{"id":"49126d10-677d-40a3-baf7-431f6ac7940e","arxiv_id":"2411.16043","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Dithered quantized random projections of received pilots suffice to recover a double-directional MIMO channel via maximum likelihood estimation, with sample complexity O(K log K) for Scheme 1 and O(K^2 log^2 K) for Scheme 2.","lead":"FDD massive MIMO base stations usually need the user to send back channel information over a narrow feedback link. This paper shows that if the user compresses and quantizes its received pilots into a few bits, the base station can still recover the channel provably and with a practical algorithm, using a number of measurements that grows with the number of propagation paths, not the array size.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 2's D is normalized so that E‖Dx‖₂² = ‖x‖₂²/T, making the claimed JL-moment property and S-REC for Scheme 2 impossible; the recoverability guarantee for Scheme 2 is unsupported as stated.","rationale":"I agree with the reader that Scheme 2's theory has a serious gap, but the load-bearing problem is different and more fundamental. The reader's item (i) about Fact 2's covering-number exponent is not actually an error: (8πκL_G²/ε²)^{2K} equals (const/ε)^{4K}, so the effective dimension of the 4K-parameter manifold is correctly captured; the 4K appears in τ as 4K log(...). The reader's item (ii) about distribution mismatch is real but secondary: the implemented a_t∼N(0,1/T²I) and s_t∼CN(0,I) make D a 1/√2-scaled version of the theorem's D, which would only change constants. The decisive defect is the 1/T normalization in the theorem's own D. With standard normal S,A, each row of D has squared expected response ‖x‖²/T² on a fixed vector x, so after T rows E‖Dx‖₂² = ‖x‖²/T. Thus D cannot satisfy the JL-moment property claimed in Lemma 3, and the S-REC lower bound in Lemma 2 cannot hold with a constant γ as T grows. This invalidates Theorem 2 as stated. The numerical success of Scheme 2 may survive a corrected normalization because the dithering/quantization can be scaled along with D, but the formal recoverability proof must be redone. Since Scheme 1's analysis appears sound and the fix for Scheme 2 may be a normalization change, I keep the reader's CONDITIONAL verdict rather than rejecting the paper.","tokens_in":29399,"tokens_out":26008,"duration_ms":231267,"concrete_test":"Analytically compute E‖Dx‖₂² for D=(1/T)(S^⊤⊙A^⊤)^⊤ with standard normal S,A and fixed unit x; the calculation yields 1/T, contradicting Lemma 3's concentration around 1. Then re-derive Lemma 2 with D=(1/√T)(S^⊤⊙A^⊤)^⊤ (or with a_t∼N(0,I/T) in the implemented Scheme 2, scaling σ_v correspondingly). If Theorem 2's T=Ω(K²log²K) bound follows under this corrected normalization, the issue is a fixable scaling typo; if the S-REC proof still fails, Scheme 2's recoverability claim is unproven.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Theorem 2 and Lemma 2, D is defined as (1/T)(S^⊤⊙A^⊤)^⊤ with S∈R^{2N×T} and A∈R^{2M×T} having standard normal entries, J=4MN. For any fixed x∈R^J, write row t as (1/T)(s_t^⊤⊗a_t^⊤). Reshaping x into X∈R^{2N×2M}, one has E[(s_t^⊤X a_t)^2] = ‖X‖_F² = ‖x‖², so E[(row_t·x)^2] = ‖x‖²/T² and E‖Dx‖₂² = ‖x‖²/T. The JL-moment property used in Lemma 3 requires E‖Dx‖₂² = ‖x‖² (or concentration of ‖Dx‖₂²/‖x‖₂² around 1); that is impossible when the mean ratio is 1/T. Lemma 3 is therefore false as stated, and the chain-of-nets proof of Lemma 2 collapses because the S-REC lower bound ‖D(h−h′)‖ ≥ γ‖h−h′‖ − ε cannot hold with γ independent of T for a matrix whose expected gain is ‖h−h′‖²/T. This is not just the distribution mismatch between the theorem and the implemented Scheme 2 (which uses a_t∼N(0,1/T²I)); even the theorem's own D has the wrong normalization. The correct near-isometric normalization is 1/√T (equivalently a_t∼N(0,I/T)), and the proof must be redone. Scheme 1's A with entries N(0,1/R) is correctly normalized, so its theory appears unaffected.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies limited-feedback downlink channel estimation in FDD massive MIMO. The UE compresses channel information using a random linear map and applies Gaussian-dithered uniform quantization; the BS solves a maximum-likelihood problem over the double-directional channel manifold. Two compression schemes are analyzed: Scheme 1 compresses an LS channel estimate, and Scheme 2 compresses the received pilot signal directly. Recoverability theorems are stated for both schemes, with sample complexity growing as O(K log K) and O(K^2 log^2 K) respectively, where K is the number of propagation paths. The paper also proposes an ADMM algorithm, REDEEM, that combines a modified RELAX harmonic-retrieval solver with an EM step, and reports extensive numerical results on synthetic and DeepMIMO channels.","tokens_in":29727,"tokens_out":27053,"duration_ms":237764,"significance":"The problem is important and the proposed pipeline is a meaningful step beyond dictionary-based sparse recovery: the recoverability analysis via KL/Hellinger divergence together with a set-restricted eigenvalue condition for a parametric channel manifold is a nontrivial extension of quantized compressive sensing. The REDEEM algorithm is a practical contribution, and the experiments show consistent gains over several baselines. However, the Scheme 2 recoverability guarantee is invalid as stated because of a normalization error in the measurement matrix, and the Scheme 1 bound, while correct as an inequality, is too weak to support the advertised sample-complexity claim without an additional J-dependent condition. The core ideas are sound and likely repairable, but the theoretical claims need substantial reworking.","major_comments":[{"comment":"The matrix D defined in Lemma 2 as D=(1/T)(S^T \\odot A^T)^T with S\\in R^{2N\\times T}, A\\in R^{2M\\times T} has two problems. First, the dimensions do not match: (S^T\\odot A^T)^T is (4MN)\\times T, while D is claimed to be T\\times(4MN); the intended object is presumably (S\\odot A)^T with rows (1/T)(s_t^T\\otimes a_t^T). Second, with the intended rows and standard-normal s_t,a_t, for any fixed real vector x one has E[(s_t^T X a_t)^2]=\\|X\\|_F^2=\\|x\\|_2^2, so E\\|Dx\\|_2^2=\\|x\\|_2^2/T, not \\|x\\|_2^2. Therefore Lemma 3's JL-moment property with mean 1 is false, and Lemma 2's S-REC with \\gamma>0 independent of T cannot hold because the expected gain of D on any nonzero vector decays as 1/\\sqrt{T}. The implemented Scheme 2 in Section III.B uses a_t\\sim N(0,I/T^2), making the actual operator even smaller. The recoverability guarantee for Scheme 2 is thus unsupported as stated; the proof must be redone with a near-isometric normalization, e.g., D=(S\\odot A)^T/\\sqrt{T} (equivalently a_t\\sim N(0,I/T) in the implementation). Note also that Lemma 5's D distribution (entries N(0,1/T)) is inconsistent with Lemma 2's definition.","section":"Section IV.C; Appendices F-H (Theorem 2, Lemmas 2-5)"},{"comment":"Even for Scheme 1, where the measurement normalization is correct, the stated bound does not deliver the advertised O(1/\\sqrt{R}) rate under the condition R=\\Omega(K\\log K). The theorem's bound contains \\tau=4(2+\\sqrt{J/R})+12\\sqrt{4K\\log(...)}, whose first term contributes O(\\sqrt{J/R}/\\sqrt{R})=O(\\sqrt{J}/R) to the final MSE. Unless R=\\Omega(\\sqrt{J}) (or a sharper Rademacher bound is used), the error is not O(1/\\sqrt{R}), and the claim that performance is insensitive to M and N is not supported by the theorem as stated. In Appendix C, the proof fixes \\mu=2+\\sqrt{J/R} in the bound \\xi(S)\\le(4\\mu+12\\sqrt{\\log C(S,\\mu)})/\\sqrt{R}; choosing \\mu\\approx\\sqrt{K} instead gives a bound of order \\sqrt{K\\log(J/R)}/\\sqrt{R}, which is much milder and restores the intended scaling up to logarithmic factors. The theorem statements and Remark 3 should be revised to either state the additional condition R=\\Omega(\\sqrt{J}) (respectively T=\\Omega(\\sqrt{J})) or incorporate the sharper Rademacher argument.","section":"Section IV.B-C; Appendix C (Theorems 1-2, Remark 3)"}],"minor_comments":[{"comment":"The covering-number exponent in Fact 2 is not dimensionally wrong: (8\\pi\\kappa/\\epsilon^2)^{2K} equals (8\\pi\\kappa)^{2K}\\epsilon^{-4K}, so the \\epsilon-scaling correctly reflects the 4K real parameters (\\theta,\\phi,\\Re\\beta,\\Im\\beta). The notation is easy to misread, so the authors may wish to write the \\epsilon-exponent explicitly.","section":"Fact 2 and Appendix B"},{"comment":"The proof uses the fact R\\le 4MN, which follows from R\\le J=2MN by the construction R\\ll J, but the theorem statement does not mention this elementary condition; adding one sentence would improve clarity.","section":"Theorem 1; Appendix C"},{"comment":"The statements refer to 'x_i for all i' without defining x_i in the theorem; these should be (Ah)_i and (D\\check h)_i in Schemes 1 and 2 respectively.","section":"Theorem 1 and Theorem 2"},{"comment":"The symbol \\phi is used both for the standard normal density in the EM surrogate and for the AoD vector; this is confusing and should be disambiguated (e.g., use \\varphi for the density).","section":"Section V.B, Eq. (35)"},{"comment":"In the proof of Lemma 4, the displayed probability 'Pr(Dh_2 \\le (1+\\alpha_i)\\|h\\|_2)' should read 'Pr(\\|Dh\\|_2 \\le (1+\\alpha_i)\\|h\\|_2)'; also, the decomposition (57) should indicate explicitly that \\check h_f is the chain tail.","section":"Appendix I"},{"comment":"The caption claims an O(1/\\sqrt{R}) (or O(1/\\sqrt{T})) decay rate; this is only justified in the regime where J/R (respectively J/T) is small, given the \\tau dependence discussed above, so a qualifier should be added.","section":"Figure 10(b) and Section VI.A.5"}],"recommendation":"major_revision","confidential_remarks":"The normalization error in Theorem 2 is a genuine load-bearing flaw, but it appears fixable: redefining D as (S\\odot A)^T/\\sqrt{T} (and the implementation with a_t\\sim N(0,I/T)) should restore the intended proof structure. The J-dependence in the stated bounds is a more subtle issue that will require either additional conditions or a sharper Rademacher argument; the authors should be asked to address it head-on. The Scheme 1 theory and the algorithmic contribution are substantially sound, so I recommend a major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my honest read. The paper's real contribution is the recoverability analysis for Scheme 1 and the REDEEM algorithm. The Scheme 1 theorem—MLE under dithered quantized Gaussian compression with sample complexity O(K log K)—is a meaningful new result for array-manifold-structured channels, and the proof pipeline (KL divergence, Hellinger, S-REC on the manifold) is a plausible extension of quantized CS. The experiments are thorough: the order-of-magnitude NMSE gains over sparse-dictionary baselines are credible, and the DeepMIMO tests add real-world support. The algorithm itself, combining RELAX for the harmonic retrieval subproblem and EM for the quantized likelihood, is clever and works numerically.\n\nBut the Scheme 2 guarantee is broken as stated. In Theorem 2, D = (1/T)(S^T ⊙ A^T)^T with standard normal entries. For any fixed x, E||Dx||_2^2 = ||x||_2^2/T, not ||x||_2^2. The JL-moment property in Lemma 3 requires the mean-squared gain to be 1; with mean 1/T, concentration around 1 is impossible, and the chain-of-nets proof of Lemma 2 falls apart. The implemented Scheme 2 uses a_t ~ N(0, 1/T^2 I), which has the same scaling problem. Rescaling D by √T and matching the implementation would fix this, but the constants and the proof need to be redone. This is not a nitpick—it invalidates the advertised sample-complexity guarantee for Scheme 2.\n\nTwo smaller issues: Theorem 1 silently uses R ≤ 4MN; that should be stated as a condition. And the covering-number bound in Fact 2: the ε exponent is actually right (ε^{-4K}), but the constant exponent deserves a second look—though this doesn't affect the K log K scaling.\n\nBottom line: Theorem 1 and the algorithm deserve referee time, but the paper as submitted overclaims. I'd send it to peer review with the expectation of major revision. If Theorem 2 can't be repaired, the paper should be re-scoped to Scheme 1 only.","headline":"Solid Scheme 1 theory and a strong algorithm, but Theorem 2's normalization error sinks the Scheme 2 recoverability claim as stated.","tokens_in":3,"tokens_out":10919,"would_cite":false,"duration_ms":151652,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper proves that dithered, quantized random projections of a K-path MIMO channel are enough for the base station to recover the full channel, with mean-squared error that decays as the reciprocal of the square root of the number of…","keywords":["FDD massive MIMO","limited feedback","downlink channel estimation","double directional channel model","dithered quantization","maximum likelihood estimation","harmonic retrieval","recoverability"],"falsifier":"Numerically estimate the covering number $C(\\Gamma,\\epsilon)$ by gridding the parameter space $(\\theta,\\phi,\\beta)$ for $K = 3,\\ldots,8$ and computing the smallest radius-$\\epsilon$ net of the channel manifold; if $\\log C(\\Gamma,\\epsilon)$ grows like $4K\\log(1/\\epsilon)$ rather than $2K\\log(1/\\epsilon)$, the union bound behind Theorem 1 would require more than $\\Omega(K\\log K)$ measurements. Running Scheme 2 with exactly the implemented distributions $a_t \\sim \\mathcal{N}(0,I/T^2)$ and $s_t \\sim \\mathcal{CN}(0,I)$ and checking whether the MSE follows the $O(1/\\sqrt{T})$ curve at the $K^2\\log^2 K$ threshold would settle whether the proven guarantee covers the implemented algorithm.","tokens_in":77,"feed_emoji":"📶","tokens_out":16305,"duration_ms":256510,"temperature":0.7,"pith_summary":"FDD massive MIMO needs the downlink channel at the base station, but the user equipment can only return a small number of feedback bits. The paper's proposal is to compress the channel (or the raw pilot observations) with a random matrix, add Gaussian dithering, and quantize each entry to a few bits; the base station then runs a maximum-likelihood estimator restricted to the K-path double-directional channel model. The central results are two recoverability theorems: with $R = \\Omega(K\\log(\\sqrt{\\kappa}\\,L_G K))$ quantized measurements the MLE's normalized squared error is $O(1/\\sqrt{R})$ (Scheme 1), and with $T = \\Omega(K^2\\log^2(\\sqrt{\\kappa}\\,L_G K))$ the same rate holds when the user compresses raw pilots directly (Scheme 2). The sample complexity depends on the number of propagation paths $K$, not on the array sizes $M$ and $N$, which matters as antennas scale up. The paper also supplies an ADMM solver, REDEEM, that couples a modified RELAX harmonic-retrieval step with an EM step, and shows in simulations that a few hundred bits beat dictionary-based baselines.","feed_headline":"Few hundred quantized bits can recover a full MIMO channel","feed_subtitle":"Two compression schemes provably reconstruct the K-path downlink channel, with error shrinking as feedback grows.","key_machinery":"The central objects are the channel manifold $\\Gamma$ (all channel matrices generated by $K$ AoAs, $K$ AoDs, and $K$ complex path losses under ULA steering vectors) and the random linear maps that compress it: the Gaussian matrix $A$ in Scheme 1 and the Khatri-Rao product matrix $D$ in Scheme 2. The proof pipeline has four load-bearing pieces: covering-number control of $\\Gamma$, which bounds the complexity of the candidate set; a set-restricted eigenvalue (S-REC) condition on the measurement matrix, which turns closeness in the compressed domain into closeness in the channel domain; a KL-divergence/Hellinger link for the dithered quantizer, which converts excess likelihood loss into Euclidean error; and, for Scheme 2 only, a JL-moment property for $D$ plus a spectral-norm bound. On the algorithmic side, the MLE is solved by an ADMM method whose $z$-subproblem is a two-dimensional harmonic retrieval problem, attacked by a modified RELAX routine (discrete Fourier initialization followed by gradient refinement), and whose $H$-subproblem is a closed-form EM update.","core_discovery":"Under the double directional model $H = \\sum_{k=1}^K \\beta_k a_r(\\theta_k) a_t(\\phi_k)^H$ with $K$ propagation paths, the paper establishes that the channel is identifiable from dithered uniform-quantized random projections. In Scheme 1 the user forms a least-squares channel estimate, compresses it with a Gaussian matrix $A$ whose entries are $\\mathcal{N}(0,1/R)$, and feeds back the quantized bits; Theorem 1 proves that when $R = \\Omega(K\\log(\\sqrt{\\kappa}\\,L_G K))$, the MLE $h^\\star$ satisfies $\\|h^{\\natural} - h^\\star\\|_2^2/(MN) \\le (64/\\sqrt{R})(4L_f/F_f(\\tau + 3\\nu/4) + 9U_f/F_f\\sqrt{2\\log(2/\\eta)}) + 32\\psi^2/R$ with probability at least $1 - 3\\eta - \\vartheta - e^{-\\Omega(R)}$. Theorem 2 gives the same type of bound for the scheme that compresses the raw received pilots, at the higher cost $T = \\Omega(K^2\\log^2(\\sqrt{\\kappa}\\,L_G K))$. The dithering level enters through the ratios $L_f/F_f$ and $U_f/F_f$, so the theorems quantify why too little dithering leaves quantization noise correlated while too much dithering overwhelms the signal.","pith_inferences":["A natural extension the paper leaves open is replacing the random compression matrices with signal-adaptive or learned ones; the same MLE-plus-ADMM construction would carry over, but the S-REC or JL-moment property would need to be re-certified for the new measurement distribution.","Because the estimator is likelihood-based, one-bit or non-uniform quantizers should fit the same construction: as long as the dithering distribution is known, the KL-to-Hellinger step should yield analogous rates with a modified constant $F_f$.","The robustness experiment with mis-specified $K$ suggests that over-estimating $K$ is nearly harmless while under-estimating it fails; an implementation could start with a generous path count and prune paths with negligible estimated gains.","The harmonic-retrieval view of the $z$-subproblem should transfer to other array geometries and to mmWave channels, since only the steering-vector structure and the K-path sum enter the algorithm."],"forward_implications":["Feedback overhead scales with the number of propagation paths $K$ rather than with the antenna counts $M$ and $N$, so enlarging the array does not inflate the bit budget under the double directional model.","At a fixed measurement budget $G$, both schemes have the same normalized-MSE upper bound, but Scheme 1 supports $K = O(G)$ paths while Scheme 2 supports only $K = O(\\sqrt{G})$; the user-side computational savings of Scheme 2 come at the price of a narrower recoverability region.","The normalized MSE decays as $O(1/\\sqrt{R})$ in Scheme 1 and $O(1/\\sqrt{T})$ in Scheme 2, giving a predictable rule for sizing feedback budgets for a target accuracy.","The REDEEM algorithm, ADMM with a modified RELAX harmonic-retrieval step and an EM quantized-likelihood step, reaches normalized mean-squared errors near $2\\times10^{-2}$ at 500 feedback bits in the basic setting, below the dictionary-based baselines, and keeps its advantage in ray-tracing scenarios."],"supporting_citations":[{"why":"supplies the set-restricted eigenvalue (S-REC) condition and its proof template, which Theorem 1's guarantee inherits.","marker":"[45]"},{"why":"provides the covering-number and Rademacher-complexity bounds used to control the empirical likelihood term.","marker":"[35]"},{"why":"Johnson-Lindenstrauss lemma used to bound the compressed distance between a channel and its closest point on the manifold.","marker":"[55]"},{"why":"non-asymptotic spectral-norm bound for Gaussian matrices, used to relate nets of the manifold to nets of the measurement set.","marker":"[57]"},{"why":"gives the JL-moment property for Khatri-Rao product matrices that underlies Lemma 2's S-REC proof for Scheme 2.","marker":"[60]"},{"why":"links KL divergence to Hellinger distance for quantized likelihoods, converting the MLE objective into a metric error.","marker":"[36]"},{"why":"supplies the lower bound from Hellinger distance to the quadratic measurement error in terms of the constant $F_f$.","marker":"[58]"},{"why":"RELAX algorithm used as the harmonic-retrieval solver inside the ADMM z-subproblem.","marker":"[24]"}],"fun_headline_variants":["Provable MIMO recovery from dithered quantized bits","Quantized feedback provably reconstructs MIMO channel","Few bits, full MIMO channel: recoverability proven","MIMO estimation from bits: provable recoverability","ADMM-based MIMO recovery from compressed feedback"],"cache_read_input_tokens":32256,"weakest_assumption_plain":"The whole result rests on the channel set being small enough in a precise geometric sense and on the random measurement matrices never collapsing the distance between two different channels; if either assumption fails, the advertised $K\\log K$ and $K^2\\log^2 K$ feedback budgets are not guaranteed.","fun_headline_variants_meta":{"raw":{"variants":["Provable MIMO recovery from dithered quantized bits","Quantized feedback provably reconstructs MIMO channel","Few bits, full MIMO channel: recoverability proven","MIMO estimation from bits: provable recoverability","ADMM-based MIMO recovery from compressed feedback"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000388,"raw_usage":{"total_tokens":2095,"prompt_tokens":1039,"completion_tokens":1056,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":655,"completion_tokens_details":{"reasoning_tokens":979}},"tokens_in":655,"tokens_out":1056,"duration_ms":9820,"temperature":1.0,"reasoning_tokens":979,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T13:37:44.718417+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Numerically estimate the covering number $C(\\Gamma,\\epsilon)$ by gridding the parameter space $(\\theta,\\phi,\\beta)$ for $K = 3,\\ldots,8$ and computing the smallest radius-$\\epsilon$ net of the channel manifold; if $\\log C(\\Gamma,\\epsilon)$ grows like $4K\\log(1/\\epsilon)$ rather than $2K\\log(1/\\epsilon)$, the union bound behind Theorem 1 would require more than $\\Omega(K\\log K)$ measurements. Running Scheme 2 with exactly the implemented distributions $a_t \\sim \\mathcal{N}(0,I/T^2)$ and $s_t \\sim \\mathcal{CN}(0,I)$ and checking whether the MSE follows the $O(1/\\sqrt{T})$ curve at the $K^2\\log^2 K$ threshold would settle whether the proven guarantee covers the implemented algorithm.","supporting_citations":[{"cited_title":"Compressed sensing using generative models,","cited_arxiv_id":null,"evidence_quote":"supplies the set-restricted eigenvalue (S-REC) condition and its proof template, which Theorem 1's guarantee inherits."},{"cited_title":"Shalev-Shwartz and S","cited_arxiv_id":null,"evidence_quote":"provides the covering-number and Rademacher-complexity bounds used to control the empirical likelihood term."},{"cited_title":"A simple proof of the restricted isometry property for random matrices,","cited_arxiv_id":null,"evidence_quote":"Johnson-Lindenstrauss lemma used to bound the compressed distance between a channel and its closest point on the manifold."},{"cited_title":"Oblivious sketching of high-degree poly- nomial kernels,","cited_arxiv_id":null,"evidence_quote":"gives the JL-moment property for Khatri-Rao product matrices that underlies Lemma 2's S-REC proof for Scheme 2."},{"cited_title":"1-bit matrix completion,","cited_arxiv_id":null,"evidence_quote":"links KL divergence to Hellinger distance for quantized likelihoods, converting the MLE objective into a metric error."},{"cited_title":"Categorical matrix completion,","cited_arxiv_id":null,"evidence_quote":"supplies the lower bound from Hellinger distance to the quadratic measurement error in terms of the constant $F_f$."},{"cited_title":"Efficient mixed-spectrum estimation with applica- tions to target feature extraction,","cited_arxiv_id":null,"evidence_quote":"RELAX algorithm used as the harmonic-retrieval solver inside the ADMM z-subproblem."}],"review_version":1}