removal (RARE), method leveraging Noise2Noise type approach that requires pre-training. An extensive list of references provided in (52). and include [38] [54] [35] 47 20 46 29 44 [53]. This research focuses on progressively training neural network such that can adapt to changing noise levels. The novelty
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of our method is that pre- pre-training is not required.
4 Method
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Equipped with self-supervised denoiser. straightforward approach deblending is to directly denoise the psculo-deblended data. However, deblending by denoising known be sub-optimal in comparison to deblending by inversion. On the other hand, because denoiser cannot naturally added as a constraint to the objective function in equation 4 it is not immediately clear how incorporate the denoiser into the inversion process. [48] proposed the PaP framework, which is directly derived from the Alternating Direction Method of Multipliers (ADMM). Whilst resembling the alternating minimization process of the classical ADMM algorithm. PnP is more flexible in explicit
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the sense that it can use any denoiser of choice, without the need for it to be linked method clearly. give short derivation of the ADMM following (14), then link it to the PnP algorithm and finally proposed algorithm. The ADMM algorithm is generally used to solve inverse problems of the form
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regularization term for the so-called y-update. To understand
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min D(M(2))) d) + R(x),
194 where M is the forward model, d is the measured data, D is data fidelity term that is generally 195 smooth, and R is a convex, possibly non-smooth regularization term. Due to the mmoothnesss
of the objective, this problem cannot be solved with standard gradient-based based methods. To account
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for the non- smoothnssss of R. an auxiliary variable y = x is introduced, yielding the equivalent
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optimization problem
min D(M(()) d) + R(y) subject to x y.
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ADMM solves this problem by forming the so-called augmented Lagrangian,
max D(M(s),d Ryy) + 211zz vll (x v).
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where the Lagrange multiplier and p scalar. This problem solved by alternatively minimizing over a and y, and maximizing over u. This yields the following scheme:
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Tk+l = mig ((M(2), d) + P I| yk + =xl13]
arg R(y) + 1x+4 mxll2
yk+1 =
0k
ui 2 1-
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The introduction of = 2 and the addition of the quadratic penalty {|1a= yll yields the y-update, which for most popular regularization terms has a simple dlosed-form solution that can cheuply evaluated [37]. The key observation
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(88 is that the y-update can be interpreted as a denoising inverse problem. As such, the authors propuse to drop the user-defined regularization R(-) and
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instead plug in denoiser of choice in the y-update of the ADMM itcrations. Although this may not
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seem straightforward choice, PnP has been shown to be competitive (or sometimes even better) than standard regularization methods in variety of settings. Given the trace-wise structure of the noise
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and equipped with the self-supervised denoiser, the PnP framework becomes natural and attractive choice for the deblending task hand. Our proposed algorithm reads follows:
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M++1
arg min
2
lBr
del13
2
f11
yk 2xx11
Me+1 StructBS (F I ux)
M6++1 ug 26+1 yk++1-
where is used here for simplicity in place of de, and the u-uude is performed using an iterative
212 solver of choice, e.g. LSQR. The y-update is now the denoiser StructBS,, where 9 denote the network parameters, The variable a couples both and y and forces them to be close together. The z-update requires the solution to satisfy the physics dictated by the equation Bx = dh, and the y-update denoises the noisy receiver gathers.
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5 Experiments
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In the following, our algorithm is tested on the openly available Mobil AVO viking graben line 218 12 marine dataset[] As the data has been originally acquired in conventional fashion. create
219 the blending operator and blend the data ourselves. In addition to containing all the challenging
220 features of field dataset, this also provides us with a ground truth, de. onto which to assess the
221 quality of our reconstruction. In this example, the original dataset is composed
n, = sources, n, 120 receivers, and n, = 1024 samples (i.e.. the total recording time per shot equals 4 seconds).
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223 For the continuous blending operator, we choose a fixed firing interval of T = 2 seconds, with
224 added random delays selected uniformly in the interval At, ~ [-1, I] seconds. This overlap is quite
225 challenging generally half of the signal overlaps with either that of the previous or that of the next shot. Moreover, some pseudo-deblended shot gathers exhibit contributions from three consecutive shots. Finally, the relative mean-square error, RM I|d,- de.truellz/ [Ide,true l2.. chosen metric of comparison in all of our numerical examples. All experiments are performed on a (R) Xcon(R) CPU 2.10H equipped with a single NVIDIA GEForce RTX 3090 GPU.
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5.1
Comparison with state-of-the-ar deblending
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To begin with, our newly proposed methodology is compared with the state-of-the-an deblending algorithm of (I] that solves the deblending problem as sparsity promoting inversion
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arg mig BFz dullž
A|E=|h, d, Fz,,
(5)
https:// //wiki. seg. htg/wixii/obbl..cmo AVD www.iiinggggaa.... 1ine_
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where F' is a linear operator that performs patched two-dimensional Fourier transform, and e, is the solution in the Fourier domain that is ultimately transformed back to the original time-space domain of the seismic data. In our experiment, the size and number of patches as well as the regularization parameter À are selected by hand to yield optimal results. Moreover, the FISTA (8) solver is used with adaptive decreasing sequence, A (as this has been shown in the literature outperform fixed A for this specific problem). We choose the sequence
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= (ge 0.05k 6) Ao. which once again tune to give the best performance. The final error is roughly 9.8% (see supplementary material 240 for details); hereon in this represents the benchmark against which we will assess the effectiveness
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241 of our sulf-supe PnP algorithm. Next, our PnP algorithm is applied to the same dataset. We
242 choose 30 outer iterations, 3 inner iterations, = 1 and 30 denoiser epochs. The choice of these
243 hyperparemeters will be justified in the ablation study. We also use the U-Net architecture in (27),
244 the L1 norm for the self-supervised training loss because it is more appropriate for burst-like noise,
245 and the Adam optimizer with default parameters. Since the denoiser is trained on all the CCGs,
246 the size of our training data 120 and we use a batch size of 8. This leads to a solution that has
247 an overall error of roughly 6.7%, which is approximately 3% lower than the conventional method.
249 As a visual comparison, figure displays the results for given CCG (top) and CSG (bottom) for both the conventional and proposed approaches, It is noteworthy that our algorithm shows a clear improvement in terms of denoising capabilities. as visible in the displayed CCG. Especially after f 28, where the signal is weak and blending noise dominates, the conventional approach tends to be more prone to signal leakage compared to our PnP algorithm. Finally. the computational cost of the conventional algorithm can he quantificd in terms of the number of forward and adjoint operations for both the blending (B) and patched Fourier (F) operators: in our example, this amounts 200 forward and adjoint passes. On the other hand, our method requires 90 forward and adjoint passes for the blending operator and a total of 900 training epochs for the network. Considering that all computations (spart from the network related ones) are performed on the CPU, the two algorithms are comparable in terms of overall computational time (2h and 34mins for the conventional algorithm and lh and 5 mins for the PnP algorithm).
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Figure 3: Deblending results for CCG (top) and CSG (bottom). Although both algorithms can successfully remove most of the blending noise, our algorithm is less prone signal leakage and provides better amplitude fidelity- key factor in seismic data processing.
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5.2
Ablation study
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This section provides an extensive analysis of some of the key components of the proposed PnP methodology and their impact on the overall solution of the deblending inverse problem.
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Pnl iterations To begin with, we assess the importance of the PnP iterations compared to simply training the self-supervised denoiser on pseudo-deblended data and applying it directly to the entire dataset. Although not shown here, the result of this one-shot denoising produces a solution with an overall error of roughly 19%. This is much worse than both the conventional and PnP method and therefore considered not suitable.
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The z-update
The ablation study with regard to the z-update is provided in the supplementary material. This includes study on the effect of the number of inner iterations and the & parameter. For continuous deblending problem, have shown that they could be safely fixed to 3 and Future experiments with different datasets and blending strategies required verify this assumption.
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The y-update In our implementation propose to start with randomly initialized network and train it for fixed number of epochs at every outer iteration. A warm start strategy is employed such that the weights of the network at given outer iteration are initialized to those obtained the end of the training of the previous outer iteration. The efficacy this approach is shown in figure [aa where we compare on-the thy--ee-ly training with and without warm starts, where the latter re-initializes the network at every y-update. From the error curves, we can safely conclude that warm starting the network is clearly beneficial. Since there is no theoretical justification for this particular strategy. we consider few other alternative strategies. The first strategy is to use a pre-trained network. Here trainigg is achieved by denoising the pseudo-deblended data in self-supervised manner; this approach could greatly reduee the computational cost of the overall algorithm since we do not need train the network at every iteration. A comparison of the relative error with that of the proposed, oh- training shown in 4i reveals that after few outer itcrations, the network unable further remove the remaining noise in the data.
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outor Ioorstions
Figure a) Error for network training with and without warm starts. b) Error when running the PnP algorithm with network pre-trained on the pscuddo-debennde data.
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Another option is to stop training the network after a few outer iterations. Ideally, the network will have learnt how to remove the noise encountered during the first iterations, and extra training will not improve the denoiser capabilities. We run experiments where we stop the training after fixed number of outer iterations see whether there added benetit to continuing training the network. Results are shown in figure 55. In all of the scenarios we clearly see that stopping the training after
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Figure 5: a) Error for on-the-fly training where training is stopped after certain number of outer iterations. b) Error for different number of training epuchs. e) Error when using the network the end the PnP algorithm for the entire process versus our proposed on-the-fly training strategy.
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a certain number of outer iterations leads to stagnation in the error, or worse to an increase
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in the error at later iterations. This behaviour is known as semiconvergence in the inverse problems community. Both results are perhaps not surprising, as the input to the network at every iteration contains different noise level compared to that of earlier iterations: the noise in 24 constantly reduces during the overall inversion. Therefore. the network is required to learn a slightly different
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task at each time. In figure Bp, we assess the impact of the number training epochs for the denoiser. We clearly observe that some point the curves for 30 and 20 epochs start to coincide, meaning that there is no additional gain in the extra 10 epochs of training. The curve for training with 10 epochs seems stagnant after the first three iterations, but eventually it picks up momentum and goes down again. Note that, in terms of overall epochs, the cost of performing 30 outer itcrations with 10 epochs each is the same as using 10 outer iterations with 30 epochs each. However, every outer iteration carries an additional cost of three inner itcrations for the z-update, which is not negligible as it requires evaluating the forward and adjoint of the blending operator. In general, it seems beneficial perform more epochs in the early outer iterations, although there is limit after which the error starts stagnate. Moreover, training with 60 epochs leads overfitting.
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Finally, to further investigate the generalization capahilities of the network for blending problems, the network weights are saved after the last outer iteration of the PnP algorithm. The PuP algorithm
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is then re-rum using the saved network without performing any on- fly training. Figure [ shows that this strategy fails, illustrating that the network may have forgotten how to deal with the higher noise levels encountered in the early iterations. This results highlights the importance of using a self- supervised denoiser that can be easily and cheaply trained on oa-the-fi fly. The use of pre- trained denoising networks such as DuCNN may instead require training multiple networks with different noise levels, unless bias-free, non-blind network is used (52).
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6 Limitations and Conelusions
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Limitations Our algorithm requires the setting of a number of hyperparameters, namely the number of inner and outer iterations, the parameter p. and the number of epochs for the self-supervised denoiser. The number of epochs seems to have major impact on the quality of the deblending process and the overall convergence properties of our algorithm. Additional hyperparameters that have not been explored in this work are associated with the network itself, e.g. the number of layers, the activation function, batch size, etc. This is also a direction for further research. Another drawback is that there is no convergence guarantce, since our operator B is underdetermined and therefore not strongly convex (39]. Empirically, we observe that iy and ys: tend to converge to similar values for some carefully selected hyperparameters, indicating that at least in our experiments the algorithm converges successfully. Similarly. to obtain convergence guarantees for the PnP method, the denoiser
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has to be Lipschitz continuous; when neural network is used, this means that spectral normalization is required during training. In (50). it was shown that PnP algorithms can be convergent when combined with carefully pre-trained denoisers that satisfy such condition.
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Societal impact Blended acquisition greatly reduces the time required to acquire seismic data, thereby limiting the impact of scismic acquisitions the environment. Apart from shooting at shorter intervals, there is no difference compared to conventional acquisition. Moreover, recent research has suggested that the energy emitted by cach source could be lowered. This may provide acquisition solutions that are more environmentally friendly for marine life.
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332 Conclusions
We have introduced novel hybrid algorithm for seismic deblending, combining the physics of the blending operator with self-supervised denoiser that is naturally embedded into the Plug-und-Play framework. We have adapted the network architecture in (27] to enforee an extended blind spot along an entire axis (time, in our case) instcad of single pixels. Because the denoiser self-su supervieee,, our approuches bypasses the need for ground truth labels that are usually unavailable for scismic applications. Experiments on a field datasct have shown that the proposed method can outperform a state-of-the-art, sparsity-based algorithm. Moreover, as show in the supplementary matcrial, our algorithm is independent on the type of acquisition, which is usually an issue for conventional algorithms. Although our algorithm requires the setting of number of hyperparameters.
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341 we have argued that the number of inner iterations and can most likely be set to a fixed number
342 and this easily generalizes to different seismic acquisitions. However, the network architecture and
343 the number of epochs may require luning for different acquisition setups. We hope address these
344 issues by having an adaptive strategy for setting the number epochs in future work.
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References
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[1] R. Abma, D. Howe, M. Foster, I. Ahmed, M. Tanis, Q. Zhang. A. Arogunmati, and G. Alexander. Independent simultaneous source acquisition and processing. Geophysics, S066:WD37-WD44, 2015.
347
348
348
[2] T. Alkhalifah, H. Wang, and O. Ovcharenko. Mircal: Bridging the gap between training on synthetic data and real data applications in machine learning. arXiv, 2021.
350
251
[3] C. Baganni. Acquisition and processing simultaneous vibroseis data. Geophysical Prospectingg 58:81-99, 2010.
352
353
[4] B. Bahia, R. Rongzhi Lin, and M. Sacchi, Regularization by denoising for simultancous source separation. Geophysies, 16(6))1942-2156 2021.
354
355
[5] J. Batson and L. Royer. Noisc2self: Blind denoising by self-supervision. International Conference Machine Learning, pages 524-533, 2019.
358
357
[6] C.J. Beasley, R.E. Chambers, and Z. Jiang. new look at simultaneous sources. 68th Meeting, SEG Expanded Abxtracts, volume 2022, pages 133-135. European Association Geoscientists & Engineers, 1998.
358
359
360
[7] G. Beaudoin and A. Ross. Field design and operation of a novel deepwater, wide-azimuth node scismic survey. The Leading Edge, -444,, 2007.
361
[8] A. Beck and M. Teboulle. fast iterative shrinkage-threshholding algorithm for lincar inverse problems. SIAM Journal on Imaging Sciences, 2:183-202, 2009.
363
384
191 A. J. G. Berkhout. Changing the mindset seismic data acquisition. The Leading Edge, 27:924-938, 2008.
385
368
[10] M. Berraki, S. Buizard, J. Ramirez, R.M. Elde, D. Eckert S.S. Roy, and J.-F. Synnevag. Grane prm from acquisition to interpretation in record time. In 79th EAGE Conference and Exhibition 2022, volume 2017, pages 1-5. European Association of Geoscientists & Engineers, 2017
367
388
360
[11] B. Biondi. 3D Seismic Imaging Seismology (2nd ed.). SEG Books, 2006.
370
[12] C. Birnie and T. Alkhalifah, Leveraging domain adaptation for efficient scismic denoising. In
371
Energy in Data Conference, Austin, Texas, 20-21 23 February 2022, pages 11-15. Energy in Data, 2022.
372
373
[13] C. Birnie, M. Ravasi, L. Sixiu, and Alkhalifah. The potential of self-supervised networks for random noise suppression in scismic data, Artificial Intelligence Geosciences, 2:47-59, 2021.
374
375
[14] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipliers. Now Publishers Inc 3, 2011.
375
377
[15] C. Broaddus, A. Krull, M. Weigert, U. Schmidt, and G. Myers. Removing structured noise with self-supervised blind-spot networks. 2020 IEEE 17th International Symposium Biomedical Imaging (ISBI), pages 159-163, 2020.
378
379
390
[16] Chatterjee and P. Milanfar, Patch-based near-optimal image denoising. Image Processing, IEEE Transactions on, (1())11611 2012.
361
382
[17] J. Cheng and M.D. Sacchi. Separation and reconstruction of simultancous souree data via iterative rank reduction. Geophysics. 80(4) 2015.
383
[18] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian. Image denoising sparse 3-d transform-
385
domain collaborative filtering. IEEE Transactions image processing, 1608):2080-0055 2007.
305
387
[19] N. Elad and M. Aharon. Image denoising via sparse and redundant representations over learned
399
dictionaries. Image Processing, IEEE Transactions on, 15(12):372-33455 2006.
399
[20] S. Gu. R. Timofte, and L. van Gool. Integrating local and non-local denoiser priors for image
restoration. In International Conference Pattern Recognition, pages 2923-2928, 2018.
10

---

391
[21] W. Huang, R. Wang. X. Gong, and Y. Chen. Iterative deblending of simultaneous source seismic data with structuring median constraint, IEEE Geoscience and Remote Sensing Letters. 15(1):58-8 62, 2017.
382
383
394
[22] Huo, Y. Luo, and P.G. Kelamis. Simultancous sources separation via multidircctional vector vector-median filtering. Geophysics, 77(4):123-131, 2012.
395
388
[23] Huo, Y. Luo, and P.G. Kelamis, Dehlending using space-varying median filter. Exploration
397
Geophysics, 46(4):332-341, 2015.
398
[24] A. Ihrahim and M.D. Sacchi. Simultancous souree separation using robust radon transform. Geaphysics, 79:VI-V11, 2014.
399
400
[25] P.R.S. Johann, E.A. Thedy, F.A. Gomes, and M.C. Schinelli. 4d scismic in brazil: Experiences in reservoir monitoring. Offshore Technology Conference, 2006.
401
402
[26] A. Krull, T.-O. Buchholz, and F. Jug. Noise2void - learning denoising from single noisy images. Proc. IEEE Conf. Comput. Vision Pattern Recognit., 2019.
403
404
[27] Laine, Karras, Lehtinen,
Aila. High-quality self- superviee deep image denoising. Advances in Neural Information Processing Systems, pages 6970-6980, 2019.
405
[28] J. Lehtinen. J. Munkberg. J. Hasselgren. S. Laine, T. Karras, M. Aittala, and T. Aila. Noise2noise: Learning image restoration without clean data. International Conference on Machine Learning (ICML), 2019.
407
408
[29] C. Li, C.C. Mosher, and Y. Ji. An amplitude-pessering deblending approach for simultancous sources. Geophysics, 84(3)-V 2019.
410
411
[30] C. Li, C.C. Mosher, and Y. Ji. Randomized marine acquisition with compressive sampling matrices. Geophysical Prospecting, 60(3):648-662, 2019.
413
[31] Jaminn Liu, Yu Sun, Cihat Eldeniz, Weijie Gan, Hongyu An, and Ulugbek S. Kamilov. Rare: Image reconstruction using deep priors learned without groundtruth. JSTSP, 14:1088-1099, 2020.
414
415
[32] S. Liu, C. Birnie, and T. Alkhalifah. Coherent noise suppression via a supervupe deep learning scheme. In 83rd EAGE Conference and Exhibition 2022, volume 2022, pages 1-5. European Association of Geoscientists & Engineers, 2022.
417
418
419
[33] A. Mahdad, Doulgeris, and G. Blacquiere. Separation of blended data by iterative estimation and subtraction of blending interference noise. Geophysics, 76:Q9 Q17.
429
421
[34] S. Mandelli, V. Lipari, Bestagini, and S. Tubaro. Interpolation and denoising of scismic data using convolutional neural networks, arXiv, 2019.
422
423
[35] T. Mcinhardt, M. Moller, C. Hazirhas, and D. Cremers. Learning proximal operators: Using
424
denoising networks for regularizing inverse imaging problems. In Proceedings of the IEEE International Conference Computer Vision, pages 1781-1790, 2017.
425
425
[36] I. Moore, B. Dragoset, T. Ommundsen, D. Wilson, C. Ward, and D. Eke. Simultaneous source separation using dithered sources. SEG Technical Program Expanded Abstracts, 2008.
428
[37] N. Parikh. Proximal Algorithmms. Foundations and Trends in Optimization, 2014.
429
[38] Romano, M. Elad, and P. Milanfar. The little engine that could: Regularization by denoising
430
(RED). SIAM Journal on Imaging Sciences, 18(4):1804-1844 2017.
431
[39] Ernest Ryu, Jialin Liu, Sicheng Wang, Xiaohan Chen, Zhangyang Wang, and Wotao Yin. aun--nnd-lay methods provably converge with properly trained denoisers. In International Conference on Machine Learning, pages 5546-5557 PMLR, 2019.
432
433
[40] Yousef Saad, Iterative methods for sparse linear systems. SIAM, 2003.
11

---

435
[41] R. E. Sheriff and L.P. Geldart. Exploration Seismology (2nd ed.). Cambridge University Press, 1995.
435
437
[42] A. Siahkoohi, M. Louboutin, and F. Herrmann. The importance of transfer learning seismic modeling and imaging. Geophysics, 84(6):A47-A52, 2019.
438
439
[43] Sun, S. Slang, Elboth, T.L. Greiner, S. McDonald, and I..J. Gelius. A convolutional neural network upprouch to deblending seismic data. Geophysics, 85(4):WA13 2020.
440
441
[44] Y. Sun, J. Liu, and U. Kamilov. Block coordinate regularization by denoising. In Advances Neural Information Processing Systems, pages 380-390, 2019.
442
463
[45] J.-B. Thibault, K.D. Sauer, C.A. Bouman, and J. Hsich. A fire-dimmensioa. statistical approach to improved image quality for multislice helical ct.
444
445
[46] Tirer and R. Giryes. Super-resolution via image-adapted de- noising CNNs: Incorporating external and internal learning. JEEE Signal Processing Letters, 26(7).
448
447
[47] T. Tirer and R. Giryes. Image restoration by iterative denoising and backward projections. IEEE Transactions on Image Processing, 28(3): 12200-1334, 2018.
448
419
[88] S.V Venkatakrishnan, C.A. Bouman, and B. Wohlberg. Plug-and-pll priors for model based reconstruction. 2013 IEEE Global Conference on Signal and Information Processing, 2013.
450
451
[49] S. Wang, W. Hu, P. Yuan, X. Wu, Q. Zhang, P. Nadukandi, G.O. Botero, and J. Chen. Seismic deblending by self-supervised deep learning with blind-trace network. SEG/AAPG/SEPM First International Meeting for Applied Geoscience Energy, 2021.
452
454
[50] Xiajian Xu, Yu Sun, Jiaming Liu, Brendt Wohlberg, and Ulugbek S. Kamilov. Provable convergence of plug-and aad-andd-paa play priors with mme denoisers. IEEE Signal Processing Letters, pages 1280-1284. 2020.
455
458
457
[51] Siwei Yu and Jianwei Ma. Deep learning for geophysics: Current and future trends. Reviews of Geophysics, 59 (233))2221RG0000000 2021.
459
[52] K. Zhang, Y. Li, W. Zuo, L. Zhang. L. van Gool, and R. Timofte. Plug-and-play image restoration with deep denoiser prior. In IEEE TPAMI, 2021.
461 [53] K. Zhang, W. Zuo. Y. Chen, D. Meng. and L. Zhang. Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising. IEEE Transactions Image Processing, pages 3142-3155 2017.
463
[54] K. Zhang, W. Zuo, S. Gu, and L. Zhang.
485
[55] H. Zhou, W. Mao, D. Zhang, Q. Ge. and H. Wang. Deblending of simultaneous source with lank-reductonn and thresholding constraints. 79th EAGE Conference and Kxhibition 20/7, 2017(1):1-5,20) 2017.
488
487
[56] Y. Zhou, W. Chen, and J. Gao. Separation of seismic blended data by sparse inversion over dictionary learning. Journal of Applied Geophysics. 106:146-155 2014.
[57] Y. Zhou, J. Gao, W. Chen, and P. Frossard. Seismic simultaneous source separation via patchwise sparse representation. IEEE Transactions Geoscience and Remote Sensing, 54(9):5271-5244 2016.
471
472
[58] S. Zu, J. Cao, S. Qu, and Y. Chen. Iterative deblending for simultancous source data using the deep neural network. Geophysics, (552):V131-V111 2020.
474
[59] S. Zu, H. Zhou, R. Wu, W. Mao, and Y. Chen. Hybrid-sparsiee constrained dictionary learning for iterative deblending of extremely noisy simultaneous- data, IEEE Transactions on Geoscience and Remote Sensing, 57(4):2249-226) 2018
475
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12


Reviews:
[{"review_id": "mIzV5vl3gCa", "reviewer": "Reviewer_TN2y", "summary": "This paper tackles the inverse problem of \"seismic deblending\" by using the well known \"Plug-And-Play\" (PnP) framework together with a recently proposed self-supervised denoiser, which is adapted to follow the noise structure of the particular problem at hand. Experiments on a real dataset artificially blended by the authors show that the approach outperforms a state-of-the-art method based on a Fourier sparsity prior, and an ablation study show that the proposed combination of PnP with a carefully trained self-supervised denoiser is efficient.", "questions": "The main question I have is: Is the proposed method without the PnP steps the same as [47] ? If so, this should be made very explicit in the method section and in the experimental results.\n\nI noted the following minor typos:\n- L136 : \"to to\"\n- L172 a image -> an image", "limitations": "The limitations and societal impact of the work are adequately addressed by the authors in section 6.", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "## Strengths\n- The paper is generally very didactic. Quite unusually, 5 out of 9 pages are devoted to the introduction, background and related work sections. In that sense, the paper can almost be regarded as a \"tutorial\" paper, giving a subsequent overview of the field of seismic deblending and of recently proposed self-supervised denoising techniques to non-expert readers.\n- The proposed approach is sound and seem to outperform a more conventional technique on a real dataset\n\n## Weaknesses\n- While 5 pages are devoted to introductory materials, only half a page is devoted to presenting the methodology. On the one hand this seems short, on the other hand, this can be explained by the fact that the proposed methodological contribution is very incremental: two relatively well-known existing techniques are straight-forwardly combined and applied to a known problem in the field.\n- The experiments are relatively limited, eventhough this may be justified by the lack of available real data for this problem. Still, more detailed quantitative results could have been provided.\n- No detail is given on the key \"StructBS\" step of the method (the self-supervised denoising), not the paper nor in the supplementary material. The reader is entirely referred to the recent reference [47] for this (in fact, the reference to [47] is implicit, and the acronym StructBS is never made explicit). This makes the methodological part of paper not self-contained, which is not good for research reproducibility and transmission.\n- A lot of important implementation details are scattered across the experimental section or in the appendix, which would make the proposed method very hard to reimplement\n- In the ablation study, not using the PnP iterations and using only self-supervised denoising seem to be equivalent to what is done in [47], but this is not explicitly stated by the authors. More details should be given on these results than a single number, since according to the authors themselves, [47] is the closest work to what they propose.\n\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "_eRv0hscmP", "reviewer": "Reviewer_okRD", "summary": "This paper proposed a plug-and-play (PnP) algorithm for reflection seismology (RS). The key concept of PnP is to leverage an image denoiser as an implicit regularizer to impose prior within an iterative optimization algorithm. By using deep image denoisers, PnP combines the physical constraints and trainable priors. Proposed algorithm in this paper combines PnP with self-supervised deep image denoisers to solve the RS problem.", "questions": "1. Besides the apparent benefits of self-supervised deep image denoiser, that is, no use of ground-truth data, what else motivates you to use such image denoiser? Why this is denoiser is necessary.\n\n2. Apart from the deep image denoiser, what else can be considered as contributions of the work?", "limitations": "Not applicable.", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strength:**\n- New application of PnP to reflection seismology (RS).\n\n**Weakness:**\n- The proposed method is not novel. The claimed novelty is the inclusion of self-supervised image denoiser in the PnP framework. However, this has been done in [1] for medical imaging.\n- The presentation of the work is not well organized. The introduction and background is too long while the method section is too short.\n\n[1] RARE: Image Reconstruction using Deep Priors Learned without Ground Truth", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "UkkONLflRVF", "reviewer": "Reviewer_Vpu2", "summary": "The paper introduces the problem of seismic deblending and provide a state-of-the art result in this problem using denoising network in the PnP setup. Denoising model is learned as a part of PnP. ", "questions": "1. Please consider weaknesses above as questions. ", "limitations": "Limitations are adequately addressed.", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 1, "contribution": 1, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "[strengths]\n1. Introduces Seismic Deblending to ML community. Seismic problems are generally less explored in ML community and this paper introduces a good problem. \n2. Good results with learned denoiser.\n\n[weaknesses]\n1. Writing : The paper devotes very less space to the main algorithm. PnP + denoiser. Also, for people who are not familiar with the ADMM algorithm like me, the section 4 reads very difficult with a lot of terms introduced but not explained like y_k , x-update, y-update, LSQR, StuctBS, theta. These details are provided partially in the supplementary. However more discussion space should be provided to the algorithmic part.\n\n2. Novelty: I am not sure if paper provides enough novelty for this conference. It uses denoiser architecture in a seismic setting and shows good results. However, it is not clear what the contributions are apart from applying existing denoiser in seismic PnP.\n\n3.  Experimental validation is limited. The experiments are performed on a single dataset. More empirical validation is needed.\n\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "HyUB-nL5gn", "reviewer": "Reviewer_fDvL", "summary": "This paper combines a self-supervised deep image denoising method and PnP framework to improve seismic deblending. The problem is interesting and significant. However, the rationale of the proposed algorithm is unclear. It seems like a combination of existing techniques and the technical contribution seems limited. ", "questions": "1. How is the blending operator decided? Why does it have the property of B^TB=I? Maybe a proper citation is needed here for the reader to better understand the background.\n2. What do t(s), x_R(m), and \\bar{\\bar{x}}_R(m) mean in Figure 1 b)? Also, why does the y-axis x_s(m) instead of x_R(m) in Figure 1 c)? What does m represent here?\n4. According to Figure 1 b), the input seems like an image. However, it is confusing how it is generated. What are the white curves and the horizontal dash line mean?\n5. What is the regularization term in the proposed optimization problem? How is y-update derived as StructBS(x+u)？\n7. How will the model perform if only adopting PnP framework but does not use the self-supervised denoiser? \n", "limitations": "The authors have adequately addressed the limitations and social impact of their work.", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strength:\n1. This paper aims to improve the performance of seismic deblending, which is a significant problem and can benefit geophysical studies.\n2. The authors explore to improve the conventional deblending problem with deep image denoising technology.\n3. The proposed method can outperform a conventional method according to the experiment.\n\nWeakness:\n1. This paper is poorly organized and the meanings of many symbols in formulas and figures are not well introduced (see Questions for detail). This makes it difficult to understand the background and the problem formulation. The reader needs to spend a long time reading this paper before understanding the problem.\n2. The authors introduced their algorithm very briefly in “Method”. The motivation of the proposed algorithm is unclear because the authors only provide the resulting update rules instead of showing the original optimization problem and the regularization term. Especially, the biggest modification to the algorithm in this paper seems to be using a self-supervised denoiser for y-update. However, the rationale behind it is confusing. I wonder how this update rule is derived. Indeed, too much essential information has been omitted. \n3. Partly because the authors did not give any theoretical illustrations for their algorithm, the technical contribution seems limited. According to the paper, the authors (1) follow the conventional optimization problem formulation of seismic blending/denoising; (2) use PnP framework to solve this optimization problem; (3) change a term for y-update (without properly explaining the rationale) based on the self-supervised image denoiser. Then, this paper seems like a combination of existing techniques. The inspiration it can bring to the community is limited.\n4. The experiments are not sound. The authors have mentioned in the related work that there are other seismic deblending/denoising methods. However, only one conventional method is used as the baseline. The authors should report their performance to better demonstrate the effectiveness of the proposed algorithm in comparison to SOTA. Otherwise, the authors should explain why the other methods are not applicable. \n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Reject