Variable Length Variable Quality Audio Steganography

1 INTRODUCTION . Natural images are redundant ( Ruderman , 1994 ) . They contain predictable structures , repeating textures , and non-uniform color distribution that contribute to their low overall entropy . Meanwhile , the human visual system is insensitive to minor changes to its visual field . These features make steganography , the science of hiding a secret data within a non-secret container data , possible . Several researches have hidden various data inside images such as binary messages ( Zhu et al. , 2018 ) , separate images ( Baluja , 2017 ; Tamimi et al. , 2013 ; Wu et al. , 2018 ; Zhang et al. , 2019a ; b ; Duan et al. , 2019 ) , and audio signals ( Kaul & Bajaj , 2013 ; Santosa & Bao , 2005 ; Huu et al. , 2019 ) . Here , we focus on the task of hiding audio inside images . Many algorithms have successfully hidden audio data inside images , especially with the recent advances on deep learning based steganography . However , the use of deep learning restricts these algorithms to only receiving input dimensions that are allowed by the design of the network architecture , which usually have fixed dimensions . This condition makes these methods difficult to operate in the real world , where the signals may easily vary in length . Naively applying these traditional models iteratively on different chunks of the audio fails to work , as the input distribution starts to diverge from that of the training set . Furthermore , as the bottleneck of most steganographic systems comes from the container data ’ s capacity , hiding a varying length signal inside a fixed-sized container requires the capability to trade-off audio quality and image fidelity . One approach to do so is by changing the coefficients of the different loss terms that each control the reconstruction quality of the container and the secret data . However , this requires the training of several systems with different coefficients , which is not only time and memory consuming , but also fails to cover the full continuous range of possible coefficient combinations . We propose a new steganographic framework VLVQ ( Variable Length Variable Quality Audio Steganography ) to encode variable length audio signals in an image and make audio quality and image fidelity trade-off with a single model on inference time . Figure 1 demonstrates an example of VLVQ encoding 19 seconds of audio inside an 224x224 image then decoding it back . Given the initial container image , VLVQ iteratively embeds an audio chunk inside the image until all of the audio has been encoded . To recover the audio back from this final container image , VLVQ isolates the latest audio chunk embedded inside the container , and update the container image to feed itself back into the decoder recursively . This is repeated until all audio is recovered . An important design choice is to use the trade-off coefficient that linearly weighs the image and audio reconstruction quality as an input to the network . By randomly sampling this coefficient at each training step and feeding it as input to the model , a single model can learn a distribution of solutions . Section 2 reviews previous works related to VLVQ . Section 3 describes the problem setup and VLVQ ’ s methodology in depth . Then , Section 4 evaluates our approach on ImageNet ( Russakovsky et al. , 2015 ) and AudioSet ( Gemmeke et al. , 2017 ) , demonstrating reasonable reconstruction quality even on signals longer than what is seen during training . Finally , Section 5 discusses various observations and possible directions for future work . 2 RELATED WORKS . Image Steganography . Steganography is the task of encoding a secret data inside a non-secret container data without making noticeable changes to the container . Image steganography describes a scenario that uses an image as the container that carries the secret data . The limitations of the human visual system in noticing slight changes in brightness or color among many pixels make these image steganography methods effective . Traditional image steganography methods exploit the image spatial domain by modifying the least significant bits ( LSB ) of the image , or the frequency domain with Discrete Fourier Transform ( DFT ) , Discrete Cosine Transform ( DCT ) , and Discrete Wavelet Transform ( DWT ) . With the help of recent advancements in learning-based algorithms , steganographic systems have seen tremendous advancements . Many of the learning-based steganographic systems employs deep neural networks that are trained end-to-end with reconstruction losses that minimize the change in the container while maximizing the similarity between the recovered secret data and the ground truth . Baluja ( 2017 ) uses convolutional architecture to hide images inside images , while Zhu et al . ( 2018 ) adopts differentiable augmentations to hide and recover binary data inside images with robustness to image corruptions . Different approaches make improvements in architectural designs ( Duan et al. , 2019 ; Cui et al. , 2020 ; Wu et al. , 2018 ) while some adopt Generative Adversarial Networks ( GANs ) ( Goodfellow et al. , 2014 ) to make the changes further imperceptible . Hiding Audio in Image . Hiding audio signal inside images is a specific instance of image steganography . Similar to image steganography in general , methods such as modifying the least significant bits ( LSB ) ( Kaul & Bajaj , 2013 ) as well as wavelet transformations ( Kaul & Bajaj , 2013 ; Santosa & Bao , 2005 ) have been applied to the task . Deep learning based approaches such as Huu et al . ( 2019 ) encodes STFT features of audio into the container image with a convolutional architecture . Ye et al . ( 2019 ) incorporates GANs . Still , these methods are limited to fixed dimensional inputs , prohibiting its applications in the real world with audio signals that vary in length . Loss-Conditional Training . Generally , deep learning handles multi-objective training by linearly combining the different sub-objective terms with their respective coefficients . If the coefficient values are closely tied to the model ’ s use cases , one must train multiple models with different coefficient combinations to cover all such cases , which is computationally expensive and impractical . Lossconditional training resolves this by conditioning the model on the randomly sampled coefficients during training . Babaeizadeh & Ghiasi ( 2018 ) first adopted loss-conditional training in style transfer to make the style and content coefficients in style transfer adjustable at inference time . Dosovitskiy & Djolonga ( 2019 ) then proposed a general framework for loss-conditional training , demonstrating its applications in autoencoder , image compression , and style transfer . Lee et al . ( 2020 ) adopts loss-conditional training in creating a dynamic residual network with adaptable sparsity . Since the importance of audio data reconstruction quality varies among the different use cases of steganography ( e.g. , in speaker identification , high audio quality may not be necessary as long as the voice is identifiable ) , we adopt an optional loss-conditional training process to allow the trade-off between these two objectives at inference time . 3 METHOD . In this section , we describe the VLVQ ( Variable Length and Variable Quality Audio Steganography ) framework in detail . We first describe the problem setting , then elaborate on the specific methods . Please refer to Algorithm 1 for an overview of the methods . 3.1 PROBLEM SETUP . In steganography , a system H takes a container data c with a secret data s to produce a modified container ĉ = H ( c , s ) that encodes s while remaining visually similar to c. Then , a system F takes ĉ to recover the secret data s ∼ ŝ = F ( ĉ ) . In Audio-in-Image Steganography , c is an image , and s is an audio of variable length . Since the container ’ s capacity is the limiting factor in what is capable of being hidden , we adopt γ to represent the trade-off parameter between the reconstruction quality of the container and the secret data . Here , a larger value of γ increases the quality of the audio reconstruction at the sacrifice of the container image quality , while a smaller value makes the change on the container image less noticeable at the sacrifice of the audio reconstruction quality . The audio data goes through STFT ( Short-Time Fourier Transform ) during the preprocessing step and converts into the frequency domain . This makes s , ŝ ∈ RN×T×2 , with N as the number of frequencies , T as the varying length of the audio , and 2 as the real and complex channel . c and ĉ is Algorithm 1 : VLVQ Framework conditioned on γ Result : Fully trainedH and F Algorithm parameters : Container image c , Secret audio s , γ range γmin , γmax , total iteration Ttotal , audio chunk number range Cmin , Cmax , frequency number and image resolution h , w ; InitializeH , F with random weights ; repeat Ttotal times Sample random integer k in range [ Cmin , Cmax ] ; Let T = w × k , c1 = c ; Sample γ from log ( γ ) ∼ U ( log ( γmin ) , log ( γmax ) ) ; Sample s ∈ Rh×T×2 and c ∈ Rh×w×3 from the dataset ; Crop s into si ∈ Rh×w×2 , i = 1 . . . k ; for i = 1 to k do ci+1 = H ( ci , si , γ ) ; end ĉk+1 = ck+1 ; for i = k + 1 to 2 do ĉi−1 , ŝi−1 = F ( ĉi , γ ) ; end Limg = 1k ∑k+1 i=2 ||ci − c1||2 ; Ldec = 1k ∑k i=1 ||ĉi − ĉi+1||2 ; Lstft = 1k ∑k i=1 ||si − ŝi||2 ; Ltotal = Limg + Ldec + γLstft ; Backpropagate and optimizeH and F with respect to Ltotal ; end an RGB image with c , ĉ ∈ Rh×w×3 . We set N = h = w for simplicity and only use h and w to denote spatial dimensions , thus s , ŝ ∈ Rh×T×2 . 3.2 RECURSIVE PATCH INFERENCE . Algorithm . T is a value that changes across different inputs . However , having T = h = w would keep the spatial resolution of both s and c identical and constant , which is an ideal condition for inference on a deep neural network . We sample s to have T as a multiple of w during training , so we can crop s into k = Tw chunks , with each chunk si ∈ R h×w×2 , i = 1 . . . k. To guarantee this during inference , we pad s to s ∈ Rh×wd Tw e×2 and crop s into k = dTw e chunks . Encoding Process . Let ci denote the container image with i − 1 audio chunks encoded inside . c1 = c , and ci+1 = H ( ci , si ) , which denotes that the current container and a chunk of the secret data is fed into H to update the container , and it is recursively fed back into H with the next chunk of the secret data until i = k + 1 . Finally , ĉk+1 = ck+1 , which denotes the final container that conceals all the audio chunks . Decoding Process . Then , ĉi−1 , ŝi−1 = F ( ĉi ) , which recursively feeds the container image to F to decode each audio chunks , while updating the container image to recursively feed itself back into F . With this process , we obtain ŝ1 . . . ŝk that corresponds to s1 . . . sk . Figure 3 visualizes both the encoding and the decoding process .

Summary: The paper presents a method for steganography, that is to encode and decode an audio signal into an image in an unnoticeable way. The feature of the proposed method is that it can handle audio with variable length, and can flexibly trade-off between audio encoding quality and image modification unnoticeability in the inference stage. The method is to learn a pair of encoder and decoder to achieve both encoding and unnoticeability up to some trade-off, and the trade-off coefficient is also input into the model to avoid retraining for an arbitrary trade-off in inference.