Wyner-Ziv video coding for wireless lightweight multimedia applications

2.1. Slepian-Wolf coding

Consider the compression of two correlated, discrete, identically and independently distributed (i.i.d.) random sources X and Y. According to Shannon's source coding theory [14], the achievable lower rate bound for lossless joint encoding and decoding is given by the joint entropy H(X, Y) of the sources. Slepian and Wolf [2] studied the lossless compression scenario in which the sources are independently encoded and jointly decoded. According to their theory, the achievable rate region for decoding X and Y with an arbitrarily small error probability is given by R _X ≥ H(X|Y), R _Y ≥ H(Y|X), R _X + R _Y ≥ H(X, Y), where H(X|Y) and H(Y|X) are the conditional entropies of the considered sources, and R _X , R _Y are the respective rates at which the sources X and Y are coded, i.e., the Slepian-Wolf theorem states that even when correlated sources are encoded independently, a total rate close to the joint entropy suffices to achieve lossless compression.

The Slepian-Wolf theorem constructs a random binning argument, in which the employed code generation is asymptotic and non-constructive. In [15], Wyner pointed out the strong relation between random binning and channel coding, suggesting the use of linear channel codes as a practical solution for Slepian-Wolf coding. Wyner's methodology was recently used by Pradhan and Ramchandran [16], in the context of practical Slepian-Wolf code design based on conventional channel codes like block and trellis codes. In the particular case of binary symmetric correlation between the sources, Wyner's scheme can be extended to state-of-the-art binary linear codes, such as Turbo [5, 17], and low-density parity-check (LDPC) codes [18], approaching the Slepian-Wolf limit. A turbo scheme with structured component codes was used in [17] while parity bits instead of syndrome bits were sent in [5]. Although breaking the close link with channel coding, characterized by syndromes and coset codes, the latter solutions offer inherent robustness against transmission errors.

2.2. Wyner-Ziv coding

Wyner-Ziv coding [3] refers to the problem of lossy compression with decoder side information. Suppose X and Y are two statistically dependent i.i.d. random sources, where X is independently encoded and decoded using Y as side information. The reconstructed source $\widehat{X}$ has an expected distortion $D=Ed\left(x,\widehat{x}\right)$. According to the Wyner-Ziv theorem [3], a rate loss is sustained when the encoder is ignorant of the side information, namely $R_{X\left|Y\right.}^{*}\left(D\right)\ge R_{X\left|Y\right.}\left(D\right)$, where $R_{X\left|Y\right.}^{*}\left(D\right)$ is the Wyner-Ziv rate and R _X|Y (D) is the rate when the side information is available to the encoder as well. However, Wyner and Ziv further showed that equality holds for the quadratic Gaussian case, namely the case where X and Y are jointly Gaussian and a mean-square distortion metric d(•,•) is used.

Initial practical Wyner-Ziv code design focused on finding good nested codes among lattice [19] and trellis-based codes [16] for the quadratic Gaussian case. However, as the dimensionality increases, lattice source codes approach the source coding limit much faster than lattice channel codes approach capacity. This observation has induced the second wave of Wyner-Ziv code design which is based on nested lattice codes followed by binning [20]. The third practical approach to Wyner-Ziv coding considers non-nested quantization followed by efficient binning, realized by a high-dimensional channel code [5]. Other constructions in the literature propose turbo-trellis Wyner-Ziv codes, in which trellis coded quantization is concatenated with a Turbo [21] or an LDPC [22] code.

2.3. DVC

One of the applications of DSC that has received a substantial amount of research attention is DVC. Except for providing low-complexity encoding solutions for video, Wyner-Ziv coding has been shown to provide error resilient video coding by means of distributed joint-source channel coding [23], or systematic forward error protection [24]. Moreover, layered Wyner-Ziv code [25] constructions support scalable video coding [23].

An early practical DVC implementation was the PRISM codec [4], combining Bose-Chaudhuri-Hocquenghem channel codes with efficient entropy coding and performing block-based joint decoding and motion estimation. An additional CRC check was sent to the decoder to select between many decoded versions of a block, each version in fact corresponding to a different motion vector. An alternative DVC architecture, that implemented Wyner-Ziv coding as quantization followed by turbo coding using a feedback channel to enable decoder-driven optimal rate control, was presented in [5]. In this architecture, side information was generated at the decoder using motion-compensated interpolation (MCI). The architecture was further improved upon, resulting in the DISCOVER codec [26], which included superior MCI [27] through block-based bidirectional motion estimation and compensation combined with spatial smoothing. The DISCOVER codec is a well-established reference in DVC, delivering state-of-the-art compression performance.

In sequences with highly irregular motion content, blind motion estimation at the decoder, by means of MCI for example, fails to deliver adequate prediction quality. One technique to overcome this problem is to perform hash-based motion estimation at the decoder. Aaron et al. [28] proposed a hash code consisting of a coarsely sub-sampled and quantized version of each block in a Wyner-Ziv frame. The encoder performed a block-based decision whether to transmit the hash. For the blocks for which a hash code was sent, hash-based motion estimation was carried out at the decoder, while for the rest of the blocks, for which no hash was sent, the co-located block in the previous reconstructed frame was used as side information. In [29], several hash generation approaches--either in the pixel or in the transform domain--were investigated. It was shown that hash information formed by a quantized selection of low-frequency DCT bands per block was outperforming the other methods [29]. In [12], a block-based selection, based on the current frame to be coded and its future and past frames in hierarchical order, was performed at the encoder. Blocks for which MCI was foreseen to fail were low-quality H.264/AVC Intra encoded and transmitted to the decoder to assist MCI. The residual frame, given by the difference between all reconstructed intra coded blocks or the central luminance value (for non-hash blocks) and the corresponding blocks in the Wyner-Ziv frame, was formed and Wyner-Ziv encoded. In our previous study [30], we have introduced a hash-based DVC, where the auxiliary information conveyed to the decoder comprised a number of most significant bit-planes of the original Wyner-Ziv frames. Such a bit-plane-based hash facilitates accurate decoder-side motion estimation and advanced probabilistic motion compensation [31]. Transform-domain Wyner-Ziv encoding was applied on the remaining least significant bit-planes, defined as the difference of the original frame and the hash [31]. In [32], hash-based motion estimation was combined with side information refinement to further improve the compression performance at the expense of minimal structural decoding delay.

Driven by the requirements of niche applications like wireless capsule endoscopy, this study proposes a novel hash-based DVC architecture introducing the following novelties. First, in contrast to our previous DVC architectures [30, 31], which employed a bit-plane hash, the presented system generates the hash as a downscaled and subsequently conventionally intra coded version of the original frames. Second, unlike our previous study [30–32], the hash is exploited in the design of a novel motion-compensated multi-hypothesis prediction scheme, which is able to adapt to the regional variations in temporal correlation in a frame by extracting information from the hash when temporal prediction is untrustworthy. Compared to alternative techniques in the literature, i.e., [12, 13, 26, 27], the proposed methodology delivers superior performance under strenuous conditions, namely, when irregular motion content is encountered as in for example endoscopic video material, where gastrointestinal contractions can generate severe morphological distortions in conjunction with extreme camera panning. Third, the way the hash is constructed and utilized to generate side information in the proposed codec also differs from the approaches in [28, 29]. Fourth, conversely to alternative hash-based DVC systems [12, 31], the proposed architecture codes the entire frames using powerful channel codes instead of coding only the difference between the original frames and the hash. Fifth, unlike existing works in the literature, this article experimentally shows the state-of-the-art compression performance of the proposed DVC not only on conventional test sequences, but also on traditional and wireless capsule endoscopic video content, while low-cost encoding is guaranteed.

3.1. Wireless lightweight many-to-many video communication

Wyner-Ziv video coding can be a key component to realize many-to-many video streaming over wireless networks. Such a setting demands optimal video streams, tailored to specific requirements in terms of quality, frame-rate, resolution, and computational capabilities imposed by a set of recorders and receivers. Consider a network of wireless visual sensors that is deployed to monitor specific scenes, providing security and surveillance. The acquired information is gathered by a central node for decoding and processing. Wireless network surveillance applications are characterized by a wide variety of scene content, ranging from complex motion sequences, e.g., crowd or traffic monitoring, to surveillance of scenes mostly devoid of significant motion, e.g., fire and home monitoring.

In such scenarios, wireless visual sensors are understood to be cheap, battery powered and modest in terms of complexity. In this concept, Wyner-Ziv video coding facilitates communications from the sensors to the central base station, by maintaining low computational requirements at the recording sensor, while simultaneously ensuring fast, highly efficient, and scalable coding. From a complementary perspective, a conventional predictive video coding format with low-complexity decoding characteristics provides a broadcast oriented one-to-many video stream for further dissemination from the base station. Such a video communications' scenario centralizes the computational complexity in the fixed network infrastructure, which would be responsible for transcoding the Wyner-Ziv video coding streams to a conventional format.

3.2. Wireless capsule endoscopy

Although the history of ingestible capsules for sensing purposes goes surprisingly back to 1957, it was the semiconductor revolution of the 1990s that created a rush in the development of miniaturized devises performing detailed sensing and signal processing inside the body [33]. Among the latest achievements in this regard is wireless capsule endoscopy, which aims at providing visual recordings of the human digestive track. From a technological perspective, capsule endoscopic video transmission poses an interesting engineering challenge. Encapsulating the appropriate system components comprising a camera, light source, power supply, CPU, or memory in a biocompatible robust ingestible housing--see Figure 1, resistant to the gatrointestinal's hostile environment, is no easy task. The reward however is great. Capsule endoscopy has been shown to have a superior positive diagnosis rate compared to other methods, including push enteroscopy, barium contrast studies, computed tomographic enteroclysis, and magnetic resonance imaging [11]. The principal drawback of contemporary capsule endoscopes is that they only detect and record but are unable to take biopsies or perform therapy. In case a pathology is diagnosed, a more uncomfortable or even surgical therapeutic procedure is necessary. Nevertheless, because of its valuable diagnostic potential, the clinical use of capsule endoscopy has a bright future. Namely, wireless endoscopy offers the only non-invasive means to examine areas of the small intestine that cannot be reached by other types of endoscopy such as colonoscopy or esophagogastroduodenoscopy [11]. In addition to this, capsule endoscopy offers a less unpleasant alternative to traditional endoscopy, lowering the threshold for preventive periodic screening procedures, where the large majority of patients are actually healthy.

Focussing on the video coding technology part, it is apparent that wireless endoscopy is subjected to severe constraints in terms of available computational capacity and power consumption. Contemporary capsule video chips employ conventional coding schemes operating in a low-complexity, intra-frame mode, i.e., Motion JPEG [34], or even no compression at all. Current capsule endoscopic video systems operate at modest frame resolutions, e.g., 256 × 256 pixels, and frame rates, e.g., 2-5 Hz, on a battery life time of approximately 7 h. Future generations of capsule endoscopes are intended to transmit at increased resolution, frame rate, and battery life time and will therefore require efficient video compression at a computational cost as low as possible. In addition, a video coding solution supporting temporal scalability has an attractive edge, enabling increased focus during the relevant stages of the capsules bodily journey. DVC is a strong candidate to fulfil the technical demands imposed by wireless capsule endoscopy, offering low-cost encoding, scalability, and high compression efficiency [10].

4.1. The encoder

Every incoming frame is categorized as a key or a Wyner-Ziv frame, denoted by K and W, respectively, as to construct groups of pictures (GOP) of the form KW ...W. The key frames are coded separately using a conventional intra codec, e.g., H.264/AVC intra [1] or Motion JPEG.^b The Wyner-Ziv frames on the other hand are encoded in two stages. For every Wyner-Ziv frame, the encoder first generates and codes a hash, which will assist the decoder during the motion estimation process. In the second stage, every Wyner-Ziv frame undergoes a discrete cosine transform (DCT) and is subsequently coded in the transform domain using powerful channel codes, thus generating a Wyner-Ziv bit stream.

4.2. The decoder

The main components of the presented DVC architecture's decoding process are treated separately, namely dealing with the hash, side information generation and Wyner-Ziv decoding. The decoder first conventionally intra decodes the key frame bit stream and stores the reconstructed frame in the reference frame buffer. In the following phase, the hash is handled, which is detailed next.

4.2.2. Side information generation

After the hash has been restored to the same frame size as the original Wyner-Ziv frames, it is used to perform decoder-side motion estimation. The quality of the side information is an important factor on the overall compression performance of any Wyner-Ziv codec, since the higher the quality the less channel code rate is required for Wyner-Ziv decoding. The proposed side information generation algorithm performs bidirectional overlapped block motion estimation (OBME) using the available hash information and a past and a future reconstructed Wyner-Ziv and/or key frame as references.

Temporal prediction is carried out using a hierarchical frame organization, similar to the prediction structures used in [5, 12, 26]. It is important to note that conversely to our previous study [30], in which motion estimation was based on bit-planes, this study follows a different approach regarding the nature of the hash as well as the block matching process. Before motion estimation is initiated, the reference frames are preprocessed. Specifically, to improve the consistency of the resulting motion vectors, the reference frames are first subjected to the same downsampling and interpolation operation as the hash.

Figure 3 contains a graphical representation of the motion estimation algorithm. To offer a clear presentation of the proposed algorithm, we introduce the following notation. Let $\tilde{W}$ be the reconstructed hash of a Wyner-Ziv frame, let Y be the side information and let ${\tilde{R}}_k$, k ∈ {0,1} be the preprocessed versions of the reference frames R _k , respectively. Also, denote by Y _m , R_k,m, ${\tilde{W}}_{\mathbf{m}}$, ${\tilde{R}}_{k,\mathbf{m}}$ the blocks of size B × B pixels with top-left coordinates m = (m₁, m₂) in Y, R _k , $\tilde{W}$ and ${\tilde{R}}_k$, respectively. Finally, let Y _m (p) designate the sample at position p = (p₁, p₂) in the block Y _m .

At the outset, the available hash frame is divided into overlapping spatial blocks, ${\tilde{W}}_{\mathbf{u}}$, with top-left coordinates u = (u₁, u₂), using an overlapping step size ε ∈ ℤ₊, 1 ≤ ε ≤ B. For each overlapping block ${\tilde{W}}_{\mathbf{u}}$, the best matching block within a specified search range ρ, is found in the reference frames ${\tilde{R}}_k$. In contrast to our earlier study [30], the proposed algorithm retains the motion vector v = (v₁, v₂), -ρ <v₁, v₂ ≤ ρ, which minimizes the sum of absolute differences (SAD) between ${\tilde{W}}_{\mathbf{u}}$ and a block ${\tilde{R}}_{k,\mathbf{u}-\mathbf{v}}$, v = (v₁, v₂), in other words

$\mathbf{v}=arg\underset{\mathbf{v}}{min}\sum _{\mathbf{p}}\left|{\tilde{W}}_{\mathbf{u}}\left(\mathbf{p}\right)-{\tilde{R}}_{k,\mathbf{u}-\mathbf{v}}\left(\mathbf{p}\right)\right|,$

(3)

where p visits all the co-located pixel positions in the blocks ${\tilde{W}}_{\mathbf{u}}$ and ${\tilde{R}}_{k,\mathbf{u}-\mathbf{v}}$, respectively. The motion search is executed at integer-pel accuracy and the obtained motion field is extrapolated to the original reference frames R _k . By construction, every pixel Y(p), p = (p₁, p₂) in the side information frame Y is located inside a number of overlapping blocks $Y_{{\mathbf{u}}_n}$ with u _n = (u_n,1, u_n,2). After the execution of the OBME, a temporal predictor block $R_{k,{\mathbf{u}}_n}$ for every block $Y_{{\mathbf{u}}_n}$ has been identified in one reference frame. As a result, each pixel Y(p) in the side information frame has a number of associated temporal predictors $r_{k,{\mathbf{u}}_n}$ in the blocks $R_{k,{\mathbf{u}}_n}$.

However, some temporal predictors may stem from rather unreliable motion vectors. Especially when the input sequence was recorded at low frame rates or when the motion content is highly irregular, as might be the case in endoscopic sequences, temporal prediction is not the preferred method for all blocks at all times. Therefore, to avoid quality degradation of the side information due to untrustworthy predictors, all obtained motion vectors are subjected to a reliability screening. Namely, when the SAD, based on which the motion vector associated with temporal predictor $r_{k,{\mathbf{u}}_n}$ was determined, is not smaller than a certain threshold T, the motion vector and associated temporal predictor is labeled as unreliable. In this case, a temporal predictor for the side information pixel Y(p) is replaced by the co-located pixel of Y(p) in the upsampled hash frame, that is $\tilde{W}\left(\mathbf{p}\right)$. In other words, when motion estimation is considered not to be trusted, the hash itself is assumed to convey more dependable information. This feature of OBME is referred to as hash-predictor-selection (HPS).

During the motion compensation process, the obtained predictors per pixel, whether being temporal predictors or taken from the upsampled hash, are combined to perform multi-hypothesis pixel-based prediction. Specifically, every side information pixel Y(p) is calculated as the mean value of the predictor values $g_{k,{\mathbf{u}}_n}$:

$Y\left(\mathbf{p}\right)=\frac{1}{N_{k,{\mathbf{u}}_n}}\sum _{{\mathbf{u}}_n}{g}_{k,{\mathbf{u}}_n},$

(4)

where, $N_{k,{\mathbf{u}}_c}$ denotes the number of predictors for pixel Y(p) and $g_{k,{\mathbf{u}}_n}=r_{k,{\mathbf{u}}_n}$ when $r_{k,{\mathbf{u}}_n}$ is reliable or $g_{k,{\mathbf{u}}_n}=\tilde{W}\left(\mathbf{p}\right)$ when $r_{k,{\mathbf{u}}_n}$ is unreliable. The derived multi-hypothesis motion field is employed in an analogous manner to estimate the chroma components of the side information frame from the chroma components of the reference frames R _k or the upsampled hash.

5. 1. Evaluation on conventional test sequences

The experimental results in Figures 4 and 5 show that the proposed hash-based DVC regularly outperforms the DISCOVER [26] codec. Notice that when the size of the GOP and the amount of motion in the sequence increases, the overall compression performance of the DISCOVER codec notably decreases with respect to the proposed DVC, which is mainly due to the quality degradation of DISCOVER's MCI-based side information generation. Hence, the proposed system consistently outperforms DISCOVER in Foreman, Ice, and Soccer, all of which contain rather complex motion patterns (above all Soccer), and this for both GOP sizes. Especially for a GOP size of 8, the recorded gains are significant with BD rate savings [42] of 24.77, 26.30, and 32.13%, in Foreman, Ice, and Soccer, respectively. Comparing the compression performance of both DVC systems on the Silent sequence, which contains a low amount of motion activity, the MCI-based DISCOVER slightly surpasses the proposed DVC. This is due to the fact that in low-motion sequences a hash is not required to accurately capture the motion pattern at the decoder, as this can be simply achieved via interpolation. The incurred loss in RD per-formance is albeit reasonable, at the level of 7.9% for GOP2, and decreasing with growing GOP size to 5.4% for GOP8.

To further evaluate the performance of our proposed scheme, the coding results of [12] are included in Figure 4. The hash-based Wyner-Ziv video codec of [12] combines MCI with hash-driven motion estimation using low quality H.264/AVC Intra coded Wyner-Ziv blocks to generate side information. Even though the codec of [12] advances over DISCOVER, our proposed hash-based solution generally exhibits higher performance bringing BD rate savings of 17.68 and 12.18% in Foreman and Soccer, in GOP8, respectively.

Lastly, the proposed DVC is compared with H.264/AVC Intra, which represents the low-complexity configuration of the state-of-the-art traditional coding paradigm. One can observe from Figure 5 that in low-motion sequences the proposed codec is superior to H.264/AVC Intra, bringing BD rate savings of up to 26.7% in Silent, GOP8. However, under difficult motion conditions like in Ice or Soccer H.264/AVC Intra is very efficient compared to DVC systems, which is in agreement with the results shown in Figures 4 and 5. We emphasize that the encoding complexity of H.264/AVC Intra is much higher than any of the presented DVC solutions, as discussed in Section 5.3.

In Figure 6, we schematically depict the contribution of the LPDCA, the hash, and the key-frame rate to the total rate of the proposed coding system. The results show that as the GOP size increases, namely as more Wyner-Ziv frames are coded, the hash and the LDPCA rates increase, whereas the key-frame rate decreases. Notice also that, for a given sequence and GOP size, as the total rate increases from RD points 1 to 4, the contribution of the hash rate diminishes in favor of the LDPCA rate. Furthermore, the relative contribution of the hash rate to the total rate becomes smaller when high-motion sequences are coded--see Figure 6b, since relatively more LDPCA rate is spent.

5.2. Evaluation on endoscopic video sequences

A major contribution of this article is the assessment of Wyner-Ziv coding for endoscopic video data, characterized by its unique content. In the proposed codec, the quantization parameters of the Wyner-Ziv frames, the key frames, and the hash are meticulously selected so as to retain high and quasi-constant decoded frames' quality, as demanded by medical applications. Furthermore, in order to deliver high-quality decoding under the strenuous conditions of highly irregular motion content and low frame acquisition rates, the proposed codec employs a GOP size of 2.

Initially, in order to prove the potential of its application in contemporary wireless capsule endoscopic technology, the proposed codec has been appraised using four capsule endoscopic test video sequences visualizing diverse areas of the gastrointestinal track. These sequences were extracted from extensive capsule endoscopic video material of two capsule examinations from two random volunteers^f performed at the Gastroenterology Clinic of the Universitair Ziekenhuis Brussels, Belgium. In the aforementioned clinical examinations, the capsule acquisition rate was two frames per second with a frame resolution of 256 × 256 pixels. The obtained test video sequences^g are termed "Capsule Test Video 1" to "Capsule Test Video 4" in the remainder of the article.

In the set of experiments comprising capsule endoscopic video content, Motion JPEG has been set as benchmark, since this technology is commonly employed in up-to-date capsule endoscopes [34]. To enable a fair comparison, Motion JPEG has also been employed to code the key and the hash frames in the proposed codec. We note that in this experimental setting the luma (Y) and the chroma (U and V) components were coded. The results, which are illustrated in Figure 7, show that the proposed codec generally outperforms Motion JPEG for the capsule endoscopic sequences. In particular, in "Capsule Test Video 1" and "Capsule Test Video 2" the proposed codec brings average Bjøntegaard rate savings of, respectively, 6.16 and 9.33% against Motion JPEG.

Figure 7 also evaluates the impact of the flexible scheme that enables the proposed OBME method to identify erroneous motion vectors and to replace the temporal predictor pixel with the decoded and interpolated hash. The results show that the proposed system with the HPS module remarkably advances over its equivalent that solely retains predictors from the reference frames. Specifically, in "Capsule Test Video 1" to "Capsule Test Video 4" adding the HPS functionality results in BD [42] rate improvements of 21.1, 16.02, 12.93, and 12.06%, respectively.

The visual assessment of the proposed codec (with HPS) compared to Motion JPEG for a Wyner-Ziv frame of "Capsule Test Video 1" and "Capsule Test Video 2" is depicted in Figures 8 and 9, respectively.

Future generations of capsule endoscopic technology aim at diminishing the quality difference with respect to conventional endoscopy by increasing the frame rate and resolution. Therefore, to confirm its capability under these conditions, the proposed Wyner-Ziv video codec is evaluated using conventional endoscopic video sequences monitoring diverse parts of the digestive track of several patients. The endoscopic test video sequences considered in this experimental setting have a frame rate of 30 Hz and a frame resolution of 480 × 320 pixels. These endoscopic test video sequences are further referred to as "Endoscopic Test Video 1" to "Endoscopic Test Video 6". In this experiment, the proposed codec employs H.264/AVC Intra (Main profile) to code the key and the hash frames. Notice that the H.264/AVC Intra codec constitutes a recognized reference for medical video compression, e.g. [43].

In Figure 10, the proposed DVC system (with and without HPS) is evaluated against the H.264/AVC Intra and our previous TDWZ codec of [13]. The latter features an MCI framework comprising overlapped block motion compensation to generate side information at the decoder. The TDWZ codec of [13] provides state-of-the-art MCI-based DVC performance, outperforming the DISCOVER [26] codec. Remark that the DISCOVER codec could not be included in the comparison since it does not support the frame resolution of the video data. The results are provided only for the luma component of the sequences "Endoscopic Test Video 1" to "Endoscopic Test Video 4", since the codec in [13] does not support chroma encoding. The experimental results depicted in Figure 10 show that the proposed codec (with HPS) delivers significant compression gains over the state-of-the-art TDWZ codec of [13]. Specifically, in "Endoscopic Test Video 1" and "Endoscopic Test Video 2" the proposed codec introduces average BD [42] rate savings of 43.14 and 43.37%, respectively. These remarkable compression gains clearly motivate the proposed hash-based Wyner-Ziv architecture comprising our novel motion-compensated multi-hypothesis prediction scheme over MCI-based solutions.

Compared to H.264/AVC Intra, the experimental results in Figure 10 show that the proposed codec delivers BD rate savings of 4.1% in "Endoscopic Test Video 2". In "Endoscopic Test Video 1" and "Endoscopic Test Video 3" the proposed codec falls behind H.264/AVC Intra, incurring a BD rate loss of 3.84 and 0.20%, respectively. Only in "Endoscopic Test Video 4", which comprises highly irregular motion, the experienced Bjøntegaard rate overhead is notable amounting to 15.68%. Notice that the benefit of the HPS functionality of the proposed codec is reduced in case of conventional endoscopic video with respect to the capsule endoscopic sequences. This is due to the fact that the former sequences were recorded at a much higher frame rate and contain more temporal correlation. Nevertheless, in "Endoscopic Test Video 4" the HPS module brings BD rate savings of 4.63%.

To benchmark the performance of the presented codec (with HPS) against H.264/AVC when all three Y, U, and V components are coded, both systems are also tested on "Endoscopic Test Video 5" and "Endoscopic Test Video 6". The results, see Figure 11, show that the proposed codec outperforms the competition. Specifically, the proposed codec delivers a significant BD rate reduction of 12.41 and 18.61% in "Endoscopic Test Video 5" and "Endoscopic Test Video 6", respectively.

Visual comparisons between TDWZ [13] and the proposed codec are given in Figures 12 and 13. The proposed codec yields significantly better visual quality and does not suffer from blocking artefacts, typically affecting TDWZ [13] at this rate. The superior visual quality delivered by the proposed system compared to the state-of-the-art TDWZ codec of [13] confirms the potential of the former in medical imaging applications, where high visual quality is a fundamental demand.

5.3. Encoding complexity

Low-cost encoding is a key aspect of distributed video compression. During the evaluation of the DISCOVER [26] codec, it was shown that the Wyner-Ziv frames' encoding complexity is very low compared to the complexity associated with the intra encoding of the key frames. Therefore, the lower the number of key frames, i.e., the longer the GOP, the higher the gain in complexity reduction offered by DVC over H.264/AVC Intra frame coding. Execution time measurements under controlled conditions, as established by the DISCOVER group [26], have shown that our codec (using H.264/AVC Intra to code the hash and the key frames) brings a reduction in average encoding time of approximately 30, 50, and 60% for a GOP size of 2, 4, and 8, respectively, compared to H.264/AVC Intra.

In contrast to hash-less Wyner-Ziv codecs, e.g. [26], our proposed codec has a higher encoding complexity caused by the additional hash formation and coding. However, the hash-related complexity overhead is kept low, since the hash dimensions were reduced to one fourth of the original frame resolution prior to coarse H.264/AVC Intra frame coding. When compared to Motion JPEG, the proposed codec (although currently not optimized for speed) exhibits similar encoding time but offers superior compression performance. We remark that compared to DISCOVER or Motion JPEG, the proposed codec offers a significant reduction of the encoding rate for a given distortion level. Such a not-able rate reduction induces an important decrease in power consumption by the transmission part of wireless video recording devices, e.g., wireless capsule endoscopes.

The proposed system links the encoder to the decoder via a feedback channel. Such a reverse channel implies that the encoder is forced to store Wyner-Ziv data in a buffer pending the decoder's directives. Based on our prior work [44], we analyze of the buffer size requirements imposed on the presented system's encoder due to the decoding delay for the capsule endoscopy application scenario. Recall that the GOP size in this scenario is restricted to 2 frames (see Section 5.2). The prime factors determining the decoding delay are the frame acquisition period t _F , the time t_SI to generate a side information frame, the transmission time (time-of-flight) t_TOF between encoder and decoder, and the LDPC soft-input soft-output decoding time, denoted by t_SISO.

Continuing our analysis, the reported capsule and the conventional endoscopic sequences were recorded using a camera with an acquisition rate of 2 and 30 Hz, respectively, corresponding to an acquisition period t _F of 500 and 33.33 ms.

An estimation of the transmission time t_TOF through the body can be made by calculating the velocity of a uniform plane in a lossy medium [45], characterized by its dielectric properties, i.e. the conductivity and permittivity. These values can be calculated based on [46, 47] for a wide range of body tissues and frequencies. It can be verified that at a frequency of 433 MHz the velocity is always greater than 10% of the speed of light through all body tissue cases included in [47], leading to a time-of-flight t_TOF in the order of 15 ns through 0.5 m of tissue.

It is clear that the time t_SI to generate a side information frame is dominated by OBME. Fortunately, several VLSI designs for hardware implementation of block motion estimation have been proposed. Considering the state-of-the-art architecture of [48], full integer-pel motion search can be executed at 4ρ² + B-1 cycles per macroblock (MB), where ρ and B are the search range and MB size, respectively. However, our presented scheme employs bidirectional OBME. Specifically, the total number of overlapping blocks per frame is (H·V)/ε², where H and V are the horizontal and vertical frame dimensions and ε is the overlap size. Hence, based on the VLSI architecture in [48], the total number of cycles per frame is given by 2·[(4·ρ² + B-1)·H·V]/ε², where the factor 2 stems from the bidirectionality. Considering a simplified decoding device with a single core CPU running at 800 MHz with a 1DIMPS/MHz/core^h and instantiating the OBME parameters for ρ = 16, ε = 4, and B = 16, yields a delay of 10.63 and 24.9 ms per frame for the capsule endoscopic (H = V = 256) and the endoscopic (H = 480, V = 320) sequences, respectively.

Based on the above approximations, Equation (8) yields an estimated buffer size of L = 2 and L = 3 frames for the capsule (t _F = 500 ms) and the conventional endoscopic (t _F = 33.33 ms) sequences, respectively, thus confirming the applicability of the proposed scheme. However, the encoder buffer size can be further restrained. An elegant solution is to constrain the number of feedback requests to a fixed number of requests for an entire Wyner-Ziv frame as proposed in our previous study [44], where we show that the loss of compression efficiency compared to unconstrained feedback is less than 5% when at most F = 5 requests per Wyner-Ziv frame are allowed. In addition to this, the structural latency induced by bidirectional temporal prediction could be reduced by employing unidirectional prediction.