[Paper Review] Consistent Reconstruction of the Input of an Oversampled Filter Bank From Noisy Subbands

Manel Abid, Michel Kieffer+1 more|arXiv (Cornell University)|Aug 29, 2011

Digital Filter Design and Implementation10 references4 citations

TL;DR

This paper proposes a maximum-likelihood reconstruction method for oversampled filter bank (OFB) inputs corrupted by bounded quantization noise and noisy channel transmission. By exploiting OFB redundancy and using interval analysis to constrain feasible quantization index vectors, the method achieves up to 9 dB SNR gain over classical decoding in AWGN channels with 3/2 oversampling ratio.

ABSTRACT

This paper introduces a reconstruction approach for the input signal of an oversampled filter bank (OFB) when the sub-bands generated at its output are quantized and transmitted over a noisy channel. This approach exploits the redundancy introduced by the OFB and the fact that the quantization noise is bounded. A maximum-likelihood estimate of the input signal is evaluated, which only considers the vectors of quantization indexes corresponding to subband signals that could have been generated by the OFB and that are compliant with the quantization errors. When considering an OFB with an oversampling ratio of 3/2 and a transmission of quantized subbands on an AWGN channel, compared to a classical decoder, the performance gains are up to 9 dB in terms of SNR for the reconstructed signal, and 3 dB in terms of channel SNR.

Motivation & Objective

• Address the performance degradation in OFB-based systems when subband quantization indexes are corrupted by noisy channel transmission.
• Overcome limitations of classical decoders that ignore signal consistency and redundancy in subband representations.
• Develop a reconstruction method that explicitly models bounded quantization noise and channel-induced impulse noise.
• Improve signal reconstruction quality by restricting candidate index vectors to those consistent with the OFB’s subband signal space.
• Enable robust reconstruction in delay-constrained applications where retransmission is not feasible.

Proposed method

• Formulate a suboptimal maximum-likelihood estimator that considers only quantization index vectors consistent with the OFB’s signal subspace and bounded quantization noise.
• Use interval analysis to compute outer approximations (boxes) of the feasible input signal polytopes corresponding to candidate index vectors.
• Apply a sequential M-algorithm to track the most likely index vectors at each time instant, limiting computational complexity.
• Integrate a parity-check test (PCT) to eliminate inconsistent candidates, improving estimation accuracy.
• Estimate the reconstructed signal as the centroid of the tightest consistent box, or use the center of the box as a proxy for the expected input value.
• Leverage the synthesis filter bank $ R(z) $ only after verifying index consistency, avoiding erroneous reconstructions from invalid index combinations.

Experimental results

Research questions

• RQ1 How can signal reconstruction from noisy, quantized subbands be improved when the channel introduces impulse noise and the quantization noise is bounded?
• RQ2 To what extent can redundancy in an oversampled filter bank be exploited to correct for corrupted subband index transmissions?
• RQ3 Can a consistent maximum-likelihood estimator be designed that respects the geometric constraints of the OFB signal space and quantization bounds?
• RQ4 What performance gains are achievable by combining interval analysis with a candidate pruning strategy (PCT) in noisy subband reconstruction?
• RQ5 How does the proposed method compare to classical decoding in terms of SNR gain under realistic noise models?

Key findings

• For an OFB with 3/2 oversampling ratio and AWGN channel, the proposed method achieves up to 9 dB SNR gain in reconstructed signal quality compared to classical decoding.
• The method provides up to 3 dB improvement in channel SNR efficiency, indicating enhanced robustness to channel impairments.
• Without PCT, the method achieves approximately 8 dB SNR gain at 7 dB channel SNR for the Lena lines signal and 2.5 dB gain at 14 dB signal SNR.
• The use of the parity-check test (PCT) improves performance by up to 2 dB in reconstructed SNR for the correlated Gaussian signal and 1 dB for the discrete-valued signal.
• The reconstruction quality remains robust even when the input signal correlation is not explicitly modeled, suggesting potential for further gains with correlation-aware estimation.
• When no consistent solution is found, the algorithm defaults to classical ML estimation, with a warning message, ensuring system stability.