Pith Number

pith:BVACLJH6

pith:2025:BVACLJH6GKTCIBCA6DJ22RDKI3

not attested not anchored not stored refs pending

Nonasymptotic Convergence Rates for Plug-and-Play Methods With MMSE Denoisers

Henry Pritchard, Rahul Parhi

The MMSE denoiser under Gaussian noise corresponds to a 1-weakly convex regularizer given by an upper Moreau envelope of the negative log-marginal density, which yields the first sublinear convergence rates for plug-and-play proximal grad

arxiv:2510.27211 v7 · 2025-10-31 · math.OC · eess.SP · stat.ML

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BVACLJH6GKTCIBCA6DJ22RDKI3}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that the MMSE denoiser corresponds to a regularizer that can be written explicitly as an upper Moreau envelope of the negative log-marginal density, which in turn implies that the regularizer is 1-weakly convex. Using this property, we derive the first sublinear convergence guarantee for PnP proximal gradient descent with an MMSE denoiser.

C2weakest assumption

The derivation assumes the noise is exactly Gaussian and that the MMSE denoiser is applied without any additional approximation or clipping; if the actual noise deviates from this model or if the denoiser is replaced by a learned network that only approximates the MMSE operator, the weak-convexity and rate guarantees no longer hold directly (see abstract and the proximal-operator equivalence stated in the introduction).

C3one line summary

MMSE denoisers correspond to 1-weakly convex regularizers via upper Moreau envelopes of negative log-marginals, enabling the first sublinear convergence rates for PnP proximal gradient descent.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-19T16:09:51.984059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d4025a4fe32a6240440f0d3ad446a46e5f4c9795bad2d393266281c8f353392

Aliases

arxiv: 2510.27211 · arxiv_version: 2510.27211v7 · doi: 10.48550/arxiv.2510.27211 · pith_short_12: BVACLJH6GKTC · pith_short_16: BVACLJH6GKTCIBCA · pith_short_8: BVACLJH6

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BVACLJH6GKTCIBCA6DJ22RDKI3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0d4025a4fe32a6240440f0d3ad446a46e5f4c9795bad2d393266281c8f353392

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7b329f9f7f8d23b6251197e581f62e929e7d70b5260fa9025da878b1b62b810",
    "cross_cats_sorted": [
      "eess.SP",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-10-31T06:12:49Z",
    "title_canon_sha256": "d41493dca1126beb10d36d1916e60112686faac6c33662d523c88ee9443cb719"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.27211",
    "kind": "arxiv",
    "version": 7
  }
}